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Non-Hermitian Stark Many-Body Localization: Utilizing exact diagonalization (ED) techniques, we investigate a
one-dimensional, non-reciprocal, interacting hard-core boson model under a
Stark potential with tail curvature. By employing the non-zero imaginary
eigenenergies ratio, half-chain entanglement entropy, and eigenstate
instability, we numerically confirm that the critical points of spectral
real-complex (RC) transition and many-body localization (MBL) phase transition
are not identical, and an examination of the phase diagrams reveals that the
spectral RC transition arises before the MBL phase transition, which suggests
the existence of a novel non-MBL-driven spectral RC transition. These findings
are quite unexpected, and they are entirely different from observations in
disorder-driven interacting non-Hermitian systems. This work provides a useful
reference for further research on phase transitions in disorder-free
interacting non-Hermitian systems. | cond-mat_quant-gas |
Thermodynamics of Trapped Photon Gases at Dimensional Crossover from 2D
to 1D: Photon Bose-Einstein condensates are characterised by a quite weak
interaction, so they behave nearly as an ideal Bose gas. Moreover, since the
current experiments are conducted in a microcavity, the longitudinal motion is
frozen out and the photon gas represents effectively a two-dimensional trapped
gas of massive bosons. In this paper we focus on a harmonically confined ideal
Bose gas in two dimensions, where the anisotropy of the confinement allows for
a dimensional crossover. If the confinement in one direction is strong enough
so that this squeezed direction is frozen out, then only one degree of freedom
survives and the system can be considered to be quasi-one dimensional. In view
of an experimental set-up we work out analytically the thermodynamic properties
for such a system with a finite number of photons. In particular, we focus on
examining the dimensional information which is contained in the respective
thermodynamic quantities. | cond-mat_quant-gas |
Current-Phase Relation of a Bose-Einstein Condensate Flowing Through a
Weak Link: We study the current-phase relation of a Bose-Einstein condensate flowing
through a repulsive square barrier by solving analytically the one dimensional
Gross-Pitaevskii equation. The barrier height and width fix the current-phase
relation $j(\delta\phi)$, which tends to $j\sim\cos(\delta\phi/2)$ for weak
barriers and to the Josephson sinusoidal relation $j\sim\sin(\delta\phi)$ for
strong barriers. Between these two limits, the current-phase relation depends
on the barrier width. In particular, for wide enough barriers, we observe two
families of multivalued current-phase relations. Diagrams belonging to the
first family, already known in the literature, can have two different positive
values of the current at the same phase difference. The second family, new to
our knowledge, can instead allow for three different positive currents still
corresponding to the same phase difference. Finally, we show that the
multivalued behavior arises from the competition between hydrodynamic and
nonlinear-dispersive components of the flow, the latter due to the presence of
a soliton inside the barrier region. | cond-mat_quant-gas |
Birth of a quasi-stationary black hole in an outcoupled Bose-Einstein
condensate: We study the evolution of an initially confined atom condensate which is
progressively outcoupled by gradually lowering the confining barrier on one
side. The goal is to identify protocols that best lead to a quasi-stationary
sonic black hole separating regions of subsonic and supersonic flow. An optical
lattice is found to be more efficient than a single barrier in yielding a
long-time stationary flow. This is best achieved if the final conduction band
is broad and its minimum not much lower than the initial chemical potential. An
optical lattice with a realistic Gaussian envelope yields similar results. We
analytically prove and numerically check that, within a spatially
coarse-grained description, the sonic horizon is bound to lie right at the
envelope maximum. We derive an analytical formula for the Hawking temperature
in that setup. | cond-mat_quant-gas |
Energy spectrum of harmonically trapped two-component Fermi gases:
Three- and Four-Particle Problem: Trapped two-component Fermi gases allow for the investigation of the
so-called BCS-BEC crossover by tuning the interspecies atom-atom $s$-wave
scattering length scattering $a^{(aa)}$ from attractive to repulsive, including
vanishing and infinitely large values. Here, we numerically determine the
energy spectrum of the equal-mass spin-balanced four-fermion system---the
smallest few-particle system that exhibits BCS-BEC crossover-like behavior---as
a function of $a^{(aa)}$ using the stochastic variational approach. For
comparative purposes, we also treat the two- and three-particle systems. States
with vanishing and finite total angular momentum as well as with natural and
unnatural parity are considered. In addition, the energy spectrum of
weakly-attractive and weakly-repulsive gases is characterized by employing a
perturbative framework that utilizes hyperspherical coordinates. The
hyperspherical coordinate approach allows for the straightforward assignment of
quantum numbers and furthermore provides great insights into the
strongly-interacting unitary regime. | cond-mat_quant-gas |
Strongly Interacting Atom Lasers in Three Dimensional Optical Lattices: We show that the dynamical melting of a Mott insulator in a three-dimensional
lattice leads to condensation at nonzero momenta, a phenomenon that can be used
to generate strongly interacting atom lasers in optical lattices. For infinite
onsite repulsion, the case considered here, the momenta at which bosons
condense is determined analytically and found to have a simple dependence on
the hopping amplitudes. The occupation of the condensates is shown to scale
linearly with the total number of atoms in the initial Mott insulator. Our
results are obtained using a Gutzwiller-type mean-field approach, gauged
against exact diagonalization solutions of small systems. | cond-mat_quant-gas |
Drag in Bose-Fermi Mixtures: We use kinetic theory to model the dynamics of a small Bose condensed cloud
of heavy particles moving through a larger degenerate Fermi gas of light
particles. Varying the Bose-Fermi interaction, we find a crossover between bulk
and surface dominated regimes -- where scattering occurs throughout the Bose
cloud, or solely on the surface. We calculate the damping and frequency shift
of the dipole mode in a harmonic trap as a function of the magnetic field
controlling an inter-species Feshbach resonance. We find excellent agreement
between our stochastic model and the experimental studies of Cs-Li mixtures. | cond-mat_quant-gas |
Analysis and resolution of the ground-state degeneracy of the
two-component Bose-Hubbard model: We study the degeneracy of the ground-state energy $E$ of the two-component
Bose-Hubbard model and of the perturbative correction $E_1$. We show that the
degeneracy properties of $E$ and $E_1$ are closely related to the connectivity
properties of the lattice. We determine general conditions under which $E$ is
nondegenerate. This analysis is then extended to investigate the degeneracy of
$E_1$. In this case, in addition to the lattice structure, the degeneracy also
depends on the number of particles present in the system. After identifying the
cases in which $E_1$ is degenerate and observing that the standard (degenerate)
perturbation theory is not applicable, we develop a method to determine the
zeroth-order correction to the ground state by exploiting the symmetry
properties of the lattice. This method is used to implement the perturbative
approach to the two-component Bose-Hubbard model in the case of degenerate
$E_1$ and is expected to be a valid tool to perturbatively study the asymmetric
character of the Mott-insulator to superfluid transition between the particle
and hole side. | cond-mat_quant-gas |
Conformal-invariance of 2D quantum turbulence in an exciton-polariton
fluid of light: The similarities of quantum turbulence with classical hydrodynamics allow
quantum fluids to provide essential models of their classical analogue, paving
the way for fundamental advances in physics and technology. Recently,
experiments on 2D quantum turbulence observed the clustering of same-sign
vortices in strong analogy with the inverse energy cascade of classical fluids.
However, self-similarity of the turbulent flow, a fundamental concept in the
study of classical turbulence, has so far remained largely unexplored in
quantum systems. Here, thanks to the unique features of exciton-polaritons, we
measure the scale invariance of velocity circulations and show that the cascade
process follows the universal scaling of critical phenomena in 2D. We
demonstrate this behaviour from the statistical analysis of the experimentally
measured incompressible velocity field and the microscopic imaging of the
quantum fluid. These results can find wide application in both quantum and
classical 2D turbulence. | cond-mat_quant-gas |
Quantum phases from competing short- and long-range interactions in an
optical lattice: Insights into complex phenomena in quantum matter can be gained from
simulation experiments with ultracold atoms, especially in cases where
theoretical characterization is challenging. However these experiments are
mostly limited to short-range collisional interactions. Recently observed
perturbative effects of long-range interactions were too weak to reach novel
quantum phases. Here we experimentally realize a bosonic lattice model with
competing short- and infinite-range interactions, and observe the appearance of
four distinct phases - a superfluid, a supersolid, a Mott insulator and a
charge density wave. Our system is based on an atomic quantum gas trapped in an
optical lattice inside a high finesse optical cavity. The strength of the
short-ranged on-site interactions is controlled by means of the optical lattice
depth. The infinite-range interaction potential is mediated by a vacuum mode of
the cavity and is independently controlled by tuning the cavity resonance. When
probing the phase transition between the Mott insulator and the charge density
wave in real-time, we discovered a behaviour characteristic of a first order
phase transition. Our measurements have accessed a regime for quantum
simulation of many-body systems, where the physics is determined by the
intricate competition between two different types of interactions and the zero
point motion of the particles. | cond-mat_quant-gas |
The role of atomic interactions in cavity-induced continuous time
crystals: We consider continuous time-crystalline phases in dissipative many-body
systems of atoms in cavities, focusing on the role of short-range interatomic
interactions. First, we show that the latter can alter the nature of the time
crystal by changing the type of the underlying critical bifurcation. Second, we
characterize the heating mechanism and dynamics resulting from the short-range
interactions and demonstrate that they make the time crystal inherently
metastable. We argue that this is generic for the broader class of dissipative
time crystals in atom-cavity systems whenever the cavity loss rate is
comparable to the atomic recoil energy. We observe that such a scenario for
heating resembles the one proposed for preheating of the early universe, where
the oscillating coherent inflation field decays into a cascade of exponentially
growing fluctuations. By extending approaches for dissipative dynamical systems
to our many-body problem, we obtain analytical predictions for the parameters
describing the phase transition and the heating rate inside the
time-crystalline phase. We underpin and extend the analytical predictions of
the heating rates with numerical simulations. | cond-mat_quant-gas |
Correlation properties of a one-dimensional repulsive Bose gas at finite
temperature: We present a comprehensive study shedding light on how thermal fluctuations
affect correlations in a Bose gas with contact repulsive interactions in one
spatial dimension. The pair correlation function, the static structure factor,
and the one-body density matrix are calculated as a function of the interaction
strength and temperature with the exact ab-initio Path Integral Monte Carlo
method. We explore all possible gas regimes from weak to strong interactions
and from low to high temperatures. We provide a detailed comparison with a
number of theories, such as perturbative (Bogoliubov and decoherent classical),
effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz)
ones. Our Monte Carlo results exhibit an excellent agreement with the tractable
limits and provide a fundamental benchmark for future observations which can be
achieved in atomic gases, cavity quantum-electrodynamic and
superconducting-circuit platforms. | cond-mat_quant-gas |
Light-induced gauge fields for ultracold atoms: Gauge fields are central in our modern understanding of physics at all
scales. At the highest energy scales known, the microscopic universe is
governed by particles interacting with each other through the exchange of gauge
bosons. At the largest length scales, our universe is ruled by gravity, whose
gauge structure suggests the existence of a particle - the graviton - that
mediates the gravitational force. At the mesoscopic scale, solid-state systems
are subjected to gauge fields of different nature: materials can be immersed in
external electromagnetic fields, but they can also feature emerging gauge
fields in their low-energy description. In this review, we focus on another
kind of gauge field: those engineered in systems of ultracold neutral atoms. In
these setups, atoms are suitably coupled to laser fields that generate
effective gauge potentials in their description. Neutral atoms "feeling"
laser-induced gauge potentials can potentially mimic the behavior of an
electron gas subjected to a magnetic field, but also, the interaction of
elementary particles with non-Abelian gauge fields. Here, we review different
realized and proposed techniques for creating gauge potentials - both Abelian
and non-Abelian - in atomic systems and discuss their implication in the
context of quantum simulation. While most of these setups concern the
realization of background and classical gauge potentials, we conclude with more
exotic proposals where these synthetic fields might be made dynamical, in view
of simulating interacting gauge theories with cold atoms. | cond-mat_quant-gas |
BCS-BEC crossover in a quasi-two-dimensional Fermi gas: We consider a two-component gas of fermionic atoms confined to a
quasi-two-dimensional (quasi-2D) geometry by a harmonic trapping potential in
the transverse direction. We construct a mean field theory of the BCS-BEC
crossover at zero temperature that allows us to extrapolate to an infinite
number of transverse harmonic oscillator levels. In the extreme BEC limit,
where the confinement length exceeds the dimer size, we recover 3D dimers
confined to 2D with weak repulsive interactions. However, even when the
interactions are weak and the Fermi energy is less than the confinement
frequency, we find that the higher transverse levels can substantially modify
fermion pairing. We argue that recent experiments on pairing in quasi-2D Fermi
gases [Y. Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)] have already
observed the effects of higher transverse levels. | cond-mat_quant-gas |
On Berezinskii-Kosterlitz-Thouless Phase Transition in Quasi-One
Dimensional Bose-Einstein Condensate: We show that quasi-one dimensional Bose-Einstein condensate under suitable
conditions can exhibit a Berezinskii-Kosterlitz-Thouless phase transition. The
role played by quantized vortices in two dimensional case, is played in this
case by dark solitons. We find that the critical temperature for this
transition lies in nano Kelvin range and below, for a wide range of
experimentally accessible parameters. It is seen that the high temperature
(disordered) phase differs from low temperature (ordered) phase in terms of
phase coherence, which can be used as an experimental signature for observing
this transition. | cond-mat_quant-gas |
Bose-Einstein condensates in an eightfold symmetric optical lattice: We investigate the properties of Bose-Einstein condensates (BECs) in a
two-dimensional quasi-periodic optical lattice (OL) with eightfold rotational
symmetry by numerically solving the Gross-Pitaevskii equation. In a stationary
external harmonic trapping potential, we first analyze the evolution of
matter-wave interference pattern from periodic to quasi-periodic as the OL is
changed continuously from four-fold periodic and eight-fold quasi-periodic. We
also investigate the transport properties during this evolution for different
interatomic interaction and lattice depth, and find that the BEC crosses over
from ballistic diffusion to localization. Finally, we focus on the case of
eightfold symmetric lattice and consider a global rotation imposed by the
external trapping potential. The BEC shows vortex pattern with eightfold
symmetry for slow rotation, becomes unstable for intermediate rotation, and
exhibits annular solitons with approximate axial symmetry for fast rotation.
These results can be readily demonstrated in experiments using the same
configuration as in Phys. Rev. Lett. 122, 110404 (2019). | cond-mat_quant-gas |
Floquet operator engineering for quantum state stroboscopic
stabilization: Optimal control is a valuable tool for quantum simulation, allowing for the
optimized preparation, manipulation, and measurement of quantum states. Through
the optimization of a time-dependent control parameter, target states can be
prepared to initialize or engineer specific quantum dynamics. In this work, we
focus on the tailoring of a unitary evolution leading to the stroboscopic
stabilization of quantum states of a Bose-Einstein condensate in an optical
lattice. We show how, for states with space and time symmetries, such an
evolution can be derived from the initial state-preparation controls; while for
a general target state we make use of quantum optimal control to directly
generate a stabilizing Floquet operator. Numerical optimizations highlight the
existence of a quantum speed limit for this stabilization process, and our
experimental results demonstrate the efficient stabilization of a broad range
of quantum states in the lattice. | cond-mat_quant-gas |
Tailoring quantum gases by Floquet engineering: Floquet engineering is the concept of tailoring a system by a periodic drive.
It has been very successful in opening new classes of Hamiltonians to the study
with ultracold atoms in optical lattices, such as artificial gauge fields,
topological band structures and density-dependent tunneling. Furthermore,
driven systems provide new physics without static counterpart such as anomalous
Floquet topological insulators. In this review article, we provide an overview
of the exciting developments in the field and discuss the current challenges
and perspectives. | cond-mat_quant-gas |
Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an
Optical Kagome Lattice: Geometric frustration of particle motion in a kagome lattice causes the
single-particle band structure to have a flat s-orbital band. We probe this
band structure by exciting a Bose-Einstein condensate into excited Bloch states
of an optical kagome lattice, and then measuring the group velocity through the
atomic momentum distribution. We find that interactions renormalize the band
structure of the kagome lattice, greatly increasing the dispersion of the third
band that, according to non-interacting band theory, should be nearly
non-dispersing. Measurements at various lattice depths and gas densities agree
quantitatively with predictions of the lattice Gross-Pitaevskii equation,
indicating that the observed distortion of band structure is caused by the
disortion of the overall lattice potential away from the kagome geometry by
interactions. | cond-mat_quant-gas |
Charge Gaps at Fractional Fillings in Boson Hubbard Ladders: The Bose-Hubbard Hamiltonian describes the competition between superfluidity
and Mott insulating behavior at zero temperature and commensurate filling as
the strength of the on-site repulsion is varied. Gapped insulating phases also
occur at non-integer densities as a consequence of longer ranged repulsive
interactions. In this paper we explore the formation of gapped phases in
coupled chains due instead to anisotropies $t_x \neq t_y$ in the bosonic
hopping, extending the work of Crepin {\it et al.} [Phys. Rev. B 84, 054517
(2011)] on two coupled chains, where a gap was shown to occur at half filling
for arbitrarily small interchain hopping $t_y$. Our main result is that, unlike
the two-leg chains, for three- and four-leg chains, a charge gap requires a
finite nonzero critical $t_y$ to open. However, these finite values are
surprisingly small, well below the analogous values required for a fermionic
band gap to open. | cond-mat_quant-gas |
Quantum annealing for the number partitioning problem using a tunable
spin glass of ions: Exploiting quantum properties to outperform classical ways of
information-processing is an outstanding goal of modern physics. A promising
route is quantum simulation, which aims at implementing relevant and
computationally hard problems in controllable quantum systems. Here we
demonstrate that in a trapped ion setup, with present day technology, it is
possible to realize a spin model of the Mattis type that exhibits spin glass
phases. Remarkably, our method produces the glassy behavior without the need
for any disorder potential, just by controlling the detuning of the spin-phonon
coupling. Applying a transverse field, the system can be used to benchmark
quantum annealing strategies which aim at reaching the ground state of the spin
glass starting from the paramagnetic phase. In the vicinity of a phonon
resonance, the problem maps onto number partitioning, and instances which are
difficult to address classically can be implemented. | cond-mat_quant-gas |
Mean-field phase diagram of the 1-D Bose gas in a disorder potential: We study the quantum phase transition of the 1D weakly interacting Bose gas
in the presence of disorder. We characterize the phase transition as a function
of disorder and interaction strengths, by inspecting the long-range behavior of
the one-body density matrix as well as the drop in the superfluid fraction. We
focus on the properties of the low-energy Bogoliubov excitations that drive the
phase transition, and find that the transition to the insulator state is marked
by a diverging density of states and a localization length that diverges as a
power-law with power 1. We draw the phase diagram and we observe that the
boundary between the superfluid and the Bose glass phase is characterized by
two different algebraic relations. These can be explained analytically by
considering the limiting cases of zero and infinite disorder correlation
length. | cond-mat_quant-gas |
Phase diagrams and multistep condensations of spin-1 bosonic gases in
optical lattices: Motivated by recent experimental processes, we systemically investigate
strongly correlated spin-1 ultracold bosons trapped in a three-dimensional
optical lattice in the presence of an external magnetic field. Based on a
recently developed bosonic dynamical mean-field theory (BDMFT), we map out
complete phase diagrams of the system for both antiferromagnetic and
ferromagnetic interactions, where various phases are found as a result of the
interplay of spin-dependent interaction and quadratic Zeeman energy. For
antiferromagnetic interactions, the system demonstrates competing magnetic
orders, including nematic, spin-singlet and ferromagnetic insulating phase,
depending on longitudinal magnetization, whereas, for ferromagnetic case, a
ferromagnetic-to-nematic-insulating phase transition is observed for small
quadratic Zeeman energy, and the insulating phase demonstrates the nematic
order for large Zeeman energy. Interestingly, at low magnetic field and finite
temperature, we find an abnormal multi-step condensation of the strongly
correlated superfluid, i.e. the critical condensing temperature of the $m_F=-1$
component with antiferromagnetic interactions demonstrates an increase with
longitudinal magnetization, while, for ferromagnetic case, the Zeeman component
$m_F = 0$ demonstrates a local minimum for the critical condensing temperature,
in contrast to weakly interacting cases. | cond-mat_quant-gas |
Time crystals: analysis of experimental conditions: Time crystals are quantum many-body systems which are able to self-organize
their motion in a periodic way in time. Discrete time crystals have been
experimentally demonstrated in spin systems. However, the first idea of
spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms
bouncing on an oscillating mirror, still awaits experimental demonstration.
Here, we perform a detailed analysis of the experimental conditions needed for
the realization of such a discrete time crystal. Importantly, the considered
system allows for the realization of dramatic breaking of discrete time
translation symmetry where a symmetry broken state evolves with a period tens
of times longer than the driving period. Moreover, atoms bouncing on an
oscillating mirror constitute a suitable system for the realization of
dynamical quantum phase transitions in discrete time crystals and for the
demonstration of various non-trivial condensed matter phenomena in the time
domain. We show that Anderson localization effects, which are typically
associated with spatial disorder and exponential localization of eigenstates of
a particle in configuration space, can be observed in the time domain when
ultra-cold atoms are bouncing on a randomly moving mirror. | cond-mat_quant-gas |
Resonant light enhances phase coherence in a cavity QED simulator of
fermionic superfluidity: Cavity QED experiments are natural hosts for non-equilibrium phases of matter
supported by photon-mediated interactions. In this work, we consider a cavity
QED simulation of the BCS model of superfluidity, by studying regimes where the
cavity photons act as dynamical degrees of freedom instead of mere mediators of
the interaction via virtual processes. We find an enhancement of long time
coherence following a quench whenever the cavity frequency is tuned into
resonance with the atoms. We discuss how this is equivalent to enhancement of
non-equilibrium superfluidity and highlight similarities to an analogous
phenomena recently studied in solid state quantum optics. We also discuss the
conditions for observing this enhanced resonant pairing in experiments by
including the effect of photon losses and inhomogeneous coupling in our
analysis. | cond-mat_quant-gas |
Bogoliubov-Cherenkov Radiation in an Atom Laser: We develop a simple yet powerful technique to study Bogoliubov-Cherenkov
radiation by producing a pulsed atom laser from a strongly confined
Bose-Einstein condensate. Such radiation results when the atom laser pulse
falls past a Bose-Einstein condensate at high-hypersonic speeds, modifying the
spatial profile to display a characteristic twin jet structure and a
complicated interference pattern. The experimental observations are in
excellent agreement with mean-field numerical simulations and an analytic
theory. Due to the highly hypersonic regime reached in our experiment, this
system offers a highly controllable platform for future studies of
condensed-matter analogs of quantum electrodynamics at ultrarelativistic
speeds. | cond-mat_quant-gas |
Spinor Condensates on a Cylindrical Surface in Synthetic Gauge Fields: We point out that by modifying the setup of a recent experiment that
generates a Dirac string, one can create a quasi 2D spinor Bose condensate on a
cylindrical surface with a synthetic magnetic field pointing radially outward
from the cylindrical surface. The synthetic magnetic field takes the form of
the Landau gauge. It is generated by the Berry's phase of a spin texture,
frozen by an external quadrupolar magnetic field. Unlike in the planar case,
there are two types of vortices (called A and B) with the same vorticity. The
ground state for $5\le S\le 9$ consists of a row of alternating AB vortices
lying at the equatorial circle of the cylinder. For higher values of $S$, the A
and B vortices split into two rows and are displaced from each other along the
cylindrical axis $z$. The fact that many properties of a BEC are altered in a
cylindrical surface implies many rich phenomena will emerge for ground states
in curved surfaces. | cond-mat_quant-gas |
Effect of an Impurity on Grey Soliton Dynamics in Cigar-Shaped
Bose-Einstein Condensate: In a cigar shaped Bose-Einstein condensate, explicit solutions of the coupled
mean-field equations, describing defect-grey soliton dynamics are obtained,
demonstrating the coexistence of grey soliton and a localized defect. Unlike
the case of dark soliton, where the defect trapping center has vanishing
superfluid density, the moving grey soliton necessarily possesses a finite
superfluid component at the defect location. The wave vector of the impurity is
controlled by the velocity of the grey soliton, which has an upper bound. It is
found that the presence of the impurity lowers the speed of the grey soliton,
as compared to the defect free case, where it can reach the sound velocity. The
grey soliton's energy gets substantially modified through its interaction with
the defect, opening up the possibility of its control through defect dynamics. | cond-mat_quant-gas |
Realizing the entanglement Hamiltonian of a topological quantum Hall
system: Topological quantum many-body systems, such as Hall insulators, are
characterized by a hidden order encoded in the entanglement between their
constituents. Entanglement entropy, an experimentally accessible single number
that globally quantifies entanglement, has been proposed as a first signature
of topological order. Conversely, the full description of entanglement relies
on the entanglement Hamiltonian, a more complex object originally introduced to
formulate quantum entanglement in curved spacetime. As conjectured by Li and
Haldane, the entanglement Hamiltonian of a many-body system appears to be
directly linked to its boundary properties, making it particularly useful for
characterizing topological systems. While the entanglement spectrum is commonly
used to identify complex phases arising in numerical simulations, its
measurement remains an outstanding challenge. Here, we perform a variational
approach to realize experimentally, as a genuine Hamiltonian, the entanglement
Hamiltonian of a synthetic quantum Hall system. We use a synthetic dimension,
encoded in the electronic spin of dysprosium atoms, to implement spatially
deformed Hall systems, as suggested by the Bisognano-Wichmann prediction. The
spectrum of the optimal variational Hamiltonian exhibits a chiral dispersion
akin to a topological edge mode, revealing the fundamental link between
entanglement and boundary physics. Our variational procedure can be easily
generalized to interacting many-body systems on various platforms, marking an
important step towards the exploration of exotic quantum systems with
long-range correlations, such as fractional Hall states, chiral spin liquids
and critical systems. | cond-mat_quant-gas |
Interacting Fermionic Atoms in Optical Lattices Diffuse Symmetrically
Upwards and Downwards in a Gravitational Potential: We consider a cloud of fermionic atoms in an optical lattice described by a
Hubbard model with an additional linear potential. While homogeneous
interacting systems mainly show damped Bloch oscillations and heating, a finite
cloud behaves differently: It expands symmetrically such that gains of
potential energy at the top are compensated by losses at the bottom.
Interactions stabilize the necessary heat currents by inducing gradients of the
inverse temperature 1/T, with T<0 at the bottom of the cloud. An analytic
solution of hydrodynamic equations shows that the width of the cloud increases
with t^(1/3) for long times consistent with results from our Boltzmann
simulations. | cond-mat_quant-gas |
Stable dilute supersolid of two-dimensional dipolar bosons: We consider two-dimensional bosonic dipoles oriented perpendicularly to the
plane. On top of the usual two-body contact and long-range dipolar interactions
we add a contact three-body repulsion as expected, in particular, for dipoles
in the bilayer geometry with tunneling. The three-body repulsion is crucial for
stabilizing the system, and we show that our model allows for stable continuous
space supersolid states in the dilute regime and calculate the zero-temperature
phase diagram. | cond-mat_quant-gas |
Quantized conductance through a spin-selective atomic point contact: We implement a microscopic spin filter for cold fermionic atoms in a quantum
point contact (QPC) and create fully spin-polarized currents while retaining
conductance quantization. Key to our scheme is a near-resonant optical tweezer
inducing a large effective Zeeman shift inside the QPC while its local
character limits dissipation. We observe a renormalization of this shift due to
interactions of a few atoms in the QPC. Our work represents the analog of an
actual spintronic device and paves the way to studying the interplay between
spin-splitting and interactions far from equilibrium. | cond-mat_quant-gas |
Self-Assembled Chains and Solids of Dipolar Atoms in a Multilayer: We predict that ultracold bosonic dipolar gases, confined within a multilayer
geometry, may undergo self-assembling processes, leading to the formation of
chain gases and solids. These dipolar chains, with dipoles aligned across
different layers, emerge at low densities and resemble phases observed in
liquid crystals, such as nematic and smectic phases. We calculate the phase
diagram using quantum Monte Carlo methods, introducing a newly devised trial
wave function designed for describing the chain gas, where dipoles from
different layers form chains without in-plane long-range order. We find gas,
solid, and chain phases, along with quantum phase transitions between these
states. Specifically, we predict a quantum phase transition from a gaseous to a
self-ordered phase, which occurs at a critical interlayer distance. Remarkably,
in the self-organized phases, the mean interparticle distance can significantly
exceed the characteristic length of the interaction potential, yielding solids
and chain gases with densities several orders of magnitude lower than those of
conventional quantum solids. | cond-mat_quant-gas |
Matter wave switching in Bose-Einstein condensates via intensity
redistribution soliton interactions: Using time dependent nonlinear (s-wave scattering length) coupling between
the components of a weakly interacting two component Bose-Einstein condensate
(BEC), we show the possibility of matter wave switching (fraction of atoms
transfer) between the components via shape changing/intensity redistribution
(matter redistribution) soliton interactions. We investigate the exact
bright-bright N-soliton solution of an effective one-dimensional (1D) two
component BEC by suitably tailoring the trap potential, atomic scattering
length and atom gain or loss. In particular, we show that the effective 1D
coupled Gross-Pitaevskii (GP) equations with time dependent parameters can be
transformed into the well known completely integrable Manakov model described
by coupled nonlinear Schr\"odinger (CNLS) equations by effecting a change of
variables of the coordinates and the wave functions under certain conditions
related to the time dependent parameters. We obtain the one-soliton solution
and demonstrate the shape changing/matter redistribution interactions of two
and three soliton solutions for the time independent expulsive harmonic trap
potential, periodically modulated harmonic trap potential and kink-like
modulated harmonic trap potential. The standard elastic collision of solitons
occur only for a specific choice of soliton parameters. | cond-mat_quant-gas |
Preparing and probing Chern bands with cold atoms: The present Chapter discusses methods by which topological Bloch bands can be
prepared in cold-atom setups. Focusing on the case of Chern bands for
two-dimensional systems, we describe how topological properties can be
triggered by driving atomic gases, either by dressing internal levels with
light or through time-periodic modulations. We illustrate these methods with
concrete examples, and we discuss recent experiments where geometrical and
topological band properties have been identified. | cond-mat_quant-gas |
Level statistics of the one-dimensional ionic Hubbard model: In this work we analyze the spectral level statistics of the one-dimensional
ionic Hubbard model, the Hubbard model with an alternating on-site potential.
In particular, we focus on the statistics of the gap ratios between consecutive
energy levels. This quantity is often used in order to signal whether a
many-body system is integrable or chaotic. A chaotic system has typically the
statistics of a Gaussian ensemble of random matrices while the spectral
properties of the integrable system follow a Poisson statistics. We find that
whereas the Hubbard model without alternating potential is known to be
integrable and its spectral properties follow a Poissonian statistics, the
presence of an alternating potential causes a drastic change in the spectral
properties which resemble the one of a Gaussian ensemble of random matrices.
However, to uncover this behavior one has to separately consider the blocks of
all symmetries of the ionic Hubbard model. | cond-mat_quant-gas |
Bound Bogoliubov quasiparticles in photon superfluids: Bogoliubov's description of Bose gases relies on the linear dynamics of
noninteracting quasiparticles on top of a homogeneous condensate. Here, we
theoretically explore the weakly-nonlinear regime of a one-dimensional photon
superfluid in which phonon-like elementary excitations interact via their
backreaction on the background flow. The generalized dispersion relation
extracted from spatiotemporal intensity spectra reveals additional branches
that correspond to bound Bogoliubov quasiparticles -- phase-locked collective
excitations originating from nonresonant harmonic-generation and wave-mixing
processes. These mechanisms are inherent to fluctuation dynamics and highlight
non-trivial scattering channels other than resonant interactions that could be
relevant in the emergence of dissipative and turbulent phenomena in
superfluids. | cond-mat_quant-gas |
Spin Orbit Coupling in Periodically Driven Optical Lattices: We propose a method for the emulation of artificial spin orbit coupling in a
system of ultracold, neutral atoms trapped in a tight-binding lattice. This
scheme does not involve near-resonant laser fields, avoiding the heating
processes connected to the spontaneous emission of photons. In our case, the
necessary spin dependent tunnel matrix elements are generated by a rapid, spin
dependent, periodic force, which can be described in the framework of an
effective, time averaged Hamiltonian. An additional radio frequency coupling
between the spin states leads to a mixing of the spin bands. | cond-mat_quant-gas |
Persistent Currents in Ferromagnetic Condensates: Persistent currents in Bose condensates with a scalar order parameter are
stabilized by the topology of the order parameter manifold. In condensates with
multicomponent order parameters it is topologically possible for supercurrents
to `unwind' without leaving the manifold. We study the energetics of this
process in the case of ferromagnetic condensates using a long wavelength energy
functional that includes both the superfluid and spin stiffnesses. Exploiting
analogies to an elastic rod and rigid body motion, we show that the current
carrying state in a 1D ring geometry transitions between a spin helix in the
energy minima and a soliton-like configuration at the maxima. The relevance to
recent experiments in ultracold atoms is briefly discussed. | cond-mat_quant-gas |
Higgs-like Excitations of Cold Atom System with Spin-orbit Coupling: The Higgs-like excitations, which distinguish from the Higgs amplitude mode
in many-body system, are single-particle excitations in system with non-Abelian
gauge potential. We investigate the Higgs-like excitations of cold atom system
in artificial non-Abelian gauge potential. We demonstrate that when a
non-Abelian gauge potential is reduced to Abelian potential, its Abelian part
constructs spin-orbit coupling, and its non-Abelian part emerges Higgs-like
excitations. The Higgs-like excitations induce a mass of the non-Abelian gauge
field, which offsets the defect of massless of the gauge theories. We show that
the mass of gauge field can affect the spin Hall currents which are produced by
the spin-orbit coupling. We also discuss the observation of these phenomena in
real experiment. | cond-mat_quant-gas |
Collective many-body bounce in the breathing-mode oscillations of a
Tonks-Girardeau gas: We analyse the breathing-mode oscillations of a harmonically quenched
Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We
predict a striking collective manifestation of impenetrability---a collective
many-body bounce effect. The effect, while being invisible in the evolution of
the in-situ density profile of the gas, can be revealed through a nontrivial
periodic narrowing of its momentum distribution, taking place at twice the rate
of the fundamental breathing-mode frequency. We identify physical regimes for
observing the many-body bounce and construct the respective nonequilibrium
phase diagram as a function of the quench strength and the initial temperature
of the gas. We also develop a finite-temperature hydrodynamic theory of the TG
gas, wherein the many-body bounce is explained by an increased thermodynamic
pressure of the gas during the isentropic compression, which acts as a
potential barrier at the inner turning points of the breathing cycle. | cond-mat_quant-gas |
Self-consistent Keldysh approach to quenches in weakly interacting
Bose-Hubbard model: We present a non-equilibrium Green's functional approach to study the
dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The
technique is based on the self-consistent solution of a set of equations which
represents a particular case of the most general set of Hedin's equations for
the interacting single-particle Green's function. We use the ladder
approximation as a skeleton diagram for the two-particle scattering amplitude
useful, through the self-energy in the Dyson equation, for finding the
interacting single-particle Green's function. This scheme is then implemented
numerically by a parallelized code. We exploit this approach to study the
correlation propagation after a quench in the interaction parameter, for one
(1D) and two (2D) dimensions. In particular, we show how our approach is able
to recover the crossover from ballistic to diffusive regime by increasing the
boson-boson interaction. Finally we also discuss the role of a thermal initial
state on the dynamics both for 1D and 2D Bose Hubbard models, finding that
surprisingly at high temperature a ballistic evolution is restored. | cond-mat_quant-gas |
Generation of spin currents by a temperature gradient in a two-terminal
device: Theoretical and experimental studies of the interaction between spins and
temperature are vital for the development of spin caloritronics, as they
dictate the design of future devices. In this work, we propose a two-terminal
cold-atom simulator to study that interaction. The proposed quantum simulator
consists of strongly interacting atoms that occupy two temperature reservoirs
connected by a one-dimensional link. First, we argue that the dynamics in the
link can be described using an inhomogeneous Heisenberg spin chain whose
couplings are defined by the local temperature. Second, we show the existence
of a spin current in a system with a temperature difference by studying the
dynamics that follows the spin-flip of an atom in the link. A temperature
gradient accelerates the impurity in one direction more than in the other,
leading to an overall spin current similar to the spin Seebeck effect. | cond-mat_quant-gas |
Quantum phases of atomic Fermi gases with anisotropic spin-orbit
coupling: We consider a general anisotropic spin-orbit coupling (SOC) and analyze the
phase diagrams of both balanced and imbalanced Fermi gases for the entire
BCS--Bose-Einstein condensate (BEC) evolution. In the first part, we use the
self-consistent mean-field theory at zero temperature, and show that the
topological structure of the ground-state phase diagrams is quite robust
against the effects of anisotropy. In the second part, we go beyond the
mean-field description, and investigate the effects of Gaussian fluctuations
near the critical temperature. This allows us to derive the time-dependent
Ginzburg-Landau theory, from which we extract the effective mass of the Cooper
pairs and their critical condensation temperature in the molecular BEC limit. | cond-mat_quant-gas |
Structure of Spin Correlations in High Temperature SU($N$) Quantum
Magnets: Quantum magnets with a large SU($N$) symmetry are a promising playground for
the discovery of new forms of exotic quantum matter. Motivated by recent
experimental efforts to study SU($N$) quantum magnetism in samples of ultracold
fermionic alkaline-earth-like atoms in optical lattices, we study here the
temperature dependence of spin correlations in the SU($N$) Heisenberg spin
model in a wide range of temperatures. We uncover a sizeable regime in
temperature, starting at $T=\infty$ down to intermediate temperatures and for
all $N\ge2$, in which the correlations have a common spatial structure on a
broad range of lattices, with the sign of the correlations alternating from one
Manhattan shell to the next, while the amplitude of the correlations is rapidly
decreasing with distance. Focussing on the one-dimensional chain and the
two-dimensional square and triangular lattice for certain $N$, we discuss the
appearance of a disorder and a Lifshitz temperature, separating the
commensurate Manhattan high-$T$ regime from a low-$T$ incommensurate regime. We
observe that this temperature window is associated to an approximately
$N$-independent entropy reduction from the $\ln(N)$ entropy at infinite
temperature. Our results are based on high-temperature series arguments and as
well as large-scale numerical full diagonalization results of thermodynamic
quantities for SU($3$) and SU($4$) square lattice samples, corresponding to a
total Hilbert space of up to $4\times 10^9$ states. | cond-mat_quant-gas |
Large-$N$ expansion for condensation and stability of Bose-Bose mixtures
at finite temperatures: The two-component mixture of Bose particles with short-range pairwise
interaction at finite temperatures in three dimensions is considered.
Particularly we examine, by means of the large-$N$ expansion technique, the
stability of mixed state below the Bose-Einstein transition point and the
temperature dependence of the condensate density for symmetric mixture of Bose
gases. The presented analysis reveals the importance of finite-temperature
excitations of the non-condensed particles in formation of the phase diagram of
two-component Bose systems. | cond-mat_quant-gas |
Forming doublons by a quantum quench: Repulsive interactions between particles on a lattice may lead to bound
states, so called doublons. Such states may be created by dynamically tuning
the interaction strength, e.g. using a Feshbach resonance, from attraction to
repulsion. We study the doublon production efficiency as a function of the
tuning rate at which the on-site interaction is varied. An expectation based on
the Landau- Zener law suggests that exponentially few doublons are created in
the adiabatic limit. Contrary to such an expectation, we found that the number
of produced doublons scales as a power law of the tuning rate with the exponent
dependent on the dimensionality of the lattice. The physical reason for this
anomaly is the effective decoupling of doublons from the two-particle continuum
for center of mass momenta close to the corners of the Brillouin zone. The
study of doublon production may be a sensitive tool to extract detailed
information about the band structure. | cond-mat_quant-gas |
Simulation of the many-body dynamical quantum Hall effect in an optical
lattice: We propose an experimental scheme to simulate the many-body dynamical quantum
Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice.
We first show that the required model Hamiltonian of a spin-1/2 Heisenberg
chain with an effective magnetic field and tunable parameters can be realized
in this system. For dynamical response to ramping the external fields, the
quantized plateaus emerge in the Berry curvature of the interacting atomic spin
chain as a function of the effective spin-exchange interaction. The
quantization of this response in the parameter space with the
interaction-induced topological transition characterizes the many-body
dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon
can be observed in practical cold-atom experiments with numerical simulations. | cond-mat_quant-gas |
BCS-BEC crossover and quantum phase transition in an ultracold Fermi gas
under spin-orbit coupling: In this work, we study the BCS-BEC crossover and quantum phase transition in
a Fermi gas under Rashba spin-orbit coupling close to a Feshbach resonance. By
adopting a two-channel model, we take into account of the closed channel
molecules, and show that combined with spin-orbit coupling, a finite background
scattering in the open channel can lead to two branches of solution for both
the two-body and the many-body ground states. The branching of the two-body
bound state solution originates from the avoided crossing between bound states
in the open and the closed channels, respectively. For the many-body states, we
identify a quantum phase transition in the upper branch regardless of the sign
of the background scattering length, which is in clear contrast to the case
without spin-orbit coupling. For systems with negative background scattering
length in particular, we show that the bound state in the open channel, and
hence the quantum phase transition in the upper branch, are induced by
spin-orbit coupling. We then characterize the critical detuning of the quantum
phase transition for both positive and negative background scattering lengths,
and demonstrate the optimal parameters for the critical point to be probed
experimentally. | cond-mat_quant-gas |
Current production in ring condensates with a weak link: We consider attractive and repulsive condensates in a ring trap stirred by a
weak link, and analyze the spectrum of solitonic trains dragged by the link, by
means of analytical expressions for the wave functions, energies and currents.
The precise evolution of current production and destruction in terms of defect
formation in the ring and in terms of stirring is studied. We find that any
excited state can be coupled to the ground state through two proposed methods:
either by adiabatically tuning the link's strength and velocity through precise
cycles which avoid the critical velocities and thus unstable regions, or by
keeping the link still while setting an auxiliary potential and imprinting a
nonlinear phase as the potential is turned off. We also analyze hysteresis
cycles through the spectrum of energies and currents. | cond-mat_quant-gas |
Hydrodynamic description of Hard-core Bosons on a Galileo ramp: We study the quantum evolution of a cloud of hard-core bosons loaded on a
one-dimensional optical lattice after its sudden release from a harmonic trap.
Just after the trap has been removed, a linear ramp potential is applied,
mimicking the so called Galileo ramp experiment. The non-equilibrium expansion
of the bosonic cloud is elucidated through a hydrodynamical description which
is compared to the exact numerical evolution obtained by exact diagonalization
on finite lattice sizes. The system is found to exhibit a rich behavior showing
in particular Bloch oscillations of a self-trapped condensate and an ejected
particle density leading to two diverging entangled condensates. Depending on
the initial density of the gas different regimes of Josephson-like oscillations
are observed. At low densities, the trapped part of the cloud is in a
superfluid phase that oscillates in time as a whole. At higher densities, the
trapped condensate is in a mixed superfluid-Mott phase that show a breathing
regime for steep enough potential ramps. | cond-mat_quant-gas |
Partial Fermionization---Spectral Universality in 1D Repulsive Bose
Gases: Due to the vast growth of the many-body level density with excitation energy,
its smoothed form is of central relevance for spectral and thermodynamic
properties of interacting quantum systems. We compute the cumulative of this
level density for confined one-dimensional continuous systems with repulsive
short-range interactions. We show that the crossover from an ideal Bose gas to
the strongly correlated, fermionized gas, i.e., partial fermionization,
exhibits universal behavior: Systems with very few up to many particles share
the same underlying spectral features. In our derivation we supplement quantum
cluster expansions with short-time dynamical information. Our nonperturbative
analytical results are in excellent agreement with numerics for systems of
experimental relevance in cold atom physics, such as interacting bosons on a
ring (Lieb-Liniger model) or subject to harmonic confinement. Our method
provides predictions for excitation spectra that enable access to
finite-temperature thermodynamics in large parameter ranges. | cond-mat_quant-gas |
Self-similar non-equilibrium dynamics of a many-body system with
power-law interactions: The influence of power-law interactions on the dynamics of many-body systems
far from equilibrium is much less explored than their effect on static and
thermodynamic properties. To gain insight into this problem we introduce and
analyze here an out-of-equilibrium deposition process in which the deposition
rate of a given particle depends as a power-law on the distance to previously
deposited particles. This model draws its relevance from recent experimental
progress in the domain of cold atomic gases which are studied in a setting
where atoms that are excited to high-lying Rydberg states interact through
power-law potentials that translate into power-law excitation rates. The
out-of-equilibrium dynamics of this system turns out to be surprisingly rich.
It features a self-similar evolution which leads to a characteristic power-law
time dependence of observables such as the particle concentration, and results
in a scale invariance of the structure factor. Our findings show that in
dissipative Rydberg gases out of equilibrium the characteristic distance among
excitations --- often referred to as the blockade radius --- is not a static
but rather a dynamic quantity. | cond-mat_quant-gas |
Proposal to directly observe the Kondo effect through enhanced
photo-induced scattering of cold fermionic and bosonic atoms: We propose an experimental protocol to directly observe the Kondo effect by
scattering ultracold atoms with spin-dependent interactions. We propose using
an optical Feshbach resonance to engineer Kondo-type spin-dependent
interactions in a system with ultracold $^6$Li and $^{87}$Rb gases. We
calculate the momentum transferred from the $^{87}$Rb gas to the $^6$Li gas in
a scattering experiment and show that it has a logarithmically enhanced
temperature dependence, characteristic of the Kondo effect and analogous to the
resistivity of alloys with magnetic impurities. Experimentally detecting this
enhancement will give a different perspective on the Kondo effect, and allow us
to explore a rich variety of problems such as the Kondo lattice problem and
heavy-fermion systems. | cond-mat_quant-gas |
Thermodynamics of Attractive and Repulsive Fermi Gases in Two Dimensions: We study the attractive and repulsive two-component Fermi gas with spin
imbalance in two dimensions. Using a generalized $T$-matrix approximation, we
examine the thermodynamic properties of both attractive and repulsive contact
interacting Fermi gases. The interaction strength, which is characterized by
the bound state energy $E_b=\hbar^2/m a_{2d}^2$ in vacuum, can be adjusted
through a Feshbach resonance. We calculate the interaction energy,
compressibility and spin susceptibility of the two branches of the Fermi gas.
For the repulsive branch, we also find a critical strength of interaction
$a_{2d}^{(c)}$ above which this metastable thermodynamic state becomes
unstable. This critical value depends on the temperature and the spin imbalance
(the "magnetization") of the system. | cond-mat_quant-gas |
Numerical Studies of Quantum Turbulence: We review numerical studies of quantum turbulence. Quantum turbulence is
currently one of the most important problems in low temperature physics and is
actively studied for superfluid helium and atomic Bose--Einstein condensates. A
key aspect of quantum turbulence is the dynamics of condensates and quantized
vortices. The dynamics of quantized vortices in superfluid helium are described
by the vortex filament model, while the dynamics of condensates are described
by the Gross--Pitaevskii model. Both of these models are nonlinear, and the
quantum turbulent states of interest are far from equilibrium. Hence, numerical
studies have been indispensable for studying quantum turbulence. In fact,
numerical studies have contributed in revealing the various problems of quantum
turbulence. This article reviews the recent developments in numerical studies
of quantum turbulence. We start with the motivation and the basics of quantum
turbulence and invite readers to the frontier of this research. Though there
are many important topics in the quantum turbulence of superfluid helium, this
article focuses on inhomogeneous quantum turbulence in a channel, which has
been motivated by recent visualization experiments. Atomic Bose--Einstein
condensates are a modern issue in quantum turbulence, and this article reviews
a variety of topics in the quantum turbulence of condensates e.g.
two-dimensional quantum turbulence, weak wave turbulence, turbulence in a
spinor condensate, $etc.$, some of which has not been addressed in superfluid
helium and paves the novel way for quantum turbulence researches. Finally we
discuss open problems. | cond-mat_quant-gas |
Deformation Dependence of Breathing Oscillations in Bose - Fermi
Mixtures at Zero Temperature: We study the breathing oscillations in bose-fermi mixtures in the
axially-symmetric deformed trap of prolate, spherical and oblate shapes, and
clarify the deformation dependence of the frequencies and the characteristics
of collective oscillations. The collective oscillations of the mixtures in
deformed traps are calculated in the scaling method. In largely-deformed
prolate and oblate limits and spherical limit, we obtain the analytical
expressions of the collective frequencies. The full calculation shows that the
collective oscillations become consistent with the analytically-obtained
frequencies when the system is deformed into both prolate and oblate regions.
The complicated changes of oscillation characters are shown to occur in the
transcendental regions around the spherically-deformed region. We find that
these critical changes of oscillation characters are explained by the level
crossing behaviors of the intrinsic oscillation modes. The approximate
expressions are obtained for the level crossing points that determine the
transcendental regions. We also compare the results of the scaling methods with
those of the dynamical approach. | cond-mat_quant-gas |
Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics: We show that quantum dynamics of any systems with $SU(1,1)$ symmetry give
rise to emergent Anti-de Sitter spacetimes in 2+1 dimensions (AdS$_{2+1}$).
Using the continuous circuit depth, a quantum evolution is mapped to a
trajectory in AdS$_{2+1}$. Whereas the time measured in laboratories becomes
either the proper time or the proper distance, quench dynamics follow geodesics
of AdS$_{2+1}$. Such a geometric approach provides a unified interpretation of
a wide range of prototypical phenomena that appear disconnected. For instance,
the light cone of AdS$_{2+1}$ underlies expansions of unitary fermions released
from harmonic traps, the onsite of parametric amplifications, and the
exceptional points that represent the $PT$ symmetry breaking in non-Hermitian
systems. Our work provides a transparent means to optimize quantum controls by
exploiting shortest paths in the emergent spacetimes. It also allows
experimentalists to engineer emergent spacetimes and induce tunnelings between
different AdS$_{2+1}$. | cond-mat_quant-gas |
Hard-core bosons in flat band systems above the critical density: We investigate the behaviour of hard-core bosons in one- and two-dimensional
flat band systems, the chequerboard and the kagom\'e lattice and
one-dimensional analogues thereof. The one dimensional systems have an exact
local reflection symmetry which allows for exact results. We show that above
the critical density an additional particle forms a pair with one of the other
bosons and that the pair is localised. In the two-dimensional systems exact
results are not available but variational results indicate a similar physical
behaviour. | cond-mat_quant-gas |
Observation of $1/k^4$-tails after expansion of Bose-Einstein
Condensates with impurities: We measure the momentum density in a Bose-Einstein condensate (BEC) with
dilute spin impurities after an expansion in the presence of interactions. We
observe tails decaying as $1/k^4$ at large momentum $k$ in the condensate and
in the impurity cloud. These algebraic tails originate from the impurity-BEC
interaction, but their amplitudes greatly exceed those expected from two-body
contact interactions at equilibrium in the trap. Furthermore, in the absence of
impurities, such algebraic tails are not found in the BEC density measured
after the interaction-driven expansion. These results highlight the key role
played by impurities when present, a possibility that had not been considered
in our previous work [Phys. Rev. Lett. 117, 235303 (2016)]. Our measurements
suggest that these unexpected algebraic tails originate from the non-trivial
dynamics of the expansion in the presence of impurity-bath interactions. | cond-mat_quant-gas |
Interactions and scattering of quantum vortices in a polariton fluid: Quantum vortices, the quantized version of classical vortices, play a
prominent role in superfluid and superconductor phase transitions. However,
their exploration at a particle level in open quantum systems has gained
considerable attention only recently. Here we study vortex pair interactions in
a resonant polariton fluid created in a solid-state microcavity. By tracking
the vortices on picosecond time scales, we reveal the role of nonlinearity, as
well as of density and phase gradients, in driving their rotational dynamics.
Such effects are also responsible for the split of composite spin-vortex
molecules into elementary half-vortices, when seeding opposite vorticity
between the two spinorial components. Remarkably, we also observe that vortices
placed in close proximity experience a pull-push scenario leading to unusual
scattering-like events that can be described by a tunable effective potential.
Understanding vortex interactions can be useful in quantum hydrodynamics and in
the development of vortex-based lattices, gyroscopes, and logic devices. | cond-mat_quant-gas |
Strong Boundary and Trap Potential Effects on Emergent Physics in
Ultra-Cold Fermionic Gases: The field of quantum simulations in ultra-cold atomic gases has been
remarkably successful. In principle it allows for an exact treatment of a
variety of highly relevant lattice models and their emergent phases of matter.
But so far there is a lack in the theoretical literature concerning the
systematic study of the effects of the trap potential as well as the finite
size of the systems, as numerical studies of such non periodic, correlated
fermionic lattices models are numerically demanding beyond one dimension. We
use the recently introduced real-space truncated unity functional
renormalization group to study these boundary and trap effects with a focus on
their impact on the superconducting phase of the $2$D Hubbard model. We find
that in the experiments not only lower temperatures need to be reached compared
to current capabilities, but also system size and trap potential shape play a
crucial role to simulate emergent phases of matter. | cond-mat_quant-gas |
Fermionization of two-component few-fermion systems in a one-dimensional
harmonic trap: The nature of strongly interacting Fermi gases and magnetism is one of the
most important and studied topics in condensed-matter physics. Still, there are
many open questions. A central issue is under what circumstances strong
short-range repulsive interactions are enough to drive magnetic correlations.
Recent progress in the field of cold atomic gases allows to address this
question in very clean systems where both particle numbers, interactions and
dimensionality can be tuned. Here we study fermionic few-body systems in a one
dimensional harmonic trap using a new rapidly converging effective-interaction
technique, plus a novel analytical approach. This allows us to calculate the
properties of a single spin-down atom interacting with a number of spin-up
particles, a case of much recent experimental interest. Our findings indicate
that, in the strongly interacting limit, spin-up and spin-down particles want
to separate in the trap, which we interpret as a microscopic precursor of
one-dimensional ferromagnetism in imbalanced systems. Our predictions are
directly addressable in current experiments on ultracold atomic few-body
systems. | cond-mat_quant-gas |
Energy spectra and fluxes of turbulent rotating Bose-Einstein
condensates in two dimensions: We investigate the scaling of the energy cascade in a harmonically trapped,
turbulent, rotating Bose-Einstein condensate (BEC) in two dimensions. We
achieve turbulence by injecting a localized perturbation into the condensate
and gradually increasing its rotation frequency from an initial value to a
maximum. The main characteristics of the resulting turbulent state depend on
the initial conditions, rotation frequency, and ramp-up time. We analyze the
energy and the fluxes of kinetic energy by considering initial profiles without
vortices and with vortex lattices. In the case without initial vortices, we
find the presence of Kolmogorov-like scaling ($k^{-5/3}$) of the incompressible
kinetic energy in the inertial range. However, with initial vortex lattices,
the energy spectrum follows Vinen scaling ($k^{-1}$) at transient iterations.
For cases with high rotating frequencies, Kolmogorov-like scaling emerges at
longer durations. We observe positive kinetic energy fluxes with both initial
states across all final frequencies, indicating a forward cascade of
incompressible and compressible kinetic energy. | cond-mat_quant-gas |
Tools for designing atom interferometers in a microgravity environment: We present a variational model suitable for rapid preliminary design of atom
interferometers in a microgravity environment. The model approximates the
solution of the 3D rotating--frame Gross--Pitaevskii equation (GPE) as the sum
of Nc Gaussian clouds. Each Gaussian cloud is assumed to have time--dependent
center positions, widths, and linear and quadratic phase parameters. We applied
the Lagrangian Variational Method (LVM) with this trial wave function to derive
equations of motion for these parameters that can be adapted to any external
potential. We also present a 1D version of this variational model. As an
example we apply the model to a 1D atom interferometry scheme for measuring
Newton's gravitational constant, G, in a microgravity environment. We show how
the LVM model can (1) constrain the experimental parameter space size, (2) show
how the value of G can be obtained from the experimental conditions and
interference pattern characteristics, and (3) show how to improve the
sensitivity of the measurement and construct a preliminary error budget. | cond-mat_quant-gas |
Motion of a Solitonic Vortex in the BEC-BCS Crossover: We observe a long-lived solitary wave in a superfluid Fermi gas of $^6$Li
atoms after phase-imprinting. Tomographic imaging reveals the excitation to be
a solitonic vortex, oriented transverse to the long axis of the cigar-shaped
atom cloud. The precessional motion of the vortex is directly observed, and its
period is measured as a function of the chemical potential in the BEC-BCS
crossover. The long period and the correspondingly large ratio of the inertial
to the bare mass of the vortex are in good agreement with estimates based on
superfluid hydrodynamics that we derive here using the known equation of state
in the BEC-BCS crossover. | cond-mat_quant-gas |
Phase space theory of Bose-Einstein condensates and time-dependent modes: A phase space theory approach for treating dynamical behaviour of
Bose-Einstein condensates applicable to situations such as interferometry with
BEC in time-dependent double well potentials is presented. Time-dependent mode
functions are used, chosen so that one, two,.. highly occupied modes describe
well the physics of interacting condensate bosons in time dependent potentials
at well below the transition temperature. Time dependent mode annihilation,
creation operators are represented by time dependent phase variables, but time
independent total field annihilation, creation operators are represented by
time independent field functions. Two situations are treated, one (mode theory)
is where specific mode annihilation, creation operators and their related phase
variables and distribution functions are dealt with, the other (field theory)
is where only field creation, annihilation operators and their related field
functions and distribution functionals are involved. The paper focuses on the
hybrid approach, where the modes are divided up between condensate (highly
occupied) modes and non-condensate (sparsely occupied) modes. It is found that
there are extra terms in the Ito stochastic equations both for the stochastic
phases and stochastic fields, involving coupling coefficients defined via
overlap integrals between mode functions and their time derivatives. For the
hybrid approach both the Fokker-Planck and functional Fokker-Planck equations
differ from those derived via the correspondence rules, the drift vectors are
unchanged but the diffusion matrices contain additional terms involving the
coupling coefficients. Results are also presented for the combined approach
where all the modes are treated as one set. | cond-mat_quant-gas |
Quantum Fluctuations of Vortex Lattices in Ultracold Gases: We discuss the effects of quantum fluctuations on the properties of vortex
lattices in rapidly rotating ultracold atomic gases. We develop a variational
method that goes beyond the Bogoliubov theory by including the effects of
interactions between the quasiparticle excitations. These interactions are
found to have significant quantitative effects on physical properties even at
relatively large filling factors. We use our theory to predict the expected
experimental signatures of quantum fluctuations of vortices, and to assess the
competition of the triangular vortex lattice phase with other phases in
finite-sized systems. | cond-mat_quant-gas |
Observation of Stückelberg oscillations in accelerated optical
lattices: We report the experimental observation of St\"{u}ckelberg oscillations of
matter waves in optical lattices. Extending previous work on Landau-Zener
tunneling of Bose-Einstein condensates in optical lattices, we study the
effects of the accumulated phase between two successive crossings of the
Brillouin zone edge. Our results agree well with a simple model for multiple
Landau-Zener tunneling events taking into account the band structure of the
optical lattice. | cond-mat_quant-gas |
Observing Properties of an Interacting Homogeneous Bose--Einstein
Condensate: Heisenberg-Limited Momentum Spread, Interaction Energy and
Free-Expansion Dynamics: We study the properties of an atomic Bose--Einstein condensate produced in an
optical-box potential, using high-resolution Bragg spectroscopy. For a range of
box sizes, up to $70~\mu$m, we directly observe Heisenberg-limited momentum
uncertainty of the condensed atoms. We measure the condensate interaction
energy with a precision of $k_B \times 100$ pK and study, both experimentally
and numerically, the dynamics of its free expansion upon release from the box
potential. All our measurements are in good agreement with theoretical
expectations for a perfectly homogeneous condensate of spatial extent equal to
the size of the box, which also establishes the uniformity of our optical-box
system on a sub-nK energy scale. | cond-mat_quant-gas |
Intersubband Polaritons in the Electrical Dipole Gauge: We provide a theoretical description for the coupling between the
intersubband excitations of a bi-dimensional electron gas with the
electromagnetic field. This description, based on the electrical dipole gauge,
applies to an arbitrary quantum heterostructure embedded in a general
multilayered waveguide or a microcavity. We show that the dipole gauge
Hamiltonian automatically takes into account the Coulomb interactions in this
system. Furthermore, it can be conveniently expressed in terms of the many-body
collective plasmon modes, which interact both with each other and with the
light field. The dipole gauge therefore provides a suitable framework for the
study of solid state Quantum Electrodynamics (QED) phenomena, such as the
ultra-strong light-matter interaction regime, occurring at very high electronic
densities. | cond-mat_quant-gas |
The Anyon Hubbard Model in One-Dimensional Optical Lattices: Raman-assisted hopping may be used to realize the anyon Hubbard model in
one-dimensional optical lattices. We propose a feasible scenario that
significantly improves the proposal of [T. Keilmann et al., Nature Commun. 2,
361 (2011)], allowing as well for an exact realization of the two-body
hard-core constraint, and for controllable effective interactions without the
need of Feshbach resonances. We show that the combination of anyonic statistics
and two-body hard-core constraint leads to a rich ground state physics,
including Mott insulators with attractive interactions, pair superfluids, dimer
phases, and multicritical points. Moreover, the anyonic statistics results in a
novel two-component superfluid of holon and doublon dimers, characterized by a
large but finite compressibility and a multipeaked momentum distribution, which
may be easily revealed experimentally. | cond-mat_quant-gas |
Instabilities of vortex-ring-bright soliton in trapped binary 3D
Bose-Einstein condensates: Instabilities of vortex-ring-bright coherent structures in harmonically
trapped two-component three-dimensional Bose-Einstein condensates are studied
numerically within the coupled Gross-Pitaevskii equations and interpreted
analytically. Interestingly, the filled vortex core with a sufficiently large
amount of the bright component is observed to reduce the parametric interval of
stability of the vortex ring. We have identified the mechanisms of several
linear instabilities and one nonlinear parametric instability in this
connection. Two of the linear instabilities are qualitatively different from
ones reported earlier, to our knowledge, and are associated with azimuthal
modes of $m=0$ and $m=1$, i.e., deviations of the vortex from the stationary
ring shape. Our nonlinear parametric resonance instability occurs between the
$m=0$ and $m=2$ modes and signals the exchange of energy between them. | cond-mat_quant-gas |
Coherent molecule formation in anharmonic potentials near
confinement-induced resonances: We perform a theoretical and experimental study of a system of two ultracold
atoms with tunable interaction in an elongated trapping potential. We show that
the coupling of center-of-mass and relative motion due to an anharmonicity of
the trapping potential leads to a coherent coupling of a state of an unbound
atom pair and a molecule with a center of mass excitation. By performing the
experiment with exactly two particles we exclude three-body losses and can
therefore directly observe coherent molecule formation. We find quantitative
agreement between our theory of inelastic confinement-induced resonances and
the experimental results. This shows that the effects of center-of-mass to
relative motion coupling can have a significant impact on the physics of
quasi-1D quantum systems. | cond-mat_quant-gas |
Periodic waves in two-component Bose-Einstein condensates with repulsive
interactions between atoms: We consider periodic waves in miscible two-component Bose-Einstein
condensates with repulsive nonlinear interactions constants. Exact one-phase
solution is found for the case when all these constants are equal to each other
(i.e., for Manakov limit). New types of nonlinear polarization waves are
considered in detail. The connection of the solutions found with experimentally
observed periodic structures in two-component condensates is discussed. | cond-mat_quant-gas |
The Efimov effect for heteronuclear three-body systems at positive
scattering length and finite temperature: We study the recombination process of three atoms scattering into an atom and
diatomic molecule in heteronuclear mixtures of ultracold atomic gases with
large and positive interspecies scattering length at finite temperature. We
calculate the temperature dependence of the three-body recombination rates by
extracting universal scaling functions that parametrize the energy dependence
of the scattering matrix. We compare our results to experimental data for the
40K-87Rb mixture and make a prediction for 6Li-87Rb. We find that contributions
from higher partial wave channels significantly impact the total rate and, in
systems with particularly large mass imbalance, can even obliterate the
recombination minima associated with the Efimov effect. | cond-mat_quant-gas |
Momentum-space Harper-Hofstadter model: We show how the weakly trapped Harper-Hofstadter model can be mapped onto a
Harper-Hofstadter model in momentum space. In this momentum-space model, the
band dispersion plays the role of the periodic potential, the Berry curvature
plays the role of an effective magnetic field, the real-space harmonic trap
provides the momentum-space kinetic energy responsible for the hopping, and the
trap position sets the boundary conditions around the magnetic Brillouin zone.
Spatially local interactions translate into nonlocal interactions in momentum
space: within a mean-field approximation, we show that increasing interparticle
interactions leads to a structural change of the ground state, from a single
rotationally symmetric ground state to degenerate ground states that
spontaneously break rotational symmetry. | cond-mat_quant-gas |
Collective excitation frequencies and stationary states of trapped
dipolar Bose-Einstein condensates in the Thomas-Fermi regime: We present a general method for obtaining the exact static solutions and
collective excitation frequencies of a trapped Bose-Einstein condensate (BEC)
with dipolar atomic interactions in the Thomas-Fermi regime. The method
incorporates analytic expressions for the dipolar potential of an arbitrary
polynomial density profile, thereby reducing the problem of handling non-local
dipolar interactions to the solution of algebraic equations.
We comprehensively map out the static solutions and excitation modes,
including non-cylindrically symmetric traps, and also the case of negative
scattering length where dipolar interactions stabilize an otherwise unstable
condensate. The dynamical stability of the excitation modes gives insight into
the onset of collapse of a dipolar BEC. We find that global collapse is
consistently mediated by an anisotropic quadrupolar collective mode, although
there are two trapping regimes in which the BEC is stable against quadrupole
fluctuations even as the ratio of the dipolar to s-wave interactions becomes
infinite. Motivated by the possibility of fragmented BEC in a dipolar Bose gas
due to the partially attractive interactions, we pay special attention to the
scissors modes, which can provide a signature of superfluidity, and identify a
long-range restoring force which is peculiar to dipolar systems. As part of the
supporting material for this paper we provide the computer program used to make
the calculations, including a graphical user interface. | cond-mat_quant-gas |
Two-dimensional dipolar Bose-Einstein condensate bright and vortex
solitons on one-dimensional optical lattice: By solving the three-dimensional Gross-Pitaevskii equation we generate
two-dimensional axially-symmetric and anisotropic dipolar Bose-Einstein
condensate bright solitons, for repulsive atomic interaction, stabilized by
only a weak one-dimensional optical lattice (OL) aligned along and
perpendicular, respectively, to the dipole polarization direction. In the
former case vortex solitons can also be created. We show that it is possible to
make a stable array of small interacting axially-symmetric dipolar solitons put
on alternate OL sites. Further, we demonstrate the elastic nature of the
collision of two such solitons. | cond-mat_quant-gas |
Properties of the signal mode in the polariton OPO regime: Theoretical analyses of the polariton optical parametric oscillator (OPO)
regime often rely on a mean field approach based on the complex
Gross-Pitaevskii equations in a three-mode approximation, where only three
momentum states, the signal, pump and idler, are assumed to be significantly
occupied. This approximation, however, lacks a constraint to uniquely determine
the signal and idler momenta. In contrast, multimode numerical simulations and
experiments show a unique momentum structure for the OPO states. In this work
we show that an estimate for the signal momentum chosen by the system can be
found from a simple analysis of the pump-only configuration. We use this
estimate to investigate how the chosen signal momentum depends on the
properties of the drive. | cond-mat_quant-gas |
Four fermions in a one-dimensional harmonic trap: Accuracy of a
variational-ansatz approach: Detailed analysis of the system of four interacting ultra-cold fermions
confined in a one-dimensional harmonic trap is performed. The analysis is done
in the framework of a simple variational ansatz for the many-body ground state
and its predictions are confronted with the results of numerically exact
diagonalization of the many-body Hamiltonian. Short discussion on the role of
the quantum statistics, i.e. Bose-Bose and Bose-Fermi mixtures is also
presented. It is concluded that the variational ansatz, although seemed to be
oversimplified, gives surprisingly good predictions of many different
quantities for mixtures of equal as well as different mass systems. The result
may have some experimental importance since it gives quite simple and validated
method for describing experimental outputs. | cond-mat_quant-gas |
Quantum phases of a spin-1 ultracold Bose gas with three body
interactions: We study the effects of both a repulsive and an attractive three body
interaction potential on a spin-1 ultracold Bose gas using mean field approach
(MFA). For an antiferromagnetic (AF) inter- action, we have found the existence
of the odd-even asymmetry in the Mott insulating (MI) lobes in presence of both
the repulsive two and three body interactions. In case of a purely three body
repulsive interaction, the higher order MI lobes stabilize against the
superfluid phase. However, the spin nematic (singlet) formation is restricted
upto the first (second) MI lobes for the former one, while there is neither any
asymmetry nor spin nematic (singlet) formation is observed for the later case.
The results are confirmed after carefully scrutinizing the spin eigen value and
spin nematic order parameter for both the cases. On the other hand, for an
attractive three body interaction, the third MI lobe is predominantly affected,
where it completely engulfs the second and the fourth MI lobes at large values
of the interaction strength. Albeit no significant change is observed beyond
the fourth MI lobe. In the ferromagnetic case, the phase diagram shows similar
features as that of a scalar Bose gas. We have compared our results on the MFA
phase diagrams for both types of the interaction potential via a perturbation
expansion in both the cases. | cond-mat_quant-gas |
Negative differential conductivity and quantum statistical effects in a
three-site Bose-Hubbard model: The use of an electron beam to remove ultracold atoms from selected sites in
an optical lattice has opened up new opportunities to study transport in
quantum systems [R. Labouvie {\it et al.\ }, Phys.\ Rev.\ Lett.\ {\bf 115},
050601 (2015)]. Inspired by this experimental result, we examine the effects of
number difference, dephasing, and initial quantum statistics on the filling of
an initially depleted middle well in the three-well inline Bose-Hubbard model.
We find that the well-known phenomenon of macroscopic self-trapping is the main
contributor to oscillatory negative differential conductivity in our model,
with phase diffusion being a secondary effect. However, we find that phase
diffusion is required for the production of direct atomic current, with the
coherent process showing damped oscillatory currents. We also find that our
results are highly dependent on the initial quantum states of the atoms in the
system. | cond-mat_quant-gas |
Mesoscopics of half-quantum vortex pair deconfinement in a trapped
spin-one condensate: Motivated by a recent experiment in an antiferromagnetic spin-1 Bose-Einstein
condensate of ${}^{23} \textrm{Na}$ atoms, we study the energetical stability
of a singly quantum vortex injected into the center of a quasi-two-dimensional
gas with zero total spin against dissocation into a pair of half-quantum
vortices. We find that the critical dissociation point of this
confinement-deconfinement type phase transition can be expressed in terms of
the ratio of density-density ($c_0$) and spin-spin ($c_2$) coupling constants.
The transition of bound to unbound vortices, in particular, sensitively depends
on (1) the ratio of system size ($R$) to density healing length ($\xi_d$), and
(2) the trap potential. Specifically, the critical ratio $(c_2 /
c_0)_{\textrm{cr}}$ increases when $R / \xi_d$ decreases, and is relatively
larger in a harmonic trap than in a box trap. Dissociation is energetically
generally favored for $c_2 / c_0 < (c_2 / c_0)_{\textrm{cr}}$, which as a
corollary implies that vortex dissociation is observed as well for negative
$c_2 < 0$, e.g., in a rubidium spin-1 BEC, whereas in a sodium spin-1 BEC
($c_2>0$) it is energetically blocked above the critical ratio $(c_2 /
c_0)_{\textrm{cr}}$. Tuning the coupling ratio $c_2/c_0$ by using microwave
control techniques, the dependence of the deconfinement phase transition on
coupling parameters, density, and system size we predict, can be verified in
experiments with ultracold spinor gases. | cond-mat_quant-gas |
Dark soliton oscillations in Bose-Einstein condensates with multi-body
interactions: We consider the dynamics of dark matter solitons moving through non-uniform
cigar-shaped Bose-Einstein condensates described by the mean field
Gross-Pitaevskii equation with generalized nonlinearities, in the case when the
condition for the modulation stability of the Bose-Einstein condensate is
fulfilled. The analytical expression for the frequency of the oscillations of a
deep dark soliton is derived for nonlinearities which are arbitrary functions
of the density, while specific results are discussed for the physically
relevant case of a cubic-quintic nonlinearity modeling two- and three-body
interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation
for which the frequencies of the oscillations are known to be independent of
background density and interaction strengths, we find that in the presence of a
cubic-quintic nonlinearity an explicit dependence of the oscillations frequency
on the above quantities appears. This dependence gives rise to the possibility
of measuring these quantities directly from the dark soliton dynamics, or to
manage the oscillation via the changes of the scattering lengths by means of
Feshbach resonance. A comparison between analytical results and direct
numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good
agreement which confirms the validity of our approach. | cond-mat_quant-gas |
Quantum Kinetic Theory of Collisionless Superfluid Internal Convection: Superfluids can transport heat via simultaneous opposite flows of their
spatially interpenetrating condensate and thermal components. While this
internal convection is usually described within Landau's phenomenological two
fluid hydrodynamics, we apply quantum kinetic theory to a dilute Bose gas held
beween thermal reservoirs at different temperatures, and show that the
phenomenon also appears in collisionless kinetic regimes, and should be
directly observable in currently feasible experiments on trapped ultracold
vapors. | cond-mat_quant-gas |
Hanbury-Brown and Twiss bunching of phonons and of the quantum depletion
in a strongly-interacting Bose gas: We report the realisation of a Hanbury-Brown and Twiss (HBT)-like experiment
with a gas of strongly interacting bosons at low temperatures. The regime of
large interactions and low temperatures is reached in a three-dimensional
optical lattice and atom-atom correlations are extracted from the detection of
individual metastable Helium atoms after a long free-fall. We observe a HBT
bunching in the non-condensed fraction of the gas whose properties strongly
deviate from the HBT signals expected for non-interacting bosons. In addition,
we show that the measured correlations reflect the peculiar quantum statistics
of atoms belonging to the quantum depletion and of the Bogoliubov phonons,
i.e., of collective excitations of the many-body quantum state. Our results
demonstrate that atom-atom correlations provide information about the quantum
state of strongly-interacting particles, extending the interest of HBT-like
experiments beyond the case of non-interacting particles. | cond-mat_quant-gas |
Theory of the Rotating Polaron: Spectrum and Self-Localization: We study a quantum impurity possessing both translational and internal
rotational degrees of freedom interacting with a bosonic bath. Such a system
corresponds to a `rotating polaron', which can be used to model, e.g., a
rotating molecule immersed in an ultracold Bose gas or superfluid Helium. We
derive the Hamiltonian of the rotating polaron and study its spectrum in the
weak- and strong-coupling regimes using a combination of variational,
diagrammatic, and mean-field approaches. We reveal how the coupling between
linear and angular momenta affects stable quasiparticle states, and demonstrate
that internal rotation leads to an enhanced self-localization in the
translational degrees of freedom. | cond-mat_quant-gas |
Signatures of the single particle mobility edge in the ground state
properties of Tonks-Girardeau and non-interacting Fermi gases in a
bichromatic potential: We explore the ground state properties of cold atomic gases, loaded into a
bichromatic lattice, focusing on the cases of non-interacting fermions and
hard-core (Tonks-Girardeau) bosons, trapped by the combination of two
potentials with incommensurate periods. For such systems, two limiting cases
have been thoroughly established. In the tight-binding limit, the
single-particle states in the lowest occupied band show a localization
transition, as the strength of the second potential is increased above a
certain threshold. In the continuous limit, when the tight-binding
approximation does not hold anymore, a mobility edge is found, whose position
in energy depends upon the strength of the second potential. Here, we study how
the crossover from the discrete to the continuum behavior occurs, and prove
that signatures of the localization transition and mobility edge clearly appear
in the generic many-body properties of the systems. Specifically, we evaluate
the momentum distribution, which is a routinely measured quantity in
experiments with cold atoms, and demonstrate that, even in the presence of
strong boson-boson interactions, the single particle mobility edge can be
observed in the ground state properties. | cond-mat_quant-gas |
Imaging of quantum Hall states in ultracold atomic gases: We examine off-resonant light scattering from ultracold atoms in the quantum
Hall regime. When the light scattering is spin dependent, we show that images
formed in the far field can be used to distinguish states of the system. The
spatial dependence of the far-field images is determined by the two-particle
spin-correlation functions, which the images are related to by a
transformation. Quasiholes in the system appear in images of the density formed
by collecting the scattered light with a microscope, where the quasihole
statistics are revealed by the reduction in density at the quasihole position. | cond-mat_quant-gas |
Persistent currents with non-quantized angular momentum: We analyze the generation of persistent currents in Bose-Einstein condensates
of ultracold gases confined in a ring. This phenomenon has been recently
investigated in an experiment [Nature \textbf{506}, 200 (2014)], where
hysteresis loops have been observed in the activation of quantized persistent
currents by rotating weak links. In this work, we demonstrate the existence of
3D stationary currents with non-quantized angular momentum. They are generated
by families of solitary waves that show a continuous variation in the angular
momentum, and provide a bridge between different winding numbers. We show that
the size of hysteresis loops is determined by the range of existence within the
weak link region of solitary waves which configure the energy barrier
preventing phase slips. The barrier vanishes when the critical rotation leads
winding numbers and solitonic states to a matching configuration. At this
point, Landau and Feynman criteria for phase slips meet: the fluid flow reaches
the local speed of sound, and stationary vortex lines (which are the building
blocks of solitons) can be excited inside the system. | cond-mat_quant-gas |
Mechanism of Tunneling in Interacting Open Ultracold Few-Boson Systems: We investigate the mechanism in the tunneling dynamics of open ultracold
few-boson systems by numerically solving the time-dependent few-boson
Schr\"{o}dinger equation exactly. By starting from a weakly repulsive,
initially coherent two-boson system we demonstrate that the decay dynamics
incorporate fragmentation. The wavefunction of the tunneling state exhibits a
pronounced dynamically-stable pattern which we explain by an analytical model.
By studying more bosons and stronger interactions we arrive to the conclusion
that the decay by tunneling is not a coherent process and exhibits a wealth of
phenomena depending on the interaction between the particles. | cond-mat_quant-gas |
Interaction-induced instability and chaos in the photoassociative
stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein
condensates: We study the effect of interactions on the conversion of atomic -to molecular
Bose-Einstein condensates via stimulated Raman adiabatic passage. Both
energetic instability during avoided crossings and dynamical instability during
chaotic intervals limit adiabaticity and impose {\em low} sweep-rate boundaries
on the efficiency of the process. For the diabatic traverse of avoided
crossings, we find a reciprocal power-law dependence of the final unconverted
population on sweep rate. For the traverse of chaos, we find a sharp low-rate
boundary determined by the dynamical instability parameters. The interplay of
these two mechanisms determines which instability controls the failure of
molecular production. A judicious choice of sweep parameters is hence required
to restore the process efficiency. | cond-mat_quant-gas |
Multi-Stability in Cavity QED with Spin-Orbit Coupled Bose-Einstein
Condensate: We investigate the occurrence of steady-state multi-stability in a cavity
system containing spin-orbit coupled Bose-Einstein condensate and driven by a
strong pump laser. The applied magnetic field splits the Bose-Einstein
condensate into pseudo-spin states, which then became momentum sensitive with
two counter propagating Raman lasers directly interacting with ultra-cold
atoms. After governing the steady-state dynamics for all associated subsystems,
we show the emergence of multi-stable behavior of cavity photon number, which
is unlike with previous investigation on cavity-atom systems. However, this
multi-stability can be tuned with associated system parameters. Further, we
illustrate the occurrence of mixed-stability behavior for atomic population of
the pseudo spin-$\uparrow$ amd spin-$\downarrow$ states, which are appearing in
so-called bi-unstable form. The collective behavior of these atomic number
states interestingly possesses a transitional interface among the population of
both spin states, which can be enhance and controlled by spin-orbit coupling
and Zeeman field effects. Furthermore, we illustrate the emergence of secondary
interface mediated by increasing the mechanical dissipation rate of the
pseudo-spin states. These interfaces could be cause by the non-trivial behavior
of synthetic spin state mediated by cavity. Our findings are not only crucial
for the subject of optical switching, but also could provide foundation for
future studies on mechanical aspect of synthetic atomic states with cavity
quantum electrodynamics. | cond-mat_quant-gas |
Superfluid properties of bright solitons in a ring: We theoretically investigate superfluid properties of a one-dimensional
annular superfluid with a boost. We derive the formula of the superfluid
fraction in the one-dimensional superfluid, which was originally derived by
Leggett in the context of supersolid. We see that the superfluid fraction given
by Leggett's formula detects the emergence of solitons in the one-dimensional
annular superfluid. The formation of a bright soliton at a critical interaction
strength decreases the superfluid fraction. At a critical boost velocity, a
node appears in the soliton and the superfluid fraction vanishes. With a
transverse dimension, the soliton alters to a more localized one and it
undergoes dynamical instability at a critical transverse length. Consequently,
the superfluid fraction decreases as one increases the length up to the
critical length. With a potential barrier along the ring, the uniform density
alters to an inhomogeneous configuration and it develops a soliton localized at
one of the potential minima by increasing the interaction strength. | cond-mat_quant-gas |
Phase-separated vortex-lattice in a rotating binary Bose-Einstein
condensate: We study circularly-symmetric phase separation of vortex lattices in a
rapidly rotating harmonically-trapped quasi--two-dimensional binary
Bose-Einstein condensate (BEC) by introducing a weak quartic trap in one of the
components. The increase of the rotational frequency in such a system is also
found to generate a phase separation of the vortex lattices of an overlapping
non-rotating BEC. The phase-separated vortex lattices have different structures
for a binary BEC with inter-species repulsion and inter-species attraction. In
the former case of a fully repulsive binary BEC the phase separation of the
vortex-lattices is accompanied by a complete phase separation of component
densities. In the latter case of inter-species attraction there is a partial
phase separation of component densities, although there could be a complete
phase separation of the generated vortex lattices in the two components. In the
case of inter-species attraction, we need to have different intra-species
repulsion in the two components for an efficient phase separation. We compare
and contrast our results with the phase separation obtained in a
harmonically-trapped binary BEC without any quartic trap. | cond-mat_quant-gas |
Spin squeezing in dipolar spinor condensates: We study the effect of dipolar interactions on the level of squeezing in
spin-1 Bose-Einstein condensates by using the single mode approximation. We
limit our consideration to the $\mathfrak{su}(2)$ Lie subalgebra spanned by
spin operators. The biaxial nature of dipolar interactions allows for dynamical
generation of spin-squeezed states in the system. We analyze the phase
portraits in the reduced mean-filed space in order to determine positions of
unstable fixed points. We calculate numerically spin squeezing parameter
showing that it is possible to reach the strongest squeezing set by the
two-axis countertwisting model. We partially explain scaling with the system
size by using the Gaussian approach and the frozen spin approximation. | cond-mat_quant-gas |
Universal quantum dynamics of Bose polarons: Predicting the emergent properties of impurities immersed in a quantum bath
is a fundamental challenge that can defy quasiparticle treatments. Here, we
measure the spectral properties and real-time dynamics of mobile impurities
injected into a homogeneous Bose--Einstein condensate, using two Feshbach
resonances to tune both the impurity-bath and intrabath interactions. We map
out both attractive and repulsive branches of polaron quasiparticles, resolving
the repulsive polaron and the molecular state associated with the Feshbach
resonance in the strongly interacting regime, and show that the latter also has
a many-body character. Our measurements reveal remarkably universal behavior,
controlled by the bath density and a single dimensionless interaction
parameter; for near-resonant interactions the polarons are no longer well
defined, but the universality still holds. | cond-mat_quant-gas |
Quantum phase transitions in the dimerized extended Bose-Hubbard model: We present an unbiased numerical density-matrix renormalization group study
of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor
Coulomb interaction and bond dimerization. It places the emphasis on the
determination of the ground-state phase diagram and shows that, besides
dimerized Mott and density-wave insulating phases, an intermediate
symmetry-protected topological Haldane insulator emerges at weak Coulomb
interactions for filling factor one, which disappears, however, when the
dimerization becomes too large. Analyzing the critical behavior of the model,
we prove that the phase boundaries of the Haldane phase to Mott insulator and
density-wave states belong to the Gaussian and Ising universality classes with
central charges $c=1$ and $c=1/2$, respectively, and merge in a tricritical
point. Interestingly we can demonstrate a direct Ising quantum phase transition
between the dimerized Mott and density-wave phases above the tricritical point.
The corresponding transition line terminates at a critical end point that
belongs to the universality class of the dilute Ising model with $c=7/10$. At
even stronger Coulomb interactions the transition becomes first order. | cond-mat_quant-gas |
Three-level Haldane-like model on dice optical lattice: We consider ultracold atoms in a two-dimensional optical lattice of the dice
geometry in a tight-binding regime. The atoms experience a laser-assisted
tunneling between the nearest neighbour sites of the dice lattice accompanied
by the momentum recoil. This allows one to engineer staggered synthetic
magnetic fluxes over plaquettes, and thus pave a way towards a realization of
topologically nontrivial band structures. In such a lattice the real-valued
next-neighbour transitions are not needed to reach a topological regime. Yet,
such transitions can increase a variety of the obtained topological phases. The
dice lattice represents a triangular Bravais lattice with a three-site basis
consisting of a hub site connected to two rim sites. As a consequence, the dice
lattice supports three dispersion bands. From this point of view, our model can
be interpreted as a generalization of the paradigmatic Haldane model which is
reproduced if one of the two rim sub-lattices is eliminated. We demonstrate
that the proposed upgrade of the Haldane model creates a significant added
value, including an easy access to topological semimetal phases relying only on
the nearest neighbour coupling, as well as enhanced topological band structures
featuring Chern numbers higher than one. The numerical investigation is
supported and complemented by an analytical scheme based on the study of
singularities in the Berry connection. | cond-mat_quant-gas |
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