Bose Gas Research Articles

Thermodynamic properties of a relativistic Bose gas under rigid rotation

We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature (T), angular velocity (Ω), and the coupling constant (α). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain T or α. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high T and for large α. Published by the American Physical Society 2024

One-dimensional Fermi polaron after a kick: Two-sided singularity of the momentum distribution, Bragg reflection and other exact results

A mobile impurity particle immersed in a quantum fluid forms a polaron - a quasiparticle consisting of the impurity and a local disturbance of the fluid around it. We ask what happens to a one-dimensional polaron after a kick, i.e. an abrupt application of a force that instantly delivers a finite impulse to the impurity. In the framework of an integrable model describing an impurity in a one-dimensional gas of fermions or hard-core bosons, we calculate the distribution of the polaron momentum established when the post-kick relaxation is over. A remarkable feature of this distribution is a two-sided power-law singularity. It emerges due to one of two processes. In the first process, the whole impulse is transferred to the polaron, without creating phonon-like excitations of the fluid. In the second process, the impulse is shared between the polaron and the center-of-mass motion of the fluid, again without creating any fluid excitations. The latter process is, in fact, a Bragg reflection at the edge of the emergent Brillouin zone. We carefully analyze the conditions for each of the two processes. The asymptotic form of the distribution in the vicinity of the singularity is derived.

Effect of nonzero temperature to non-condensed fraction of a homogeneous dilute weakly interacting Bose gas

This study aims to investigate the effect of nonzero temperature to the non-condensed fraction of a homogeneous repulsive weakly interacting Bose gas in region of sufficiently low temperature. Within improved Hartree-Fock approximation, the Cornwall–Jackiw–Tomboulis effective action approach shows that the thermal fluctuations make the non-condensed fraction increase as a second and fourth-order power law of temperature. Indeed, the effect of non-infinite size of the trap is also integrated. The result is compared with experimental data.

Bose–Einstein condensation of photons in a vertical-cavity surface-emitting laser

Many bosons can occupy a single quantum state without a limit. It is described by the quantum-mechanical Bose–Einstein statistic, which allows Bose–Einstein condensation at low temperatures and high particle densities. Photons, historically the first considered bosonic gas, were late to show this phenomenon, observed in rhodamine-filled microcavities and doped fibre cavities. These findings have raised the question of whether condensation is also common in other laser systems with potential technological applications. Here we show the Bose–Einstein condensation of photons in a broad-area vertical-cavity surface-emitting laser with a slight cavity-gain spectral detuning. We observed a Bose–Einstein condensate in the fundamental transversal optical mode at a critical phase-space density. The experimental results follow the equation of state for a two-dimensional gas of bosons in thermal equilibrium, although the extracted spectral temperatures were lower than the device’s. This is interpreted as originating from the driven-dissipative nature of the photon gas. In contrast, non-equilibrium lasing action is observed in the higher-order modes in more negatively detuned device. Our work opens the way for the potential exploration of superfluid physics of interacting photons mediated by semiconductor optical nonlinearities. It also shows great promise for enabling single-mode high-power emission from a large-aperture device.

Universal vortex statistics and stochastic geometry of Bose-Einstein condensation

The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry. Published by the American Physical Society 2024

Imaging spinor Bose gases using off-axis holography

Imaging spinor Bose gases using off-axis holography

Analytic thermodynamic properties of the Lieb-Liniger gas

We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics-thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures.

Ring solids and supersolids in spherical shell-shaped dipolar Bose-Einstein condensates

We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas under the confinement of a bubble trapping potential. We do so in terms of the scattering length a and the number of particles. We observe the emergence of a wide variety of dipolar solids, consisting on arrangements of different number of droplets along a ring over the equator of the spherical shell confinement. We also show that the transition between the different phases of the system can be engineered by varying a, the number of particles or the radius of the trap, parameters, which can be experimentally tuned. Finally, we show the importance of working in microgravity conditions as gravity unstabilizes the observed dipolar solids. Published by the American Physical Society 2024

Thermometry with a dissipative heavy impurity

Improving the measurement precision of low temperature is significant in fundamental science and advanced quantum technology application. However, the measurement precision of temperature T usually diverges as T tends to zero. Here, by utilizing a heavy impurity to measure the temperature of a Bose gas, we obtain the Landau bound to precision δ2T∝T2 to avoid the divergence. When the initial momentum of the heavy impurity is close to be fixed and nonzero, the measurement precision can be δ2T∝T3 to break the Landau bound. We derive the momentum distribution of the heavy impurity at any moment and obtain the optimal measurement precision of the temperature by calculating the Fisher information. As a result, we find that increasing the expectation value P0 and reducing the variance Δ/2 of the initial momentum can help to improve the measurement precision. Moreover, under certain conditions, Δ/P0 is a relevant parameter, the smallness of which helps improve the thermometric precision of the probe. In addition, the momentum measurement is the optimal measurement of the temperature in the case that the initial momentum is close to be fixed and not equal to zero. The kinetic energy measurement is the optimal measurement in the case that the expectation value of the initial momentum is close to zero. Finally, we obtain that the temperatures of two Bose gases can be measured simultaneously. The simultaneous measurement precision is proportional to T2 when two temperatures are close to T. Published by the American Physical Society 2024

Nanomechanically-induced nonequilibrium quantum phase transition to a self-organized density wave of a Bose-Einstein condensate

We report on a nonequilibrium quantum phase transition (NQPT) in a hybrid quantum many-body system consisting of a vibrational mode of a damped nanomembrane interacting optomechanically with a cavity, whose output light couples to two internal states of an ultracold Bose gas held in an external quasi-one-dimensional box potential. For small effective membrane-atom couplings, the system is in a homogeneous Bose-Einstein condensate (BEC) steady state, with no membrane displacement. Depending on the transition frequency between the two internal atomic states, either one or both internal states are occupied. By increasing the atom-membrane couplings, the system transitions to a symmetry-broken self-organized BEC phase, which is characterized by a considerably displaced membrane steady-state and density-wave-like BEC profiles. This NQPT can be both discontinuous and continuous for a certain interval of transition frequencies and is purely discontinuous outside of it. Published by the American Physical Society 2024

Quantum simulations with bilayer 2D Bose gases in multiple-RF-dressed potentials

Quantum simulations with bilayer 2D Bose gases in multiple-RF-dressed potentials

The Simplified Approach to the Bose Gas Without Translation Invariance

The simplified approach to the Bose gas was introduced by Lieb in 1963 to study the ground state of systems of interacting Bosons. In a series of recent papers, it has been shown that the simplified approach exceeds earlier expectations, and gives asymptotically accurate predictions at both low and high density. In the intermediate density regime, the qualitative predictions of the simplified approach have also been found to agree very well with quantum Monte Carlo computations. Until now, the simplified approach had only been formulated for translation invariant systems, thus excluding external potentials, and non-periodic boundary conditions. In this paper, we extend the formulation of the simplified approach to a wide class of systems without translation invariance. This also allows us to study observables in translation invariant systems whose computation requires the symmetry to be broken. Such an observable is the momentum distribution, which counts the number of particles in excited states of the Laplacian. In this paper, we show how to compute the momentum distribution in the simplified approach, and show that, for the simple equation, our prediction matches up with Bogolyubov’s prediction at low densities, for momenta extending up to the inverse healing length.

Path integral Monte Carlo study of a doubly dipolar Bose gas

Path integral Monte Carlo study of a doubly dipolar Bose gas

Prethermalization in coupled one-dimensional quantum gases

We consider the problem of the development of steady states in one-dimensional Bose gas tubes that are weakly coupled to one another through a density-density interaction. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of the collision integral, where single particle-hole excitations are created in individual gases, is dominant, the state of the gas evolves first to a non-thermal fixed point, i.e. a prethermalization plateau. This order is dominant when a pair of tubes are inequivalent with, say, different temperatures or different effective interaction parameters, \gammaγ. When both tubes are in the strongly interacting regime we additionally characterize this non-thermal prethermalization plateau by constructing the quasi-conserved quantities that control the existence of this plateau as well as the associated generalized Gibbs ensemble.

Large Deviations for the Ground State of Weakly Interacting Bose Gases

AbstractWe consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit $$N \rightarrow \infty $$ N → ∞ bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.

Condensation of ideal Dunkl–Bose gas in power-law traps

Condensation of ideal Dunkl–Bose gas in power-law traps

Condensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation

We study the condensate and superfluid fraction of a homogeneous gas of weakly interacting bosons in three spatial dimensions by adopting a self-consistent Popov approximation, comparing this approach with other theoretical schemes. Differently from the superfluid fraction, we find that at finite temperature the condensate fraction is a non-monotonic function of the interaction strength, presenting a global maximum at a characteristic value of the gas parameter, which grows as the temperature increases. This non-monotonic behavior has not yet been observed, but could be tested with the available experimental setups of ultracold bosonic atoms confined in a box potential. We clearly identify the region of parameter space that is of experimental interest to look for this behavior and provide explicit expressions for the relevant observables. Finite size effects are also discussed within a semiclassical approximation.

Controlling many-body quantum chaos: Bose–Hubbard systems

This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. It is long known how to harness exponential sensitivity to changes in initial conditions for control purposes in classically chaotic systems. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Recently, this classical targeting has been generalized to quantum systems either by periodically countering the inevitable quantum state spreading or by introducing a control Hamiltonian, where both enable localized states to be guided along special chaotic trajectories toward any of a broad variety of desired target states. Only strictly unitary dynamics are involved; i.e. it gives a coherent quantum targeting. In this paper, the introduction of a control Hamiltonian is applied to Bose–Hubbard systems in chaotic dynamical regimes. Properly selected unstable mean field solutions can be followed particularly rapidly to states possessing precise phase relationships and occupancies. In essence, the method generates a quantum simulation technique that can access rather special states. The protocol reduces to a time-dependent control of the chemical potentials, opening up the possibility for application in optical lattice experiments. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices (three-dimensional applications are similarly possible).

Algebraic Bethe ansatz approach to the correlation functions of the one-dimensional bosons with attraction

We consider a model of a one-dimensional Bose gas with attraction. We study ground state equal-time correlation functions in this model using the algebraic Bethe ansatz. In cases of strong interaction or/and large-volume systems, we obtain very simple explicit formulas for correlations.

Observation of collapse and revival of atomic four-wave mixing in Bose gases

Observation of collapse and revival of atomic four-wave mixing in Bose gases