Bose Gas Research Articles

Ultrawide Dark Solitons and Droplet-Soliton Coexistence in a Dipolar Bose Gas with Strong Contact Interactions.

We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a nonzero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments revealing the coexistence of a dark soliton inside a quantum droplet.

Dissipative dynamics of an impurity with spin-orbit coupling

Brownian motion of a mobile impurity in a bath is affected by spin-orbit coupling (SOC). Here, we discuss a Caldeira-Leggett-type model that can be used to propose and interpret quantum simulators of this problem in cold Bose gases. First, we derive a master equation that describes the model and explore it in a one-dimensional (1D) setting. To validate the standard assumptions needed for our derivation, we analyze available experimental data without SOC; as a byproduct, this analysis suggests that the quench dynamics of the impurity is beyond the 1D Bose-polaron approach at temperatures currently accessible in a cold-atom laboratory---motion of the impurity is mainly driven by dissipation. For systems with SOC, we demonstrate that 1D spin-orbit coupling can be gauged out even in the presence of dissipation---the information about SOC is incorporated in the initial conditions. Observables sensitive to this information (such as spin densities) can be used to study formation of steady spin polarization domains during quench dynamics.

Thermalization of Interacting Quasi-One-Dimensional Systems.

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intrachain interactions and the weak interchain coupling. When the intrachain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally nonexponential, even for spatially uniform perturbations.

Solution of the BEC to BCS Quench in One Dimension.

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the quench action approach. We provide an experimentally accessible characterization of the stationary state by computing local pair correlation function as well as the quasiparticle distribution functions. We find that the steady state is increasingly dominated by two-particle spin singlet bound states for stronger interaction strength, but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power-law decay suggesting a violation of Tan's contact relations.

The Bose Gas in a Box with Neumann Boundary Conditions

We consider a gas of n bosonic particles confined in a box \([-\ell /2,\ell /2]^3\) with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box \([-\ell /2,\ell /2]^3\) implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box \([-L/2,L/2]^3\) with density \(\rho =N/L^3\) in the thermodynamic limit.

Ground state of Rydberg-dressed Bose gas confined in periodic moiré lattices

The experimental realization of Rydberg dressing and spin-orbit coupling greatly broadens the research field of ultracold atoms as a quantum simulation platform. Very recently, moiré lattices have attracted intensive study, ranging from condensed matter to ultracold physics. In this paper, the ground-state structure of Rydberg-dressed Bose gas with spin-orbit coupling and confined in moiré lattices is studied, and the effects of nonlocal Rydberg interaction and spin-orbit coupling on the ground state of the system are explored. Our results show that the system has no translational symmetry due to the presence of nonlocal Rydberg interaction, and more and more regular periodic structures present with the increases of the strength of nonlocal Rydberg interaction. In the presence of spin-orbit coupling, the Hamiltonian of the system has an imaginary part, and the phase of the system is not uniformly distributed. It is found that the ground state of the system with spin-orbit coupling present more abundant internal structure base on these periodic structures. The results pave the way for future study of moiré physics in ultracold atom system.

Optimal control of quasi-1D Bose gases in optical box potentials

In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective mean-field dynamics of the gas can be described by a one-dimensional non-polynomial Schrödinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borzì (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach is then applied to optimally compress a quasi-1D Bose gase in an (optical) box potential, i.e., to find a so-called short-cut to adiabaticity, by solving the optimality conditions numerically. The behavior of the proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach.

Validity of Bogoliubov’s approximation for translation-invariant Bose gases

We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy $E_N$ is given by $E_N=Ne_\mathrm{H}+\inf \sigma\left(\mathbb{H}\right)+o_{N\rightarrow \infty}(1)$, where $N$ is the number of particles, $e_\mathrm{H}$ is the minimal Hartree energy and $\mathbb{H}$ is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states $\Psi_N$, i.e. states satisfying $\langle H_N\rangle_{\Psi_N}=E_N+o_{N\rightarrow \infty}(1)$, exhibiting complete Bose--Einstein condensation with respect to one of the Hartree minimizers.

Phonon decay in one-dimensional atomic Bose quasicondensates via Beliaev-Landau damping

In a one-dimensional Bose gas, there is no nontrivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such three-wave mixing processes (Beliaev and Landau damping) account for their decay via interactions with thermal fluctuations. Within an appropriate time window where the Fermi golden rule is expected to apply, the occupation number of the initially occupied mode decays exponentially and the rate takes a simple analytic form. The result is shown to compare favorably with simulations based on the truncated Wigner approximation. It is also shown that the same processes slow down the exponential growth of phonons induced by a parametric oscillation.

Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case

In the present paper, discussion of the canonical quantization of a weakly nonideal Bose gas at zero temperature within the framework of the Bogolyubov approach is continued. Contrary to the previous paper on this subject, here the two-body interaction potential is considered in the general form. It is shown that in such a case consideration of the first nonlinear correction also leads to the automatic particle number conservation without any additional assumptions or modification of the resulting effective Hamiltonian.

Method of difference-differential equations for some Bethe-ansatz-solvable models

In studies of one-dimensional Bethe ansatz solvable models, a Fredholm integral equation of the second kind with a difference kernel on a finite interval often appears. This equation does not generally admit a closed-form solution and hence its analysis is quite complicated. Here we study a family of such equations, concentrating on their moments. We find exact relations between the moments in the form of difference-differential equations. The latter results significantly advance the analysis, enabling one to practically determine all the moments from the explicit knowledge of the lowest one. As applications, several examples are considered. First, we study the moments of the quasimomentum distribution in the Lieb-Liniger model and find explicit analytical results. The latter moments determine several basic quantities, e.g., the $N$-body local correlation functions. We prove the equivalence between different expressions found in the literature for the three-body local correlation functions and find an exact result for the four-body local correlation function in terms of the moments of the quasimomentum distributions. We eventually find the analytical results for the three- and four-body correlation functions in the form of asymptotic series in the regimes of weak and strong interactions. Next, we study the exact form of the low-energy spectrum of a magnon (a polaron) excitation in the two-component Bose gas described by the Yang-Gaudin model. We find its explicit form, which depends on the moments of the quasimomentum distributions of the Lieb-Liniger model. Then, we address a seemingly unrelated problem of capacitance of a circular capacitor and express the exact result for the capacitance in the parametric form. In the most interesting case of short plate separations, the parametric form has a single logarithmic term. This should be contrasted with the explicit result that has a complicated structure of logarithms.

Emergent Pauli Blocking in a Weakly Interacting Bose Gas

The relationship between many-body interactions and dimensionality is integral to numerous emergent quantum phenomena. A striking example is the Bose gas, which upon confinement to one dimension (1D) obeys an infinite set of conservation laws, prohibiting thermalization and constraining dynamics. In our experiment, we demonstrate that such a 1D behavior can extend much further into the dimensional crossover toward 3D than expected. Starting from a weakly interacting Bose gas trapped in a highly elongated potential, we perform a quench to instigate the dynamics of a single density mode. Employing the theory of generalized hydrodynamics, we identify the dominant relaxation mechanism as the 1D dephasing of the relevant collective excitations of the system, the rapidities. Surprisingly, the dephasing remains dominant even for temperatures far exceeding conventional limits of one dimensionality where thermalization should occur. We attribute our observations to an emergent Pauli blocking of transverse excitations caused by the rapidities assuming fermionic statistics, despite the gas being purely bosonic. Thus, our study suggests that 1D physics is less fragile than previously thought, as it can persist even in the presence of significant perturbations. More broadly, by employing the exact Bethe ansatz solutions of the many-body system, we facilitate an interpretation of how the emergent macroscopic behavior arises from the microscopic interactions.5 MoreReceived 24 June 2022Accepted 15 November 2022DOI:https://doi.org/10.1103/PhysRevX.12.041032Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum quenchPhysical Systems1-dimensional systemsUltracold gasesCondensed Matter, Materials & Applied PhysicsStatistical Physics

Viscous Drude weight of dual Bose and Fermi gases in one dimension

We continue to study frequency-dependent complex bulk viscosities of one-dimensional Bose and Fermi gases with contact interactions, which exhibit the weak-strong duality according to our recent work. Here we show that they are contributed to by Drude peaks divergent at zero frequency as typical for transport coefficients of quantum integrable systems in one dimension. In particular, their Drude weights are evaluated based on the Kubo formula in the high-temperature limit at arbitrary coupling as well as in the weak-coupling and strong-coupling limits at arbitrary temperature, where systematic expansions in terms of small parameters are available. In all three limits, the Drude peaks are found at higher orders compared to the finite regular parts.

Complex Langevin approach to interacting Bose gases

Quantitative numerical analyses of interacting dilute Bose-Einstein condensates are most often based on semiclassical approximations. Since the complex-valued field-theoretic action of the Bose gas does not offer itself to standard Monte Carlo techniques, simulations beyond their scope almost exclusively rely on quantum-mechanical techniques, which are inherently limited to small particle numbers. Here we explore an alternative approach based on a Langevin-type sampling in an extended state space, known as complex Langevin (CL) algorithm. While the use of the CL technique has a long-standing history in high-energy physics, in particular in the simulation of QCD at finite baryon density, applications to ultracold atoms are still in their infancy. Here we examine the applicability of the CL approach for a one- and two-component, three-dimensional non-relativistic Bose gas in thermal equilibrium, below and above the Bose-Einstein phase transition. By comparison with analytic descriptions at the Gaussian level, including Bogoliubov and Hartree-Fock theory, we find that the method allows computing reliably and efficiently observables in the regime of experimentally accessible parameters. Close to the transition, quantum corrections lead to a shift of the critical temperature which we reproduce within the numerical range known in the literature. With this work, we aim to provide a first test of CL as a potential out-of-the-box tool for the simulation of experimentally realistic situations, including trapping geometries and multicomponent/-species models.

Suppression of spontaneous defect formation in inhomogeneous Bose gases

The authors demonstrate the suppression of the spontaneous defect formation, ascribed to the causality effect, in an inhomogeneous system. They measure the defect position in an atomic Bose gas quenched into a superfluid phase and show that the defect formation is more suppressed in the higher atomic density gradient region.

Thermal conductivity of a weakly interacting Bose gas in quasi-one-dimension.

Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight matter waveguide, an effective three-body interaction inevitably arises as leading perturbation to break the integrability. This fact motivates us to study the thermal conductivity of a Bose gas in one dimension with both two-body and three-body interactions. In particular, we evaluate the Kubo formula exactly to the lowest order in perturbation by summing up all contributions that are naively higher orders in perturbation but become comparable in the zero-frequency limit due to the pinch singularity. Consequently, a self-consistent equationfor a vertex function is derived, showing that the thermal conductivity in quasi-one-dimension is dominated by the three-body interaction rather than the two-body interaction. Furthermore, the resulting thermal conductivity in the weak-coupling limit proves to be identical to that computed based on the quantum Boltzmann equation and its temperature dependence is numerically determined.

A Second Order Upper Bound for the Ground State Energy of a Hard-Sphere Gas in the Gross–Pitaevskii Regime

We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius mathfrak {a}/N, moving in the three-dimensional unit torus Lambda . Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N rightarrow infty . The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose–Einstein condensate and describing correlations on large scales.

Loading a quantum gas from a hybrid dimple trap to a shell trap

Starting from a degenerate Bose gas in a hybrid trap combining a magnetic quadrupole trap and an attractive optical trap resulting from a focused laser beam, we demonstrate the efficient loading of this quantum gas into a shell-shaped trap. The shell trap is purely magnetic and relies on adiabatic potentials for atoms in an inhomogeneous magnetic field dressed by a radiofrequency (rf) field. We show that direct rf evaporation in the hybrid trap enables an efficient and simple preparation of the cold sample, well adapted to the subsequent loading procedure. The transfer into the shell trap is adiabatic and limits the final excitation of the center-of-mass motion to below 2 μm.

The thermodynamic limit of an ideal Bose gas by asymptotic expansions and spectral ζ-functions

We analyze the thermodynamic limit—modeled as the open-trap limit of an isotropic harmonic potential—of an ideal, non-relativistic Bose gas with a special emphasis on the phenomenon of Bose–Einstein condensation. This is accomplished by the use of an asymptotic expansion of the grand potential, which is derived by ζ-regularization techniques. Herewith, we can show that the singularity structure of this expansion is directly interwoven with the phase structure of the system: In the non-condensation phase, the expansion has a form that resembles usual heat kernel expansions. By this, thermodynamic observables are directly calculable. In contrast, the expansion exhibits a singularity of infinite order above a critical density, and a renormalization of the chemical potential is needed to ensure well-defined thermodynamic observables. Furthermore, the renormalization procedure forces the system to exhibit condensation. In addition, we show that characteristic features of the thermodynamic limit, such as the critical density or the internal energy, are entirely encoded in the coefficients of the asymptotic expansion.

On the linearized system of equations for the condensate–normal fluid interaction at very low temperature

AbstractThe linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density is studied. A simple and transparent argument gives a necessary and sufficient condition for the existence of global solutions satisfying the conservation of the total number of particles and energy. The global solutions describe the evolution in time of the density of the thermal cloud and, unlike in previous work, that of the condensate's density. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.