Trapped Bose Gas Research Articles

Temperature-induced miscibility of impurities in trapped Bose gases

We study the thermal properties of impurities embedded in a repulsive Bose gas under a harmonic trapping potential. In order to obtain the exact structural properties in this inhomogeneous many-body system, we resort to the path-integral Monte Carlo method. We find that, at low temperatures, a single impurity is expelled to the edges of the bath cloud if the impurity-boson coupling constant is larger than the boson-boson one. However, when the temperature is increased, but still in the Bose-condensed phase, the impurity occupies the center of the trap and, thus, the system becomes miscible. This thermal-induced miscibility crossover is also observed for a finite concentration of impurities in this inhomogeneous system. We find that the transition temperature for miscibility depends on the impurity-boson interaction and we indicate a different nondestructive method to measure the temperature of a system based on the studied phenomenon. Published by the American Physical Society 2024

Spin-orbit-coupling-induced phase separation in trapped Bose gases

Spin-orbit-coupling-induced phase separation in trapped Bose gases

Energy cascade in a far-from-equilibrium inhomogeneous trapped Bose gas obtained by power spectrum analysis

Energy cascade in a far-from-equilibrium inhomogeneous trapped Bose gas obtained by power spectrum analysis

Bogoliubov excitation spectrum of trapped Bose gases in the Gross–Pitaevskii regime

We consider an inhomogeneous system of N bosons in R3 confined by an external potential and interacting via a repulsive potential of the form N2V(N(x−y)). We prove that the low-energy excitation spectrum of the system is determined by the eigenvalues of an effective one-particle operator, which agrees with Bogoliubov's approximation.

Vortices number and the critical atoms number of a rotating Bose–Einstein condensates in two-dimensional optical lattice

In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann–Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential [Formula: see text]. The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.

Optimal rate of condensation for trapped bosons in the Gross–Pitaevskii regime

We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in the large particle number limit, and provide the optimal convergence rate. Our work extends the previous results of Lieb, Seiringer and Yngvason on the leading order convergence, and of Boccato, Brennecke, Cenatiempo and Schlein on the homogeneous gas. Our method relies on the idea of 'completing the square', inspired by recent works of Brietzke, Fournais and Solovej on the Lee-Huang-Yang formula, and a general estimate for Bogoliubov quadratic Hamiltonians on Fock space.

Many-body excitations in trapped Bose gas: A non-Hermitian approach

We study a physically motivated model for a trapped dilute gas of Bosons with repulsive pairwise atomic interactions at zero temperature. Our goal is to describe aspects of the excited many-body quantum states of this system by accounting for the scattering of atoms in pairs from the macroscopic state. We start with an approximate many-body Hamiltonian, H a p p \mathcal {H}_{\mathrm {app}} , in the Bosonic Fock space. This H a p p \mathcal {H}_{\mathrm {app}} conserves the total number of atoms. Inspired by Wu [J. Math. Phys. 2 (1961), 105–123], we apply a non-unitary transformation to H a p p \mathcal {H}_{\mathrm {app}} . Key in this procedure is the pair-excitation kernel, which obeys a nonlinear integro-partial differential equation. In the stationary case, we develop an existence theory for solutions to this equation by a variational principle. We connect this theory to a system of partial differential equations for one-particle excitation (“quasiparticle”-) wave functions derived by Fetter [Ann. Phys. 70 (1972), 67–101], and prove existence of solutions for this system. These wave functions solve an eigenvalue problem for a J J -self-adjoint operator. From the non-Hermitian Hamiltonian, we derive a one-particle nonlocal equation for low-lying excitations, describe its solutions, and recover Fetter’s energy spectrum. We also analytically provide an explicit construction of the excited eigenstates of the reduced Hamiltonian in the N N -particle sector of Fock space.

Thermodynamic geometry of harmonically trapped ideal quantum gases

In this paper, we consider the thermodynamic geometry of harmonic trapped Bose and Fermi gases. We construct a thermodynamic geometry for these systems and evaluate the corresponding metric tensor and thermodynamic curvature. By observing that the thermodynamic curvature of the trapped Bose (Fermi) gas is always positive (negative), we conclude that the trapping potential does not affect the intrinsic statistical interactions. By inspecting the singular points of the thermodynamic curvature, we argue that the confinement dimension and the frequency of the trapping potential change the critical value of fugacity for the Bose gas.

Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy

We apply the theory of quantum generalized hydrodynamics (QGHD) introduced in (2020 Phys. Rev. Lett. 124 140603) to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks–Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher–Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.

Effective scaling approach to frictionless quantum quenches in trapped Bose gases

We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case.

Angular Momentum Josephson Effect between Two Isolated CondensatesSupported by the National Key Research and Development Program in China (Grant Nos. 2017YFA0304504 and 2017YFA0304103), and the National Natural Science Foundation of China (Grant No. 11774328).

We demonstrate that the two degenerate energy levels in spin–orbit coupled trapped Bose gases, coupled by a quenched Zeeman field, can be used for angular momentum Josephson effect. In a static quenched field, we can realize a Josephson oscillation with a period ranging from millisecond to hundreds of milliseconds. Moreover, by a driven Zeeman field, we realize a new Josephson oscillation, in which the population imbalance may have the same expression as the current in the direct-current Josephson effect. When the dynamics of the condensate cannot follow up the modulation frequency, it is in the self-trapping regime. This new dynamic is understood from the time-dependent evolution of the constant-energy trajectory in the phase space. This model has several salient advantages compared to the previous ones. The condensates are isolated from their excitations by a finite gap, thus can greatly suppress the damping effect induced by thermal atoms and Bogoliubov excitations. The oscillation period can be tuned by several orders of magnitude without influencing other parameters. In experiments, the dynamics can be mapped out from spin and momentum spaces, thus it is not limited by the spatial resolution in absorption imaging. This system can serve as a promising platform for matter wave interferometry and quantum metrology.

Another proof of BEC in the GP-limit

We present a fresh look at the methods introduced by Boccato, Brennecke, Cenatiempo, and Schlein [Commun. Math. Phys. 359(3), 975–1026 (2018); Acta Math. 222(2), 219–335 (2019); Commun. Math. Phys. 376, 1311 (2020)] concerning the trapped Bose gas and give a conceptually very simple and concise proof of Bose–Einstein condensation in the Gross–Pitaevskii limit for small interaction potentials.

Low-Energy Collective Oscillations and Bogoliubov Sound in an Exciton-Polariton Condensate.

We report the observation of low-energy, low-momenta collective oscillations of an exciton-polariton condensate in a round "box" trap. The oscillations are dominated by the dipole and breathing modes, and the ratio of the frequencies of the two modes is consistent with that of a weakly interacting two-dimensional trapped Bose gas. The speed of sound extracted from the dipole oscillation frequency is smaller than the Bogoliubov sound, which can be partly explained by the influence of the incoherent reservoir. These results pave the way for understanding the effects of reservoir, dissipation, energy relaxation, and finite temperature on the superfluid properties of exciton-polariton condensates and other two-dimensional open-dissipative quantum fluids.

A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases

When the temperature of a trapped Bose gas is below the Bose-Einstein transition temperature and above absolute zero, the gas is composed of two distinct components: the Bose-Einstein condensate and the cloud of thermal excitations. The dynamics of the excitations can be described by quantum Boltzmann models. We establish a connection between quantum Boltzmann models and chemical reaction networks. We prove that the discrete differential equations for these quantum Boltzmann models converge to an equilibrium point. Moreover, this point is unique for all initial conditions that satisfy the same conservation laws. In the proof, we then employ a toric dynamical system approach, similar to the one used to prove the global attractor conjecture, to study the convergence to equilibrium of quantum kinetic equations.

Dark-antidark spinor solitons in spin-1 Bose gases

We consider a one-dimensional trapped spin-1 Bose gas and numerically explore families of its solitonic solutions, namely antidark-dark-antidark (ADDAD), as well as dark-antidark-dark (DADD) solitary waves. Their existence and stability properties are systematically investigated within the experimentally accessible easy-plane ferromagnetic phase by means of a continuation over the atom number as well as the quadratic Zeeman energy. It is found that ADDADs are substantially more dynamically robust than DADDs. The latter are typically unstable within the examined parameter range. The dynamical evolution of both of these states is explored and the implication of their potential unstable evolution is studied. Some of the relevant observed possibilities involve, e.g., symmetry-breaking instability manifestations for the ADDAD, as well as splitting of the DADD into a right- and a left-moving dark-antidark pair with the anti-darks residing in a different component as compared to prior to the splitting. In the latter case, the structures are seen to disperse upon long-time propagation.

Measurement of the Canonical Equation of State of a Weakly Interacting 3D Bose Gas.

Using a multiple-image reconstruction method applied to a harmonically trapped Bose gas, we determine the equation of state of uniform matter across the critical transition point, within the local density approximation. Our experimental results provide the canonical description of pressure as a function of the specific volume, emphasizing the dramatic deviations from the ideal Bose gas behavior caused by interactions. They also provide clear evidence for the nonmonotonic behavior with temperature of the chemical potential, which is a consequence of superfluidity and Bose-Einstein condensation. The measured thermodynamic quantities are compared to mean-field predictions available for the interacting Bose gas. The limits of applicability of the local density approximation near the critical point are also discussed, focusing on the behavior of the isothermal compressibility.

Bose–Einstein Condensation: Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase (Ann. Phys. 8/2020)

Bose–Einstein Condensation: Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase (Ann. Phys. 8/2020)

Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase

AbstractIn this study, ideal free and harmonically trapped Bose gases confined by two plates in the x–y‐plane in‐between distance d are considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti‐periodic boundary conditions. The Casimir force is then obtained for the Bose–Einstein condensate phase and for the non‐condensate phase . It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non‐condensate phase with the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.

Information Entropy and Information Distances in Atoms, Nuclei and Bosonic Systems

The universal property for the information entropy S = a + h In Ζ is verified for atoms using a systematic study with Roothaan-Hartree-Fock (RHF) wave functions with atomic number Ζ — 2 — 54. The above relation was proposed previously for atoms, nuclei, atomic clusters and correlated atoms in a trap. Kullback-Leibler relative entropy Κ and Jensen-Shannon divergence J are employed to compare RHF with Thomas-Fermi (TF) density of atoms as well as another phenomenological density obtained by Sagar et al. Two-body density distributions in position- and momentum-space are used to calculate and compare the corresponding information entropies for correlated and uncorrelated nuclei and bosonic systems (correlated atoms in a trap). It is seen that short-range correlations (SRC) increase the values of S. One-body information entropy entropy S\ is compared with two-body information entropy and a conjecture is made for TV-body information entropy SN- The entropy Κ and the divergence J are also used to evaluate the information distance between correlated and uncorrelated densities both at the one- and the two-body levels for nuclei and trapped Bose gases.

Stability analysis of ground states in a one-dimensional trapped spin-1 Bose gas

In this work we study the stability properties of the ground states of a spin-1 Bose gas in presence of a trapping potential in one spatial dimension. To set the stage we first map out the phase diagram for the trapped system by making use of a, so-called, continuous-time Nesterov method. We present an extension of the method, which has been previously applied to one-component systems, to our multi-component system. We show that it is a powerful and robust tool for finding the ground states of a physical system without the need of an accurate initial guess. We subsequently solve numerically the Bogoliubov de-Gennes equations in order to analyze the stability of the ground states of the trapped spin-1 system. We find that the trapping potential retains the overall structure of the stability diagram, while affecting the spectral details of each of the possible ground state waveforms. It is also found that the peak density of the trapped system is the characteristic quantity describing dynamical instabilities in the system. Therefore replacing the homogeneous density with the peak density of the trapped system leads to good agreement of the homogeneous Bogoliubov predictions with the numerically observed maximal growth rates of dynamically unstable modes. The stability conclusions in the one-dimensional trapped system are independent of the spin coupling strength and the normalized trap strength over several orders of magnitude of their variation.