Bose Gas Research Articles

The Ground State Energy of a Two-Dimensional Bose Gas

We prove the following formula for the ground state energy density of a dilute Bose gas with density ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} in 2 dimensions in the thermodynamic limit e2D(ρ)=4πρ2Y(1-Y|logY|+(2Γ+12+log(π))Y)+o(ρ2Y2),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} e^{\ ext {2D}}(\\rho ) = 4\\pi \\rho ^2 Y\\Big (1 - Y \\vert \\log Y \\vert + \\Big ( 2\\Gamma + \\frac{1}{2} + \\log (\\pi ) \\Big ) Y \\Big ) + o(\\rho ^2 Y^{2}), \\end{aligned}$$\\end{document}as ρa2→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho a^2 \\rightarrow 0$$\\end{document}. Here Y=|log(ρa2)|-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Y= |\\log (\\rho a^2)|^{-1}$$\\end{document} and a is the scattering length of the two-body potential. This result in 2 dimensions corresponds to the famous Lee–Huang–Yang formula in 3 dimensions. The proof is valid for essentially all positive potentials with finite scattering length, in particular, it covers the crucial case of the hard core potential.

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation.

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.

Quantum degeneracy and spin entanglement in ideal quantum gases

Quantum degeneracy is the central many-body feature of ideal quantum gases stemming from quantum mechanics. In this work we address its relationship to the most fundamental form of non-classicality in many-body system, i.e. many-body entanglement. We aim at establishing a quantitative link between quantum degeneracy and entanglement in spinful ideal gases, using entanglement witness criteria based on the variance of the collective spin of the spin ensemble. We show that spin-1/2 ideal Bose gases do not possess entanglement which can be revealed from such entanglement criteria. On the contrary, ideal spin-1/2 Fermi gases exhibit spin entanglement revealed by the collective-spin variances upon entering quantum degeneracy, due to the formation of highly non-local spin singlets. We map out the regime of detectable spin entanglement for Fermi gases in free space as well as in a parabolic trap, and probe the robustness of spin entanglement to thermal effects and spin imbalance. Spin entanglement in degenerate Fermi gases is amenable to experimental observation using state-of-the-art spin detection techniques in ultracold atoms.

Critical exponents and fluctuations at BEC in a 2D harmonically trapped ideal gas

The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose–Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.

Effects of atom losses on a one-dimensional lattice gas of hard-core bosons

Effects of atom losses on a one-dimensional lattice gas of hard-core bosons

Energy-space random walk in a driven disordered Bose gas

Energy-space random walk in a driven disordered Bose gas

Critical velocity and arrest of a superfluid in a pointlike disordered potential

Superfluid flow past a potential barrier is a well studied problem in ultracold Bose gases, however, fewer studies have considered the case of flow through a disordered potential. Here we consider the case of a superfluid flowing through a channel containing multiple point-like barriers, randomly placed to form a disordered potential. We begin by identifying the relationship between the relative position of two point-like barriers and the critical velocity of such an arrangement. We then show that there is a mapping between the critical velocity of a system with two obstacles, and a system with a large number of obstacles. By establishing an initial superflow through a point-like disordered potential, moving faster than the critical velocity, we study how the superflow is arrested through the nucleation of vortices and the breakdown of superfluidity, a problem with interesting connections to quantum turbulence and coarsening. We calculate the vortex decay rate as the width of the barriers is increased, and show that vortex pinning becomes a more important effect for these larger barriers. Published by the American Physical Society 2024

Linear rotor in an ideal Bose gas near the threshold for binding

Linear rotor in an ideal Bose gas near the threshold for binding

Ultracold Bose Gases in Frame Rotating—The Beautiful Vortex in the Extremely Deep and Cold Quantum World

Ultracold Bose Gases in Frame Rotating—The Beautiful Vortex in the Extremely Deep and Cold Quantum World

Trapped vortex dynamics implemented in composite Bessel beams

The divergence-free nature of Bessel beams can be harnessed to effectively trap optical vortices in free space laser propagation. We show how to generate arbitrary vortex configurations in Bessel traps to investigate few-body vortex interactions within a dynamically evolving fluid of light, which is a formal analog to a non-interacting Bose gas. We implement—theoretically and experimentally—initial conditions of vortex configurations first predicted in harmonically trapped quantum fluids, in the limit of weak atomic interactions, and model and measure the resultant dynamics. These hard trap dynamics are distinct from the harmonic trap predictions due to the non-local interactions that occur among the hard-wall boundary and steep phase gradients that nucleate other vortices. By simultaneously presenting experimental demonstrations with the theoretical proposal, we validate the potential application of using Bessel hard-wall traps as testing grounds for engineering few-body vortex interactions within trapped, two-dimensional compressible fluids.

Ground state of Rydberg-dressed Bose gas confined in a toroidal trap

The experimental realization of Rydberg dressing technology in ultracold atomic systems provides another superior platform for studying novel states of matter and macroscopic quantum phenomena. In this work, based on the mean-field theory, we have investigated the ground-state phases of a two-component Bose–Einstein condensate with Rydberg interaction and confined in a toroidal trap. The effects of the Rydberg interaction and external potential, especially the Rydberg blockade radius, on the ground-state structure of such a system have been investigated in full parameter space. Our results show that the Rydberg blockade radius, which can be regarded as another controllable parameter, can be used to obtain a variety of ground-state phases. More interestingly, it is found that for weak Rydberg interactions, the Rydberg blockade radius breaks the spontaneous rotational symmetry of the system, leading to the formation of a discrete unit cell structure. For strongly interacting cases, it can be used to realize different orders of discrete rotational symmetry breaking.

Impurity properties in quasi-one-dimensional unitary Bose gas

Impurity properties in quasi-one-dimensional unitary Bose gas

Floating Block Method for Quantum MonteCarlo Simulations.

Quantum MonteCarlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum MonteCarlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. These new applications require something that is missing from the published literature, an efficient quantum MonteCarlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of ^{4}He, ^{8}Be, ^{12}C, and ^{16}O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

Exponential decay of the number of excitations in the weakly interacting Bose gas

We consider N trapped bosons in the mean-field limit with coupling constant λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation. We prove that the probability of finding ℓ particles outside the condensate wave function decays exponentially in ℓ.

Macroscopic squeezing in quasi-one-dimensional two-component Bose gases

We investigate the ground-state properties and the dynamics of quasi-one-dimensional quantum droplets of binary Bose condensates by employing the Gaussian state theory. We show that there exists three quantum phases for the ground states of the droplets, including a coherent state and two macroscopic squeezed states. The phase transition between two macroscopic squeezed states is of the third order; while between the macroscopic squeezed state and the coherent is of a crossover type. As for the dynamics, we find that, by tuning the reduced scattering length to a negative value, a significant fraction of the atoms can be transferred from a coherent state to a macroscopic squeezed state. Our studies open up the possibility of generating macroscopic squeezed states using binary condensates.

Two-dimensional supersolidity in a planar dipolar Bose gas

Two-dimensional supersolidity in a planar dipolar Bose gas

Density of a one-dimensional weakly interacting Bose gas far from an impurity

Density of a one-dimensional weakly interacting Bose gas far from an impurity

Ground states of attractive Bose gases in rotating anharmonic traps

This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap V(x)=ω(|x|2+k|x|4) rotating at the velocity Ω>0, where ω>0 denotes the trapping frequency, and k>0 represents the strength of the quartic term. It is known that for any Ω>0, ground states exist in such traps if and only if 0<a<a⁎, where a⁎:=‖Q‖22 and Q>0 is the unique positive solution of ΔQ−Q+Q3=0 in R2. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant C>0, independent of 0<a<a⁎, such that ground states do not have any vortex in the region R(a):={x∈R2:|x|≤C(a⁎−a)−1−6β20} as a↗a⁎, for the case where ω=3Ω24, k=16, and Ω=C0(a⁎−a)−β varies for some β∈[0,16) and C0>0.

Force on a moving object in an ideal quantum gas

We consider a heavy external object moving in an ideal gas of light particles. Collisions with the gas particles transfer momentum to the object, leading to a force that is proportional to the object's velocity but in the opposite direction. In an ideal classical gas at temperature T, the force acting on the object is proportional to T. Quantum statistics causes a deviation from the T-dependence and shows that the force scales with T2 at low temperatures. At T = 0, the force vanishes in a Bose gas but is finite in a Fermi gas.

Integrals Involving Jacobi Theta Functions and Applications in Quantum Systems

We study four expressions involving the integrals of Jacobi’s theta functions. From Poisson’s summation formula, we write the integrals of the functions θi, (i = 1,2,3,4) in terms of modified Bessel functions of the second kind. For the integrals of θ1 , θ2 and θ3, we get expressions with real arguments, but for the integral of θ4 , we find an expression with imaginary argument. In addition, we apply our results to the description of two kinds of interacting quantum systems: boson gas and fermion gas both under a thermal bath and an external magnetic field. PACS numbers: