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Physical Review A

Properties of Bose-Einstein condensates in a quasi-one-dimensional box trap

Chongshan Zhang, Kwangsik T. Nho, David Paul Landau

Published Feb 11, 2008• 6 citations
Publisher

Abstract

We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the $s$-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.

DOI
10.1103/physreva.77.025601

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We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the sss-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.
We evaluate the zero temperature properties and Bose-Einstein condensation (BEC) of hard sphere bosons in a harmonic trap using Quantum Monte Carlo methods. The chief purpose of this work is to go beyond the dilute limit, to test the limits of the Gross-Pitaevskii equation and related mean field approximations and to explore the role of interactions in determining the zero temperature properties of the trapped Bose gas. The density is increased by adjusting both the number of trapped bosons, N , and the s-wave scattering length, a, to study systems from the highly dilute region corresponding to early experiments in trapped BEC [2, 3] up to liquid He densities and beyond. Rather than relying on the perturbative Bogoliubov approximation (which assumes a large condensate fraction) to describe the condensate, we use the one-body density matrix (OBDM) formulation of BEC so that the properties of the condensate for systems with arbitrarily large interactions may be studied. In this formulation of BEC, condensate properties are obtained by diagonalizing the OBDM and obtaining the corresponding single particle “natural orbitals” and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital(s) with macroscopic occupation (N0 >> 1). Within this framework, we calculate the effects of interactions and increased density on the ground state energy, the density profile, the momentum distribution, the condensate fraction and condensate “wave-function” and several other properties.
Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, sss-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.
Several properties of trapped hard-sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single-particle Gaussian and a hard-sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard-sphere radius and the number of particles. Special attention is given to diagonalizing the one-body density matrix and obtaining the corresponding single-particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single-particle orbital with the highest occupation. The effect of interaction on other quantities such as the ground-state energy, the mean radial displacement, and the momentum distribution is calculated as well. Results are compared with mean-field theory in the dilute limit.
This work reports studies of a mixture of two interacting Bose condensates in a quasi-one-dimensional geometry using a finite-temperature path-integral Monte Carlo method. For weakly interacting dilute gases, the interactions between atoms are modeled by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interspecies interaction on the static properties, such as the density profile and the superfluid fraction, is discussed. Our results show that for repulsive intra- and interspecies interactions, the presence of the interspecies interactions dramatically changes the structure of both the density profile and the superfluid fraction, and two species are seen to partially separate in space, and there is a finite-size effect on the phase separation between two partially separating Bose-Einstein condensates. In general, our results agree with the theoretical predictions and experimental observations.
Abstract We study both static and dynamic properties of a weakly interacting Bose–Einstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross–Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas–Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.
The path-integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range sss-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range sss-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.