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arXiv:cond-mat/0207613 · Physical Review A

Quantum Monte Carlo study of the three- to one-dimensional crossover for a trapped Bose gas

G. E. Astrakharchik, S. Giorgini

Published Nov 15, 2002• 39 citations
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Abstract

We investigate the crossover from three to one dimension in a Bose gas confined in highly anisotropic traps. By using quantum Monte Carlo techniques, we solve the many-body Schr\"odinger equation for the ground state and obtain exact results for the energy per particle and the mean square radii of the cloud in the transverse and longitudinal direction. Results are compared with the predictions of mean-field theory obtained from the Gross-Pitaevskii equation and with the one-dimensional Lieb-Liniger equation of state. We explicitly prove the occurrence of important beyond mean-field effects, including the appearance of Fermi-like properties as the system enters the Tonks gas regime.

DOI
10.1103/physreva.66.053614

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Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.
Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T = 0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. We also consider the highly polarized gas and the competition between a polaronic and a molecular picture.
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The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix, and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.