Ground state of a homogeneous Bose gas: A diffusion Monte Carlo calculation

Abstract

We use a diffusion Monte Carlo method to calculate the lowest energy state of a uniform gas of bosons interacting through different model potentials, both strictly repulsive and with an attractive well. We explicitly verify that at low density the energy per particle follow a universal behavior fixed by the gas parameter na 3 . In the regime of densities typical for experiments in trapped Bose-condensed gases the corrections to the mean-field energy greatly exceed the differences due to the details of the potential.02.70. Lq, 05.30.Jp, 03.75.Fi The achievement of Bose-Einstein condensation (BEC) in magnetically trapped atomic vapours [1] has revived interest in the theoretical study of Bose gases. Mean-field methods provide us with relatively simple predictions both for the equilibrium properties of these systems (energy per particle, density profiles, condensate fraction) and for the dynamic behavior (frequency of collective excitations, interference effects), which have been found in close agreement with experiments (for a review see Ref.[2]). In fact, the atomic clouds realized in experiments are very dilute, the average distance between particles being significantly larger than the range of interatomic forces, and mean-field approaches are well suited. However, the investigation of effects beyond mean-field theory is an important task, which would make these systems even more interesting from the point of view of many-body physics. Theoretical studies of these effects have already been proposed, either by analytic inclusion of fluctuations around mean-field [3,4] or through numerical calculations based on quantum Monte Carlo methods [5] and, more recently, also on correlated basis function approaches [6]. All these investigations are based on the idea that, for the values of density relevant in experiments, the details of the interatomic potential can be neglected and one can safely use the hard-sphere model in numerical simulations, and the expansion in powers of the gas parameter na 3 , fixed by the number density n and the s-wave scattering length a, in analytic corrections beyond mean-field. The main motivation of the present work is to verify the validity of this approach. By using a diffusion Monte Carlo (DMC) method we calculate the ground-state energy of a system of bosons interacting through different two-body model potentials. We explicitly show that for the values of the gas parameter reached in magnetic traps (na 3 ≃ 1E-5 -1E-4) the behavior is universal and fixed by na 3 and that the corrections to the mean-field energy are much larger than the differences due to the details of the interatomic potential.The ground state of a homogeneous dilute Bose gas was intensively studied in the 50's and early 60's. One of the main results of this investigation is that the ground-state energy can be expanded in powers of √ na 3 . In units of h 2 /2ma 2 the energy per particle takes the formThe first term corresponds to the mean-field prediction and was already calculated by Bogoliubov [7]. The corrections...

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