Bose atoms in a trap: a variational Monte Carlo formulation for the universal behavior at the Van der Waals length scale

TL;DR

This paper develops a variational Monte Carlo method to compute universal equations of state for Bose atoms in a trap at the Van der Waals length scale, highlighting the role of long-range correlations under strong confinement.

Contribution

It introduces a VMC formulation for universal equations of state at the Van der Waals scale, enabling exact computation and analysis of long-range correlations in confined Bose gases.

Findings

Numerical results for N=3 and 5 atoms demonstrate the method's effectiveness.

Quantitative insights into shape-dependent confinement corrections.

Confirmation of the significance of long-range correlations in strongly confined Bose gases.

Abstract

We present a variational Monte Carlo (VMC) formulation for the universal equations of state at the Van der Waals length scale [B. Gao, J. Phys. B \textbf{37}, L227 (2004)] for $N$ Bose atoms in a trap. The theory illustrates both how such equations of state can be computed exactly, and the existence and the importance of long-range atom-atom correlation under strong confinement. Explicit numerical results are presented for N=3 and 5, and used to provide a quantitative understanding of the shape-dependent confinement correction that is important for few atoms under strong confinement.