Norm preserving stochastic field equation for an ideal Bose gas in a trap: numerical implementation and applications

TL;DR

This paper introduces a quantum stochastic field equation for trapped Bose gases that avoids ultraviolet cutoff issues, enabling detailed numerical simulations of ground state properties and coherence in finite systems.

Contribution

It presents a novel quantum stochastic field equation formulated for fixed particle number, with detailed derivation, numerical implementation, and applications to various trapping potentials.

Findings

Accurate ground state occupation numbers and fluctuations

Analysis of spatial coherence through correlation functions

Demonstration of the method's applicability to different potentials

Abstract

Stochastic field equations represent a powerful tool to describe the thermal state of a trapped Bose gas. Often, such approaches are confronted with the old problem of an ultraviolet catastrophe, which demands a cutoff at high energies. In [arXiv:0809.1002, Phys. B 42, 081001 (2009)] we introduce a quantum stochastic field equation, avoiding the cutoff problem through a fully quantum approach based on the Glauber-Sudarshan P-function. For a close link to actual experimental setups the theory is formulated for a fixed particle number and thus based on the canonical ensemble. In this work the derivation and the non-trivial numerical implementation of the equation is explained in detail. We present applications for finite Bose gases trapped in a variety of potentials and show results for ground state occupation numbers and their equilibrium fluctuations. Moreover, we investigate spatial coherence properties by studying correlation functions of various orders.