First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

TL;DR

This paper enhances first-principles quantum simulations of interacting Bose gases by introducing stochastic gauges, significantly reducing sampling errors and extending simulation times, with confirmed improvements in various system regimes.

Contribution

It introduces stochastic gauges to improve the positive P representation, reducing sampling errors and enabling longer, more accurate quantum dynamics simulations of Bose gases.

Findings

Stochastic gauges greatly reduce sampling error.

Numerical simulations show improved convergence.

Wave-like correlations observed after interaction quench.

Abstract

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analyzed. In a companion paper, we showed how the positive P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double-, and multi-mode systems in the weak mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant.This could in principle be tested experimentally using Feshbach resonance methods.