Hybrid phase-space simulation method for interacting Bose fields

TL;DR

This paper presents a hybrid phase-space simulation method combining Wigner and positive-P representations to efficiently simulate quantum dynamics of interacting Bose fields, especially Bose-Einstein condensates, with improved accuracy and longer simulation times.

Contribution

The paper introduces a novel hybrid phase-space approach that self-consistently combines Wigner and positive-P representations for different modes in Bose systems, reducing systematic errors.

Findings

Hybrid method predicts atomic quadratures 60 times longer than positive-P.

Hybrid method accurately predicts correlations in quantum nondemolition measurements.

Truncated Wigner performs well but has larger systematic errors in some cases.

Abstract

We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive-P representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The Hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive-P method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the Hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.