Hybrid phase-space simulation method for interacting Bose fields

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.

13 pages; 6 figures; references added; figures corrected

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• Quantum fluctuation effects on the quench dynamics of thermal quasicondensates
• Grassmann Phase Space Methods for Fermions. II. Field Theory
• Initial states and apodisation for quantum field simulations in phase-space
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Decoherence effects in Bose-Einstein condensate interferometry. I General Theory
• Phase space theory of Bose-Einstein condensates and time-dependent modes
• Quantum-field-theoretical approach to phase-space techniques: Symmetric Wick theorem and multitime Wigner representation
• Norm preserving stochastic field equation for an ideal Bose gas in a trap: numerical implementation and applications
• Benchmarking quantum phase-space methods for near-resonant light propagation