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Title

Hybrid phase-space simulation method for interacting Bose fields

Author(s)

Hoffmann, Scott E.;  Corney, Joel F.;  Drummond, P. D.

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.

Publication type

Journal article

Source

Physical Review A, Vol. 78, no. 1 (2008), article no. 013622

Publication year

2008

FOR Code(s)

0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics;  0204 Condensed Matter Physics;  0205 Optical Physics

Keyword(s)

Anharmonic oscillators;  BEC;  Bose-Einstein Condensate;  Difference equations;  Finite time;  Fokker Planck equation;  Forecasting;  FPE;  Hybrid methods;  Hybrid sensors;  Industrial economics;  Interacting bosons;  Phase space methods;  Phase spaces;  QND;  Quantum dynamics;  Quantum nondemolition measurement;  Quantum theory;  Separation;  Simulation time;  Steam condensers;  Systematic;  Systems engineering;  Turbulent flow;  Wigner representation

Publisher

American Physical Society

ISSN

1050-2947

Publisher URL

http://dx.doi.org/10.1103/PhysRevA.78.013622

Copyright

Copyright © 2008 The American Physical Society. Published version of this paper reproduced here in accordance with the copyright policy of the publisher.

Full text

Peer reviewed