Functional Wigner representation of BEC quantum dynamics

TL;DR

This paper introduces a functional Wigner representation method for simulating the quantum dynamics of multi-mode Bose-Einstein condensates, enabling the study of quantum effects like squeezing and entanglement in large systems.

Contribution

It develops a probabilistic, stochastic approach using the truncated Wigner representation for quantum field dynamics of BECs, including nonlinear losses and spatial evolution.

Findings

Valid for large mode occupation numbers

Accounts for nonlinear losses and spatial evolution

Explains previous inconsistencies in loss equations

Abstract

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects like quantum squeezing, entanglement, EPR correlations and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.