Variational truncated Wigner approximation for weakly interacting Bose fields: Dynamics of coupled condensates

TL;DR

This paper introduces a computationally efficient variational approach to simulate the non-equilibrium dynamics of weakly interacting Bose gases, improving upon the traditional truncated Wigner approximation by reducing simulation complexity.

Contribution

The authors develop a variational truncated Wigner method that simplifies the simulation of Bose gas dynamics by decomposing the field into an ansatz and residual, enabling more tractable calculations.

Findings

Accurately predicts non-equilibrium dynamics of Bose gases in optical lattices.

Demonstrates computational efficiency over traditional methods.

Shows good agreement with experimental data.

Abstract

The truncated Wigner approximation is an established approach that describes the dynamics of weakly interacting Bose gases beyond the mean-field level. Although it allows a quantum field to be expressed by a stochastic c-number field, the simulation of the time evolution is still very demanding for most applications. Here, we develop a numerically inexpensive approximation by decomposing the c-number field into a variational ansatz function and a residual field. The dynamics of the ansatz function is described by a tractable set of coupled ordinary stochastic differential equations for the respective variational parameters. We investigate the non-equilibrium dynamics of a three-dimensional Bose gas in a one-dimensional optical lattice with a transverse isotropic harmonic confinement and neglect the influence of the residual field. The accuracy and computational inexpensiveness of our method are demonstrated by comparing its predictions to experimental data.