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

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 scheme by approximating the c-number field with a variational ansatz. 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. The accuracy and computational inexpensiveness of our method are demonstrated by comparing its predictions to experimental data.