SU(3) truncated Wigner approximation for strongly interacting Bose gases

TL;DR

This paper introduces an SU(3) truncated Wigner approximation to analyze the quantum dynamics of strongly interacting Bose gases, comparing its performance with exact methods and applying it to experimental scenarios.

Contribution

The paper develops an SU(3) TWA framework with a discrete sampling technique, enabling efficient simulation of complex quantum dynamics in Bose-Hubbard systems.

Findings

Both SU(3) TWA approaches accurately capture dynamics up to a certain timescale.

The methods successfully simulate correlation spreading in large systems.

Deviations from experiments suggest the need to include spatial inhomogeneity effects.

Abstract

We develop and utilize the SU(3) truncated Wigner approximation (TWA) in order to analyze far-from-equilibrium quantum dynamics of strongly interacting Bose gases in an optical lattice. Specifically, we explicitly represent the corresponding Bose--Hubbard model at an arbitrary filling factor with restricted local Hilbert spaces in terms of SU(3) matrices. Moreover, we introduce a discrete Wigner sampling technique for the SU(3) TWA and examine its performance as well as that of the SU(3) TWA with the Gaussian approximation for the continuous Wigner function. We directly compare outputs of these two approaches with exact computations regarding dynamics of the Bose--Hubbard model at unit filling with a small size and that of a fully-connected spin-1 model with a large size. We show that both approaches can quantitatively capture quantum dynamics on a timescale of $\hbar/(Jz)$, where $J$ and $z$ denote the hopping energy and the coordination number. We apply the two kinds of SU(3) TWA to dynamical spreading of a two-point correlation function of the Bose--Hubbard model on a square lattice with a large system size, which has been measured in recent experiments. Noticeable deviations between the theories and experiments indicate that proper inclusion of effects of the spatial inhomogeneity, which is not straightforward in our formulation of the SU(3) TWA, may be necessary.