Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice

TL;DR

This paper introduces a time-dependent variational Monte Carlo method to study the dynamic response of one-dimensional Bose gases in optical lattices, successfully capturing excitation spectra and nonlinear effects with good accuracy.

Contribution

The authors develop a novel tVMC approach using a Jastrow-Feenberg wave function to simulate real-time dynamics and extract excitation spectra without explicit perturbations.

Findings

Good agreement with exact diagonalization for deep lattices

Observation of higher band effects in shallow lattices

Extraction of excitation spectra from density fluctuation power spectra

Abstract

We study the dynamics of a one-dimensional Bose gas at unit filling in both shallow and deep optical lattices and obtain the dynamic structure factor ${S(k,\omega)}$ by monitoring the linear response to a weak probe pulse. We introduce a new procedure, based on the time-dependent variational Monte Carlo method (tVMC), which allows to evolve the system in real time, using as a variational model a Jastrow-Feenberg wave function that includes pair correlations. Comparison with exact diagonalization results of ${S(k,\omega)}$ obtained on a lattice in the Bose-Hubbard limit shows good agreement of the dispersion relation for sufficiently deep optical lattices, while for shallow lattices we observe the influence of higher Bloch bands. We also investigate non-linear response to strong pulses. From the power spectrum of the density fluctuations we obtain the excitation spectrum, albeit broadened, by higher harmonic generation after a strong pulse with a single low wave number. As a remarkable feature of our simulations we furthermore demonstrate that the full excitation spectrum can be retrieved from the power spectrum of the density fluctuations due to the stochastic noise inherent in any Monte Carlo method, without applying an actual perturbation.