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

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.

arXiv comment12 pages, 3 figures

References in corpus (24)

• Many-Body Physics with Ultracold Gases
• Theory of Bose-Einstein condensation in trapped gases
• Cold bosonic atoms in optical lattices
• The density-matrix renormalization group
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Efficient simulation of one-dimensional quantum many-body systems
• Quantum many-body systems out of equilibrium
• Nonequilibrium dynamical mean-field theory and its applications
• Bragg spectroscopy of a Bose-Einstein condensate
• Continuous Matrix Product States for Quantum Fields
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Time-step targetting methods for real-time dynamics using DMRG
• Introduction to the Diffusion Monte Carlo Method
• Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
• Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids
• Ab-initio low-energy dynamics of superfluid and solid 4He
• One-dimensional liquid ${}^4$He: dynamical properties beyond Luttinger liquid theory
• Observation of superfluidity in a strongly correlated two-dimensional Fermi gas
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
• Unitary dynamics of strongly-interacting Bose gases with time-dependent variational Monte Carlo in continuous space
• Bragg spectroscopy of clean and disordered lattice bosons in one dimension: a spectral fingerprint of the Bose glass
• Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function