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Unitary Dynamics of Strongly Interacting Bose Gases with the Time-Dependent Variational Monte Carlo Method in Continuous Space

Giuseppe Carleo

Lorenzo Cevolani

Laurent Sanchez-Palencia

Markus Holzmann

  • Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland

  • Laboratoire Charles Fabry, Institut d’Optique, CNRS, Univ Paris Sud 11, 2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France

  • Laboratoire Charles Fabry, Institut d’Optique, CNRS, Univ Paris Sud 11, 2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France and Centre de Physique Théorique, Ecole Polytechnique, CNRS, Univ Paris-Saclay, F-91128 Palaiseau, France

  • LPMMC, UMR 5493 of CNRS, Université Grenoble Alpes, F-38042 Grenoble, France and Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France

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Phys. Rev. X 7, 031026 – Published 8 August, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031026

Abstract

We introduce the time-dependent variational Monte Carlo method for continuous-space Bose gases. Our approach is based on the systematic expansion of the many-body wave function in terms of multibody correlations and is essentially exact up to adaptive truncation. The method is benchmarked by comparison to an exact Bethe ansatz or existing numerical results for the integrable Lieb-Liniger model. We first show that the many-body wave function achieves high precision for ground-state properties, including energy and first-order as well as second-order correlation functions. Then, we study the out-of-equilibrium, unitary dynamics induced by a quantum quench in the interaction strength. Our time-dependent variational Monte Carlo results are benchmarked by comparison to exact Bethe ansatz results available for a small number of particles, and are also compared to quench action results available for noninteracting initial states. Moreover, our approach allows us to study large particle numbers and general quench protocols, previously inaccessible beyond the mean-field level. Our results suggest that it is possible to find correlated initial states for which the long-term dynamics of local density fluctuations is close to the predictions of a simple Boltzmann ensemble.

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Popular Summary

Everyday objects move pretty predictably. When an apple falls from a tree, its motion is fully and easily described by its trajectory. Quantum particles such as electrons and protons are much more complex. Describing their motion requires a complex mathematical tool called a wave function to determine the probability of where the quantum “apple” is at a given time. This becomes even harder when many quantum particles are involved. Predicting their exact motion in those circumstances is far beyond reach, even on the most powerful supercomputer. In our work, we have developed a new theoretical approach to accurately study the dynamics of a gas of quantum particles that can help solve the most puzzling problems concerning the collective behavior of quantum objects over long times.

A fundamental open question we address is whether a strongly interacting quantum gas, well isolated from the external environment, still obeys the laws of thermodynamics after being driven out of equilibrium. Despite impressive theoretical and experimental progress over the last years, this and other fundamental questions about quantum thermalization remain open. Our new stochastic method (time-dependent variational Monte Carlo) allows us to accurately study the dynamics of one-dimensional strongly interacting bosons. We show that the absence and occurrence of thermalization of the potential energy can be observed in ultracold atom experiments in a controlled way using a switch from noninteracting to interacting initial states followed by a sudden quench of the interacting strength.

Our methods pave the way for predicting the out-of-equilibrium dynamics of two- and three-dimensional quantum gases and fluids more accurately than current approximation methods.

Article Text

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Phys. Rev. X 7, 031026– Published 8 August, 2017
  • Received 19 December 2016
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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