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arXiv:1105.2340 · Physical Review A

Direct simulation Monte Carlo method for cold-atom dynamics: Classical Boltzmann equation in the quantum collision regime

Andrew C. J. Wade, D. Baillie, P. B. Blakie

Published Aug 8, 2011• 30 citations
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Abstract

In this paper, we develop a direct simulation Monte Carlo method for simulating highly nonequilibrium dynamics of nondegenerate ultracold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas et al. Phys. Rev. Lett. 93, 173201 (2004)], which requires the inclusion of beyond $s$-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.

DOI
10.1103/physreva.84.023612

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In this paper, we develop a direct simulation Monte Carlo method for simulating highly nonequilibrium dynamics of nondegenerate ultracold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas et al. Phys. Rev. Lett. 93, 173201 (2004)], which requires the inclusion of beyond sss-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.
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This is a review of recent developments in Monte Carlo methods in the field of ultracold gases. For bosonic atoms in an optical lattice we discuss path-integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons and spinful bosonic systems. For repulsive fermionic systems, determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.
Abstract We investigate nonequilibrium steady states in an isolated system of few ultracold cesium atoms (Cs). Numerically and experimentally, we study the dynamics and fluctuations of the extracted position distributions and find the formation of nonthermal steady states for absent interactions. Atomic collisions in the s-wave regime, however, ensue thermalization of the few-particle system. We present numerical simulations of the microscopic equations of motion with a simple representation of the s-wave scattering events. Based on these simulations, a parameter range is identified, where the interaction between few atoms is sufficiently strong to thermalize the nonequilibrium steady state on experimentally accessible time scales, which can be traced by monitoring the atomic position distribution. Furthermore, the total energy distribution, which is also accessible experimentally, is found to be a powerful tool to observe the emergence of a thermal state. Our work provides a pathway for future experiments investigating the effect interactions in few-particle systems and underlines the role of fluctuations in investigating few-particle systems.
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Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al. [1], in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis [2], nonequilibrium mass transport [1], dynamical fermionization [3], and transient phenomena such as quantum distillation or dynamical quasicondensation [4]. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems [1] and in determining the asymptotic state after a quantum quench [5]. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics [6]. [1] Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013) [2] Sorg et al., Phys. Rev. A 90, 033606 (2014) [3] Vidmar et al., Phys. Rev. B 88, 235117 (2013) [4] Vidmar et al., Phys. Rev. Lett. 115, 175301 (2015) [5] Mei et al., arXiv:1509.00828 [6] Hauschild, Pollmann, FHM, arXiv:1509.00696
Recently the general form of a translation-covariant quantum Boltzmann equation has been derived, which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full three-dimensional Monte Carlo simulations of this equation. The simulation method is used to study the approach to equilibrium for various scattering cross sections and to determine dynamical deviations from Gaussian statistics through an investigation of higher-order cumulants. Moreover, we examine the loss of coherence of superpositions of momentum eigenstates and determine the corresponding decoherence time scales to quantify the transition from quantum to classical behavior of the state of the test particle.