Time-dependent semiclassics for ultracold bosons

Abstract

We study the out-of-equilibrium dynamics of ultracold bosons in a double-and triple-well potential within the Bose-Hubbard model by means of the semiclassical Herman-Kluk propagator and compare the results to the frequently applied "classical dynamics" calculation in terms of the truncated Wigner approximation (TWA). For the double-well system we find the semiclassical results in excellent agreement with the numerically exact ones, while the TWA is not able to reproduce any revivals of the wave function. The triple-well system turns out to be more difficult to handle due to the irregularity of the corresponding classical phase space. Here, deviations of the TWA from the exact dynamics appear even for short times, while better agreement is obtained using the semiclassical approach presented in this article.

Describing many‐body bosonic waveguide scattering with the truncated Wigner method

“…Indeed, while the conventional implementation of the tW method is not expected to yield reliable predictions for long evolution times that exceed the Ehrenfest time of such a chaotic system, average transport observables, which are obtained, e.g., in the presence of disorder, are nevertheless expected to be correctly reproduced by this approach provided we can safely assume classical ergodicity (and account for systematic quantum interference effects such as coherent backscattering in Fock space [27]). This new semiclassical perspective of the tW approach will also form a useful basis for the development of a truly semiclassical van Vleck-Gutzwiller (or Herman-Kluk) approach that is able to capture interference effects beyond the diagonal approximation [27,31,32].…”

“…This phase-space distribution can contain non-classical correlations which is, however, not the case in our present problem. Finally, a fullfledged semiclassical approximation is obtained by coherently adding amplitudes associated with classical trajectories, in order to address quantum interference effects [31]. The second stage in this hierarchy of levels of approximation is the tW method.…”

The dissipative Bose-Hubbard model

“…As a final note, we report that a semiclassical approach based on interfering paths in Fock space has been recently introduced directly for discrete systems, such as for a closed BoseHubbard model [174][175][176]. Also a semiclassical Gutzwiller trace formula is brought forward [177] for the Bose-Hubbard model in the chaotic regime [178][179][180][181].…”

Understanding quantum work in a quantum many-body system

“…The interactions between the bosons can be characterized by a dimensionless coupling parameter [36,[43][44][45][46][47][48] …”

“…For the two-site case, depending on the values of λ, one can identify three qualitatively different regimes [43][44][45][46][47][48]. The Rabi regime (λ < 1), the Josephson regime (1 < λ ≪ N 2 ), and the Fock regime (λ ≫ N 2 ).…”