Paula Ostmann | Searcharxiv

arXiv2017

Cooling and frequency shift of an impurity in a ultracold Bose gas using an open system approach

We investigate the quantum dynamics of a harmonically trapped particle (e.g. an ion) that is immersed in a Bose--Einstein condensate. The ultracold environment acts as a refrigerator, and thus, the influence on the motion of the ion is dissipative. We study the fully coupled quantum dynamics of particle and Bose gas in a linearized regime, treating the quasi-particle excitations of the gas as a (non-Markovian) environment for the particle dynamics. The density operator of the latter follows a known non-Markovian master equation with a highly non-trivial bath correlation function that we determine and study in detail. The corresponding damping rate and frequency shift of the particle oscillations can be read off. We are able to identify a Quantum Landau criterion for harmonically trapped particles in a superfluid environment: for frequencies $ω$ well below the chemical potential, the damping rate is strongly suppressed by a power law $ω^4$. This criterion can be seen as emerging from the classical Landau criterion involving a critical velocity combined with Heisenberg's uncertainty principle for the localized wave packet of the quantum particle. Furthermore, due to the finite size of the Bose gas, after some time we observe memory effects and thus non-Markovian dynamics of the quantum oscillator.

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arXiv2016

Dynamics of interacting bosons using the Herman-Kluk semiclassical initial value representation

Recent experimental progress using ultracold gases in optical lattices necessitates a quantitative theoretical description for a significant number of bosons. In the present paper, we investigate if time-dependent semiclassical initial value methods, with propagators expressed as integrals over phase space using classical trajectories, is suitable to describe interacting bosons, concentrating on a single mode. Despite the nonlinear contribution from the self-interaction, the corresponding classical dynamics allows for a largely analytical treatment of the semiclassical propagator. We find that the Herman-Kluk (HK) propagator conserves unitarity in the semiclassical limit ($n\to\infty$), but a decay of the norm is seen for low $n$. The frozen Gaussian approximation (FGA, i.e. HK with unit prefactor) is explicitly shown to violate unitarity in the present system for non-vanishing interaction strength, even in the semiclassical limit. Furthermore, we show by evaluating the phase space integral in steepest descent approximation, that the HK propagator reproduces the exact spectrum correctly in the limit $n\to \infty$. An error is, however, incurred in next-to-next-to-leading order (small parameter $1/n$), as seen upon numerical evaluation of the integral or by considering finite $n$ corrections to steepest descent. The FGA, in contrast, is only accurate to lowest order, and an erroneous next-to-leading order term in the energy spectrum was found analytically. Finally, as an example application, we study the dynamics of wave packets by computing the time evolution of the Wigner function. While the often-used truncated Wigner approximation cannot capture any interferences present in the exact quantum mechanical solution (known analytically), we find that the HK approach, despite also using classical information only, reproduces the salient features of the exact solution correctly.

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