Non-equilibrium steady states of ideal bosonic and fermionic quantum gases

TL;DR

This paper explores non-equilibrium steady states of ideal bosonic and fermionic quantum gases under driving and dissipation, introducing analytical and numerical methods to understand phenomena like Bose selection and bath engineering.

Contribution

It develops a comprehensive framework combining mean-field, augmented mean-field, and quantum-jump simulations to analyze non-equilibrium states of ideal quantum gases, including new insights into Bose selection.

Findings

Identification of mechanisms for heat transport in Bose selected states

Development of algorithms to determine selected states

Demonstration of exotic states via bath engineering in fermionic models

Abstract

We investigate non-equilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also non-trivial two-particle correlations, and quantum-jump-type Monte-Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a non-equilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose selected state.