Nonequilibrium steady states of ideal bosonic and fermionic quantum gases

Abstract

We investigate nonequilibrium 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 nontrivial 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 nonequilibrium 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.

Describing many-body localized systems in thermal environments

“…This expression resembles the expression found for the ideal gas [62], where the many-particle rate is the singleparticle rate R qk multiplied by the occupation of the departure state n k and the Pauli blocking factor (1−n q ) of the target state. The difference is that due to interactions, the transition rate depends on the whole configuration, rather than only on the two single-particle states involved in the transition.…”

“…For a quantum many-body system, this is generally difficult. Non-interacting systems however can be treated readily [62,63], since the many-body eigenstates are given by the Fock states of the single-particle Hamiltonian. As we discuss in the following, MBL systems provide another exception, due to an emergent form of integrability [43][44][45][46].…”

“…A.1. Quantum-jump Monte Carlo simulation We use the Gillespie algorithm [62] to perform the time evolution. For each trajectory, the system is initially prepared in a random state.…”

Colloquium: Atomic quantum gases in periodically driven optical lattices

“…The resulting asymptotic non-equilibrium steady states can have unconventional properties (to mention just a few examples, see, e.g. recent work by Breuer et al, 2000;Dehghani et al, 2015;Foa Torres et al, 2014;Goldstein et al, 2015;Iadecola et al, 2015;Ketzmerick and Wustmann, 2010;Seetharam et al, 2015;Shirai et al, 2015Shirai et al, , 2016Tsuji et al, 2009;Vorberg et al, 2013Vorberg et al, , 2015. A powerful tool for the treatment of open driven systems is the Floquet-variant of dynamical mean-field theory (see Aoki et al, 2014, and references therein).…”

Design and characterization of a quantum heat pump in a driven quantum gas

“…The diagonal elements are given by timeindependent probabilities p {nc±} , which are determined by the rates (1 − n c± )R * c± and n c± R † c± for the gain ("birth" * ) and the loss ("death" †) of a fermion in state c±, respectively. The rates have contributions from both reservoirs (d = l, r), R η c± = R ηl c± + R ηr c± with η = * , †, and can be obtained using Floquet-Born-Markov theory in combination with the secular approximation [22][23][24][25]. They are given by a sum of golden-rule type terms describing processes where the system exchanges m energy quanta ω with the drive, For small driving amplitudes one has J m (α) (α/2) m /m!.…”