Fermionic formalism for driven-dissipative multi-level systems

Abstract

We present a fermionic description of non-equilibrium multi-level systems. Our approach uses the Keldysh path integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on the Majorana fermion representation of spin-1/2 models which follows earlier applications in the context of spin and Kondo systems. We apply this formalism to problems of increasing complexity: a dissipative two-level system, a driven-dissipative multi-level atom, and a generalized Dicke model describing many multi-level atoms coupled to a single cavity. We compare our theoretical predictions with recent QED experiments and point out the features of a counter-lasing transition. Our technique provides a convenient and powerful framework for analyzing driven-dissipative quantum systems, complementary to other approaches based on the solution of Lindblad master equations.

arXiv comment22 pages, 6 figures, 5 appendices

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• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
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• Emergent dark states from superradiant dynamics in multilevel atoms in a cavity
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• Non-equilibrium diagrammatic approach to strongly interacting photons
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• Kondo Compensation in a Pseudogap Phase: a Renormalization Group Study