Fermionic formalism for driven-dissipative multilevel systems

We present a fermionic description of nonequilibrium multilevel 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 multilevel atom, and a generalized Dicke model describing many multilevel atoms coupled to a single cavity. We compare our theoretical predictions with recent QED experiments and point out the features of a counterlasing 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.