Fermionic formalism for driven-dissipative multi-level systems

TL;DR

This paper introduces a fermionic formalism using the Keldysh path integral and Majorana fermions to analyze non-equilibrium driven-dissipative multi-level quantum systems, providing a new theoretical framework.

Contribution

It develops a novel fermionic approach for non-equilibrium multi-level systems, extending previous methods to include periodic drives and dissipation, and applies it to complex models.

Findings

Successfully models dissipative two-level and multi-level systems

Predicts features of counter-lasing transitions in cavity QED

Provides a framework aligned with recent experimental results

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.