David Roberts
It has been well-known that classical Markov processes satisfying detailed balance are exactly solvable. Attempts to solve quantum problems in a similar way have often relied on artificial phase-space representations to map onto effectively classical problems. In this talk, we derive an quantum-mechanical formulation of detailed balance for quantum master equations, which enables solutions of nontrivial steady states. These ”quantum” detailed balance conditions can be rephrased as the condition of a certain cascaded network relaxing into a dark state, and hence represent a generalization of coherent quantum absorber (CQA) approaches to finding steady states in quantum optics. Finally, we connect quantum detailed balance with its classical counterpart, unveiling the existence of a hidden "quantum-classical dictionary" that shows how these quantum detailed balance conditions ultimately enabled the symmetries exploited by classical phase space methods first used to solve driven-nonlinear cavity problems in quantum optics.