Non-Markovian Dynamics of Open Quantum Systems Via Auxiliary Particles with Exact Operator Constraint

We introduce an auxiliary-particle field theory to treat the non-Markoviandynamics of driven-dissipative quantum systems of the Jaynes-Cummings type. Itassigns an individual quantum field to each reservoir state and provides ananalytic, faithful representation of the coupled system-bath dynamics. We applythe method to a driven-dissipative photon Bose-Einstein condensate (BEC)coupled to a reservoir of dye molecules with electronic and vibronicexcitations. The complete phase diagram of this system exhibits a hidden,non-Hermitian phase transition separating temporally oscillating frombiexponentially decaying photon density correlations within the BEC. On onehand, this provides a qualitative distinction of the thermal photon BEC from alaser. On the other hand, it shows that one may continuously tune from the BECto the lasing phase by circumventing a critical point. This auxiliary-particlemethod is generally applicable to the dynamics of open, non-Markovian quantumsystems.