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

TL;DR

This paper presents an auxiliary-particle field theory for accurately modeling non-Markovian dynamics in open quantum systems, applied to a photon BEC, revealing a hidden phase transition and enabling continuous BEC-lasing tuning.

Contribution

It introduces a novel auxiliary-particle approach that faithfully captures non-Markovian dynamics and reveals a non-Hermitian phase transition in driven-dissipative quantum systems.

Findings

Identifies a hidden non-Hermitian phase transition in photon BECs.

Demonstrates continuous tuning from BEC to lasing phase.

Provides an analytic, faithful representation of system-bath dynamics.

Abstract

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