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.

• Received 1 August 2023
• Accepted 24 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013220

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society