Auxilliary particle field theory for generalised and non-Markovian Jaynes-Cummings Models*

The interaction of photons with molecules or atoms coupled to vibrations are often described by Jaynes-Cummings or spin-boson models. Commonly, these models are treated via a rate-equation approach [1] due to the non-canonical dynamics of the (spin-like) electronic excitations. However, this approach does not account for non-Markovian dynamics of the internal vibrational states. We introduce a novel auxilliary-particle formulation for the electronic and vibrational state of the molecules. This field-theoretical approach can be applied in and out of equilibrium and can capture non-Markovian dynamics, large reservoir sizes as well as spontaneously broken U(1) symmetry due to Bose-Einstein condensation. We present results for a pump cavity system filled with a dilute dye solution showing a BEC transition of photons [2]. Further generalisations of this formulation can be applied to various open or closed multi-level systems.

[1] P. Kirton, J. Keeling, Phys. Rev. Lett. 111, 100404 (2013).

[2] J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).