1210.3623 (Emanuele G. Dalla Torre et al.)

Keldysh approach for non-equilibrium phase transitions in quantum
optics: Dicke model in optical cavities    [PDF]

Emanuele G. Dalla Torre, Sebastian Diehl, Mikhail Lukin, Philipp Strack

We investigate non-equilibrium phase transitions for driven atomic ensembles interacting with a cavity mode that is subject to dissipation. We first discuss that the relevant modes in the photon spectrum of the driven Dicke model are effectively thermal at low frequencies. The effective temperature of the photons is set by the atom-photon interaction strength and characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path integral approach to describe phase transitions in open quantum-optical systems. This approach is used to compute both the low-frequency and the high frequency dynamics and of the driven Dicke model with Markovian dissipation for the cavity photons and for the atoms. We re-derive the thermal properties of the low-temperature dynamics, while at higher frequencies, we show that the photon and atom distribution functions exhibit quantum and non-equilibrium regimes.

View original: http://arxiv.org/abs/1210.3623