Dalla Torre, EmanueleDiehl, SebastianLukin, MikhailSachdev, SubirStrack, Philipp2014-02-112013Torre, Emanuele, Sebastian Diehl, Mikhail Lukin, Subir Sachdev, and Philipp Strack. 2013. “Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities.” Physical Review A 87 (2) (February 21). doi:10.1103/PhysRevA.87.023831. http://dx.doi.org/10.1103/PhysRevA.87.023831.1050-2947http://nrs.harvard.edu/urn-3:HUL.InstRepos:11688797We investigate non-equilibrium phase transitions for driven atomic ensembles, interacting with a cavity mode, coupled to a Markovian dissipative bath. In the thermodynamic limit and at low-frequencies, we show that the distribution function of the photonic mode is thermal, with an e↵ective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated su- perradiance transition. Motivated by these considerations, we develop a general Keldysh path integral approach, that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number of atoms N. For finite N, the photon mode behaves as a damped, classical non-linear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any N and correctly captures the atoms’ depolarization due to dissipative dephasing.en-USJournal Article2014-02-1110.1103/PhysRevA.87.023831