Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

By E. Torre, S. Diehl, Mikhail D. Lukin, S. Sachdev, Philipp Strack. 2012

186 citations recorded by the source corpus.

We 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 superradiance 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/51f64335f3fcc5816bd7656c0f54b706fe08f43a

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Citations in the corpus

Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition (2020, background): “An alternative proposal using multilevel systems with external pump fields [58, 59] has been experimentally realized [60, 61].”
Keldysh field theory for driven open quantum systems (2015, background): “[112], where it has been found that in the presence of photon decay, the critical mode becomes purely imaginary before the transition happens, and the corresponding critical dynamics corresponds to a classical finite temperature transition, see also Fig.”
Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance (2018, unknown): “[39] E.”
Quantum trajectories and open many-body quantum systems (2014, background): “This could include the realisation of more complicated collective dissipative spin models [335], and quantum phases associated with the motion of atoms within the cavity [156, 158, 159].”