Nonequilibrium Dyson equations for strongly coupled light and matter: spin glass formation in multi-mode cavity QED

Hossein Hosseinabadi, Darrick E. Chang, Jamir Marino
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistical Mechanics (cond-mat.stat-mech), Quantum Physics (quant-ph)
2023-12-18 00:00:00
Light-matter interfaces have now entered a new stage marked by the ability to engineer quantum correlated states under driven-dissipative conditions. To propel this new generation of experiments, we are confronted with the need to model non-unitary many-body dynamics in strongly coupled regimes, by transcending traditional approaches in quantum optics. In this work, we contribute to this program by adapting a functional integral technique, conventionally employed in high-energy physics, in order to derive nonequilibrium Dyson equations for interacting light-matter systems. Our approach is grounded in constructing two-particle irreducible (2PI) effective actions, which provide a non-perturbative and conserving framework for describing quantum evolution at a polynomial cost in time. One of the aims of the article is to offer a pedagogical introduction designed to bridge readers from diverse scientific communities, including those in quantum optics, condensed matter, and high-energy physics. We apply our method to complement the analysis of spin glass formation in the context of frustrated multi-mode cavity quantum electrodynamics, initiated in our accompanying work [H. Hosseinabadi, D. Chang, J. Marino, arXiv:2311.05682]. Finally, we outline the capability of the technique to describe other near-term platforms in many-body quantum optics, and its potential to make predictions for this new class of experiments.
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