Quantum chaotic cavities via optomechanical coupling: A controlled environment for open-system dynamics in quantum materials

Interacting quantum many-body systems provide a route to quantum chaos and thermalization, and can serve as effective environments for local quantum degrees of freedom beyond conventional noninteracting baths. We propose a system of three cavity modes coupled through optomechanical interactions and show that, after integrating out the mechanical degrees of freedom, the cavity dynamics exhibit signatures of quantum chaos and satisfy the eigenstate thermalization hypothesis. We then couple one cavity mode to a quantum material, a graphene monolayer, and study the dynamics of a single graphene electron coupled to a chaotic cavity. Using exact time evolution, we demonstrate the thermalization of graphene electron that is induced by the chaotic cavity environment. In a parameter regime where the Markov approximation is justified, we derive a Lindblad master equation for the electron, and find agreement between the open-system description and the exact dynamics. These results establish optomechanically engineered cavities as a controllable platform for studying thermalization and open-system dynamics in quantum materials.