Nonequilibrium quantum many-body dynamics of hybrid atom-optomechanical condensate systems

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In this project, we are interested in an exotic quantum state of matter, which we foresee to exist in the form of a supersolid in a hybrid atom-optomechanical system of an ultracold atom gas coupled via light to the quantum motion of a nanomechanical oscillator. The supersolid state of this hybrid quantum many-body systems is expected in the form of quantum droplets in the atom gas, shown by spontaneous density modulations in the gas. The droplets are quantum coherent macroscopic objects. The formation of quantum droplets requires either a mixture of Bose gases or an intrinsic long-range interaction between the atoms. In a hybrid atom-optomechanical systems in the internal-state coupling configuration, both ingredients are present at the same time. The coherent long-range interaction is induced by the coupling to the mechanical oscialltor. The hybrid quantum system could provide an efficient platform to realize such a supersolid state, also with the particularly interesting aspect that this exotic quantum many-body state is triggered by a macroscopic nanomechanical oscillator which is itself in a trivial classical solid state of matter, albeit its dynamics occurs in a quantum coherent nanomechanical mode. From a fundamental point of view, a supersolid and the appearance of quantum droplets are a clear manifestation of the quantum many-body character of the system which goes far beyond a common mean-field picture.