Cavity-mediated entanglement between levitated nanoparticles

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In this project we will develop a comprehensive and realistic theory for correlating the ro-translational dynamics of optically levitated nanoparticles to realize fundamental quantum tests and sensing applications. The particles are trapped by optical tweezers inside a high Q-cavity and they interact via coherent scattering of tweezer photons into common cavity modes. This can cool the nanoparticle motion into the deep quantum regime and generate quantum correlations as well as synchronization by conditioning the tweezer detunings and polarizations on quantum measurements of the cavity field. By accounting for the aspherical shape, large extension, and nonlinear couplings between the particles, and by realistically modeling all relevant decoherence mechanisms, measurement back-actions, and conditioned feedback drivings, we provide a framework for designing experimentally realistic schemes that are amenable to optimization by stochastic algorithms.