We report the experimental study of a hybrid quantum solid state system comprising two-level artificial atoms coupled to cavity confined optical and vibrational modes. In this system combining cavity quantum electrodynamics and cavity optomechanics, excitons in quantum wells play the role of the two-level atoms and are strongly coupled to the optical field leading to mixed polariton states. The planar optical microcavities are laterally microstructured, so that polaritons can be confined in wires, 3D traps, and arrays of traps, providing an additional tuning degree of freedom for the polariton energies. Upon increasing the non-resonant laser excitation power, a Bose-Einstein condensation of the polaritons is observed. Optomechanical induced amplification type of experiments with an additional weak laser probe clearly identify the coupling of these Bose-Einstein condensates to 20~GHz breathing-like vibrations confined in the same cavities. With single continuous wave non-resonant laser excitation, and once the laser power overpasses the threshold for Bose-Einstein condensation in trap arrays, mechanical self-oscillation similar to phonon ``lasing is induced with the concomitant observation of Mollow-triplet type mechanical sidebands on the Bose-Einstein condensate emission. High-resolution spectroscopic photoluminescence experiments evidence that these vibrational side-band resolved lines are enhanced when neighboring traps are red-detuned with respect to the BEC emission at overtones of the fundamental 20 GHz breathing mode frequency. These results constitute the first demonstration of coherent cavity polariton optomechanics and pave the way towards a novel type of hybrid devices for quantum technologies, phonon lasers, and phonon-photon bidirectional translators.
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