Reservoir engineering and dynamical phase transitions in optomechanical arrays

Abstract

We study the driven-dissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photon-number conserving non-unitary dynamics, which features a steady state with long-range photonic coherence. If the leakage of photons out of the cavity is counteracted by incoherent driving of the photonic modes, we show that the system undergoes a dynamical phase transition to the state with long-range coherence. A minimal system, composed of two micromechanical membranes in a cavity, is studied in detail, and it is shown to be a realistic setup where the key processes of the driven-dissipative dynamics can be seen.

16 pages, 9 figures

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• Harnessing symmetry to control quantum transport
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• Photon propagation in a one-dimensional optomechanical lattice
• Optomechanical cooling in a continuous system
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