Optomechanical parametric oscillation of a quantum light-fluid lattice

Abstract

Two-photon coherent states are one of the main building pillars of nonlinear and quantum optics. They are the basis for the generation of minimum-uncertainty quantum states and entangled photon pairs, applications not obtainable from standard coherent states or one-photon lasers. Here, we describe a fully resonant optomechanical parametric amplifier involving a polariton condensate in a trap lattice quadratically coupled to mechanical modes. The quadratic coupling derives from nonresonant virtual transitions to extended discrete excited states induced by the optomechanical coupling. Nonresonant continuous-wave laser excitation leads to striking experimental consequences, including the emergence of optomechanically induced intersite parametric oscillations and intersite tunneling of polaritons at discrete intertrap detunings corresponding to sums of energies of the two involved mechanical oscillations (20- and 60-GHz confined vibrations). We show that the coherent mechanical oscillations correspond to parametric resonances with a threshold condition different from that of standard linear optomechanical self-oscillation. The associated Arnold tongues display a complex scenario of states within the instability region. The observed phenomena can have applications for the generation of entangled phonon pairs and squeezed mechanical states relevant in sensing and quantum computation and for the bidirectional frequency conversion of signals in a technologically relevant range.