Quantum-induced Stochastic Optomechanical Dynamics

We study the effective stochastic dynamics of a semiclassical probe induced by linear optomechanical interactions with a quantum oscillator. To do so, we introduce path integrals and the method of Feynman-Vernon influence functionals in quantum optics and analyze the semiclassical dynamics of a levitated nanoparticle interacting with quantum light, as well as with another quantum particle. In all cases, quantum fluctuations ubiquitously lead to state-dependent non-equilibrium noise. Notably, this noise can be exponentially enhanced by wavepacket delocalization, i.e., quantum squeezing, and displays both a stationary and a non-stationary contribution with intricate dependence on the squeezing angle. For the case of nanoparticles coupled by the Coulomb interaction such noise can imprint potentially measurable signatures in multiparticle levitation experiments. We also discuss the case in which the mechanical oscillators are coupled by gravity, and the relation of the quantum-induced noise to gravitational-induced entanglement. Quantum-induced optomechanical fluctuations also hold strong analogy to quantum gravitational wave noise and interconnect stochastic thermodynamics, graviton physics, and the detection of gravity-mediated entanglement.