Mechanical oscillator thermometry in the nonlinear optomechanical regime

Optomechanical systems are promising platforms for controlled light-matter interactions. They are capableof providing several fundamental and practical novel features when the mechanical oscillator is cooled down tonearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhapsthe most relevant step in the characterization of those systems. In conventional schemes, the cavity is drivenstrongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, wedepart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressureinteraction. To measure the temperature of the mechanical oscillator, initially in a thermal state, we use lightas a probe to coherently interact with it and create an entangled state. We show that the optical probe getsa nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusionprocess. To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinearKerr medium before a homodyne detector. Remarkably, placing the Kerr medium enhances the precision tonearly saturate the ultimate quantum bound given by the quantum Fisher information. Furthermore, it alsosimplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature.