Mechanical oscillator thermometry in the nonlinear optomechanical regime

TL;DR

This paper introduces a nonlinear optomechanical thermometry method using non-Gaussian interactions and a Kerr medium to achieve high-precision temperature measurements of mechanical oscillators in the nonlinear regime.

Contribution

It proposes a novel thermometry scheme in the nonlinear optomechanical regime employing a Kerr medium to enhance precision and simplify measurement protocols.

Findings

Achieves near-quantum-limited temperature estimation precision.

Enhances measurement robustness with a Kerr medium.

Simplifies thermometry by removing the need for adaptive protocols.

Abstract

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