Standard Quantum Limit for Probing Mechanical Energy Quantization

TL;DR

This paper establishes a fundamental quantum limit for detecting mechanical energy quantization, highlighting the need for strong coupling and specific system conditions in optomechanical setups.

Contribution

It derives a standard quantum limit for probing mechanical energy quantization in systems with parametric coupling, clarifying conditions for single quantum resolution.

Findings

Strong coupling regime is required to resolve a single mechanical quantum.

Zero-point motion must be comparable to the optical system's linear dynamical range.

The limit depends on the decay rate of external degrees of freedom and the parametric coupling rate.

Abstract

We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a strong-coupling regime -- the decay rate of external degrees of freedom is smaller than the parametric coupling rate. In the case for cavity-assisted optomechanical systems, e.g. the one proposed by Thompson et al., zero-point motion of the mechanical oscillator needs to be comparable to linear dynamical range of the optical system which is characterized by the optical wavelength divided by the cavity finesse.