Back action cancellation in resolved sideband regime

TL;DR

This paper analyzes a measurement scheme of a mechanical oscillator using a Fabry-Pérot cavity in the resolved sideband regime, demonstrating back action cancellation in reflected waves but confirming the Standard Quantum Limit remains due to dynamic back action.

Contribution

It shows fluctuation back action cancellation in the reflected wave within the resolved sideband regime, clarifying limitations imposed by dynamic back action.

Findings

Back action cancellation occurs in reflected waves.

Standard Quantum Limit cannot be bypassed due to dynamic back action.

The model applies to detuned laser measurements of mechanical oscillators.

Abstract

We consider the simple model of measurement of mechanical oscillator position via Fabry-Pero cavity pumped by detuned laser (end mirror of cavity is mass of oscillator) in resolved sideband regime when laser is detuned from cavity's frequency by frequency of mechanical oscillator $\pm\omega_m$ and relaxation rate $\gamma$ of cavity is small: $\gamma\ll \omega_m$. We demonstrate fluctuation back action cancellation in reflected wave. However, it does not allow to circumvent Standard Quantum Limit, the reason of it is the dynamic back action.