Beating the standard quantum limit for force sensing with a coupled two-mode optomechanical system

TL;DR

This paper demonstrates that a coupled two-mode optomechanical system can surpass the standard quantum limit in force sensing by utilizing normal mode splitting, strong driving, and near-instability operation, with potential for high squeezing.

Contribution

It introduces a two-mode model for force sensing that can be reduced to an effective single-mode system, enabling surpassing the standard quantum limit through specific driving and detection strategies.

Findings

Optimal sensitivity is achieved near cavity instability.

Sensitivity is limited by thermal noise and optical losses.

High squeezing at DC is possible with high-Q mechanical oscillators.

Abstract

Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force-sensing using a mirror-in-the-middle setup and use two coupled cavity modes originated from normal mode splitting for separating pump and probe fields. We find that this two-mode model can be reduced to an effective single-mode model, if we drive the pump mode strongly and detect the signal from the weak probe mode. The optimal force detection sensitivity at zero frequency (DC) is calculated and we show that one can beat the standard quantum limit by driving the cavity close to instability. The best sensitivity achievable is limited by mechanical thermal noise and by optical losses. We also find that the bandwidth where optimal sensitivity is maintained is proportional to the cavity damping in the resolved sideband regime. Finally, the squeezing spectrum of the output signal is calculated, and it shows almost perfect squeezing at DC is possible by using a high quality factor and low thermal phonon-number mechanical oscillator.