Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit

TLDR

Optomechanics enables the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. The study investigates force sensing in a mirror‑in‑the‑middle optomechanical setup using two coupled cavity modes to separate pump and probe fields. The authors employ two coupled cavity modes arising from normal mode splitting to implement this separation. The two‑mode model reduces to an effective single‑mode model under strong pump drive, allowing dc force sensitivity below the standard quantum limit via squeezing, limited by mechanical thermal noise and optical losses, with bandwidth scaling with cavity damping and near‑perfect dc squeezing achievable using high‑Q, high‑frequency oscillators, and a 99 % homodyne efficiency yielding up to 23 dB squeezing at reduced input power.

Abstract

Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force sensing in a mirror-in-the-middle optomechanical 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. We show that the optimal force sensitivity at zero frequency (dc) beats the standard quantum limit via squeezing and is limited by mechanical thermal noise and optical losses. We also find that the bandwidth is proportional to the cavity damping in the resolved sideband regime. Finally, the squeezing spectrum of the output signal is calculated and it shows that almost perfect squeezing at dc is possible by using a high-quality factor and high-frequency mechanical oscillator. Considering a homodyne measurement efficiency of 99%, the squeezing will be limited to 23 dB, with requires input power ${10}^{\ensuremath{-}2}$ smaller than conventional single-mode optomechanical systems.