Optomechanical dual-beam backaction-evading measurement beyond the rotating-wave approximation

Abstract

We present the exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-beam backaction-evasion measurement of a single mechanical oscillator quadrature due to Braginsky, Vorontsov and Thorne beyond the commonly used rotating-wave approximation. We show that counterrotating terms lead to extra sidebands in the optical and mechanical spectra and to a modification of the main peak. Physically, the backaction of the measurement is due to periodic coupling of the mechanical resonator to a light field quadrature that only contains cavity-filtered shot noise. Since this fact is independent of other degrees of freedom the resonator might be coupled to, our solution can be generalized, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction evasion measurements.

10 pages, 3 figures. v2: Title change, minor typos

References in corpus (5)

• Back-action evasion and squeezing of a mechanical resonator using a cavity detector
• Evading quantum mechanics
• Quantum back-action evading measurement of collective mechanical modes
• Observation and interpretation of motional sideband asymmetry in a quantum electro-mechanical device
• Trajectories without quantum uncertainties

Cited by in corpus (4)

• Ultra-precision quantum sensing and measurement based on nonlinear hybrid optomechanical systems containing ultracold atoms or atomic Bose-Einstein condensate
• Unconditional mechanical squeezing via back-action evading measurements and non-optimal feedback control
• Invariant-based pulse design for three-level systems without the rotating-wave approximation
• Quantum noise spectra for periodically-driven cavity optomechanics