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We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then, we consider stationary force sensing and study the necessary conditions to minimise the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields, however, the force noise power spectral density cannot be reduced below the level of thermal fluctuations. Therefore, we consider a nonstationary protocol that involves non-thermal dissipative state preparation followed by a finite time measurement, which allows one to perform measurements with a signal-to-noise much greater than the maximum possible in a stationary measurement scenario. We analyse two different measurement schemes in the nonstationary transient regime, a back-action evading measurement, which implies modifying the drive asymmetry configuration upon arrival of the force, and a nonstationary measurement that leaves the drive asymmetry configuration unchanged. Conditions for optimal force noise sensitivity are determined, and the corresponding force noise power spectral densities are calculated.
We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon
State-of-the-art sensors of force, motion and magnetic fields have reached the sensitivity where the quantum noise of the meter is significant or even dominant. In particular, the sensitivity of the best optomechanical devices has reached the Standar
Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces. Here we give a theoretical study of a hybrid atom-optomechanical system in which the steady-state squeezin
The emergence of parity-time ($mathcal{PT}$) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum $mathcal{PT}$-symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin n
We investigate the squeezed regions in the phase plane for non-dissipative dynamical systems controlled by SU(1,1) Lie algebra. We analyze such study for the two SU(1,1) generalized coherent states, namely, the Perelomov coherent state (PCS) and the Barut-Girardello Coherent state (BGCS).