Detection of weak stochastic forces in a parametrically stabilized micro-optomechanical system

Abstract

Measuring a weak force is an important task for micromechanical systems, both when using devices as sensitive detectors and, particularly, in experiments of quantum mechanics. The optimal strategy for resolving a weak stochastic signal force on a huge background (typically given by thermal noise) is a crucial and debated topic, and the stability of the mechanical resonance is a further, related critical issue. We introduce and analyze the parametric control of the optical spring, which allows us to stabilize the resonance and provides a phase reference for the oscillator motion, yet conserving a free evolution in one quadrature of the phase space. We also study quantitatively the characteristics of our micro-optomechanical system as detector of stochastic force for short measurement times (for quick, high-resolution monitoring) as well as for the longer-term observations that optimize the sensitivity. We compare a simple strategy based on the evaluation of the variance of the displacement which is a widely used technique) with an optimal Wiener-Kolmogorov data analysis. We show that, due to the parametric stabilization of the effective susceptibility, we can more efficiently implement Wiener filtering, and we investigate how this strategy improves the performance of our system. We finally demonstrate the possibility to resolve stochastic force variations well below 1% of the thermal noise.

Ultranarrow-linewidth levitated nano-oscillator for testing dissipative wave-function collapse

“…To simplify the notation, we consider only one degree of freedom and denote its resonance frequency with ω o . If γ ω o , the dynamical equations for the slowly varying quadratures are [35]…”

Optomechanical force sensor in a non-Markovian regime

“…On the other hand, the thermal noise from the environment should be reduced because the noise can be coequally amplified with the detecting signal by the system. In the Markovian regime, the two requirements will demand a high mechanical quality factor and low bath temperature [1]. But it is more complex in that the non-Markovian condition, m c w ( )totally depends on the self-energy correction w å ( ), which is a frequency-dependent parameter up to the structure of the bath.…”

“…Optomechaical systems provide us a platform for high precision measurements including ultra-sensitive force detection [1], small quantities of adsorbed mass detection [2] and low-reflectivity object detection [3]. Such systems exploit the huge susceptibility around the resonance frequency of oscillators with excellent mechanical quality factor Q m , combined with high-sensitivity interferometric measurements [1,4].…”

Low-Loss Optomechanical Oscillator for Quantum-Optics Experiments

“…Actually, our previous generation devices allowed us to demonstrate useful physical effects, such as frequency-noise cancellation [21], parametric modulation and stabilization of the optical spring [22], and optimal filtering and detection [23]. However, in spite of the continuous progress [24,25], the system's quality factor is still far from optimal, and they showed residual coupling with the wafer modes, energy leakage through the supporting structure (clamping losses), and performance strongly affected by the supporting system.…”