Abstract
We exploit local quantum estimation theory to investigate the measurement of linear and quadratic coupling strengths in a driven-dissipative optomechanical system. For experimentally realistic values of the model parameters, we find that the linear coupling strength is considerably easier to estimate than the quadratic one. Our analysis also reveals that the majority of information about these parameters is encoded in the reduced state of the mechanical element, and that the best estimation strategy for both coupling parameters is well approximated by a direct measurement of the mechanical position quadrature. Interestingly, we also show that temperature does not always have a detrimental effect on the estimation precision, and that the effects of temperature are more pronounced in the case of the quadratic coupling parameter.
Highlights
Quantum optomechanics focuses on the interaction between the electromagnetic radiation and motional degrees of freedom of mechanical oscillators [1,2,3]
For parameters inspired by recent experimental works, we find that at low intracavity photon numbers the linear coupling strength is easier to estimate than the quadratic one
A membrane-in-the-middle optomechanical system allows for great flexibility in the choice of both g1 and g2, so that both regimes g1 > g2 and g2 < g1 are in principle possible [2, 32]
Summary
Quantum optomechanics focuses on the interaction between the electromagnetic radiation and motional degrees of freedom of mechanical oscillators [1,2,3]. The simplest optomechanical system consists of a single cavity mode interacting with a single mechanical mode and is realised, for example, in an optical cavity with a movable mirror. In this case the mechanism responsible for the interaction is radiation pressure, which entails momentum exchange between light and matter. The presence of a cavity boosts the otherwise weak radiation pressure force, enhancing the light-matter interaction. The quantum effects of radiation pressure forces and the associated limits they set on the precision of mirrordisplacement measurements are of great importance for many applications including gravitational wave detectors, scanning probe microscopy and force sensing [1,2,3,4]. The step beyond the linear approach is to expand the cavity frequency up to and including second order in Xb, lead-
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