Investigations of Metrology in Optomechanics and Quantum Information Theory

Abstract

We analyse the dynamics of a one-dimensional vertical Fabry-Perot cavity where the upper mirror levitates due to intracavity radiation pressure force, providing a foundation for understanding how levitated cavity schemes may be used as stable metrological platforms. The nonlinear dynamics are solved in the classical regime using a perturbative approach - the first characterisation of the levitated optical spring. This analysis is then applied to a variety of experimental schemes including two-laser cooling, and a detailed investigation of photothermal effects.

Next we consider parameter estimation incorporating prior knowledge from an information-theoretic viewpoint. We introduce a new quantity, the coherence of encoding, which quantifies how much information is lost due to choice of projective measurement basis, and apply this to derive new bounds on the error of an estimator which incorporates prior information. This is then generalised to phase estimation. We show that circular statistics motivates a natural measure of error on the circle, on which we derive new entropic bounds. Finally we discuss how the coherence of encoding may be used to design an adaptive estimative algorithm which maximises the information gained from each measurement.