Qvarfort, Sofia; (2020) Quantum metrology with optomechanical systems in the nonlinear regime. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis focuses on the mathematical description and application of nonlinear cavity optomechanical systems. The first part is concerned with solving the dynamics of the standard nonlinear optomechanical Hamiltonian with an additional time-dependent mechanical displacement and single-mode squeezing term. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system, which reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. We derive analytic solutions when possible, and otherwise consider perturbation theory for specific cases. The second part of this thesis applies the solutions of the extended optomechanical Hamiltonian to the study of non-Gaussianity. We compute the non-Gaussian character of an optomechanical state as a function of the parameters in the Hamiltonian, and investigate the interplay between the non-Gaussianity, the strength of the nonlinear coupling and the strength of a single-mode mechanical squeezing term. While we find that the strength and form of the nonlinear coupling strongly impacts the non-Gaussianity, its relationship with the squeezing term is highly complex. The third part of this thesis concerns the use of nonlinear optomechanical systems as quantum sensors. We derive a general expression of the quantum Fisher information given the extended optomechanical Hamiltonian, and demonstrate its applicability through three concrete examples: estimating the strength of a nonlinear light--matter coupling, the strength of a time-modulated mechanical displacement, and the strength of a single-mode mechanical squeezing parameter, all of which are modulated at resonance. In the last Chapter of the thesis, we consider the estimation of a constant gravitational acceleration with an optomechanical system. We derive the fundamental limits to gravity sensing and prove that homodyne detection saturates the quantum Fisher information bound. Our results suggest that optomechanical systems could, in principle, be used as powerful quantum sensors.

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