Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model

Sala, Kamila (2023) Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model. PhD thesis, University of Nottingham.

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This thesis examines the optimal estimation of parameters in a variety of quantum oscillator models, including cavity quantum optomechanics and the quantum van der Pol oscillator. To achieve this, we employ theoretical tools from open quantum systems, quantum estimation theory and Gaussian states. In all cases, we compare the ultimate limits to parameter estimation (quantum Cramer-Rao bounds) to the performance of experimentally feasible observables (e.g. quadrature or number operator measurements).

The majority of the thesis addresses the estimation of the ``linear" and ``quadratic" coupling constants in strongly driven and dissipative optomechanical models, which are well described by bilinear master equations and Gaussian steady states. In this framework, we explore how the estimation precision can be affected by temperature, drive strength, detuning and higher order corrections to the optomechanical Hamiltonian. Through a combination of analytical and numerical methods, we find that temperature is not always detrimental to the estimation precision. We also find that quadrature measurements can perform close to the ultimate bounds in appropriate parameter regimes.

The last chapter focuses instead on estimating the ratio ($\lambda$) between linear amplification and non-linear damping in a quantum van der Pol oscillator. We present both numerical and (approximate) analytical results covering all parameter regimes. In the steady state, we find that the quantum Cramer-Rao bound can in principle be saturated by a measurement of the number operator. We also observe divergent behaviour of the quantum Fisher information (which implies a vanishing quantum Cramer-Rao bound) for $\lambda\to0$. The origin and interpretation of such singular behaviour is left as an investigation for future work.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Tufarelli, Tommaso
Armour, Andrew
Adesso, Gerardo
Keywords: Quantum optomechanics, open quantum systems, quantum estimation theory, Gaussian states
Subjects: Q Science > QA Mathematics > QA273 Probabilities
Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 72093
Depositing User: Sala, Kamila
Date Deposited: 31 Aug 2023 08:27
Last Modified: 31 Aug 2023 08:27
URI: https://eprints.nottingham.ac.uk/id/eprint/72093

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