Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model
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. I...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2023
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| Online Access: | https://eprints.nottingham.ac.uk/72093/ |
| _version_ | 1848800714736795648 |
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| author | Sala, Kamila |
| author_facet | Sala, Kamila |
| author_sort | Sala, Kamila |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:55:57Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-72093 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:55:57Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-720932023-08-31T08:27:32Z https://eprints.nottingham.ac.uk/72093/ Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model Sala, Kamila 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. 2023-07-26 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/72093/1/Sala%2C%20Kamila%2014341866%20corrections.pdf Sala, Kamila (2023) Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model. PhD thesis, University of Nottingham. Quantum optomechanics open quantum systems quantum estimation theory Gaussian states |
| spellingShingle | Quantum optomechanics open quantum systems quantum estimation theory Gaussian states Sala, Kamila Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model |
| title | Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model |
| title_full | Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model |
| title_fullStr | Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model |
| title_full_unstemmed | Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model |
| title_short | Quantum Estimation in Driven-Dissipative Optomechanics: Beyond the Linear Model |
| title_sort | quantum estimation in driven-dissipative optomechanics: beyond the linear model |
| topic | Quantum optomechanics open quantum systems quantum estimation theory Gaussian states |
| url | https://eprints.nottingham.ac.uk/72093/ |