Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics

DAWSON, CHRISTOPHER

doi:10.23889/SUthesis.56947

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Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics / CHRISTOPHER DAWSON

Swansea University Author: CHRISTOPHER DAWSON

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DOI (Published version): 10.23889/SUthesis.56947

Abstract

In levitated optomechanics, nano-scale objects are optically trapped so that their motion can be studied. These trapped nanoparticles are held in a 3D quadratic potential and act as damped harmonic oscillators; they are thermally and mechanically decoupled from the apparatus and their position is me...

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Published:	Swansea 2020
Institution:	Swansea University
Degree level:	Doctoral
Degree name:	Ph.D
Supervisor:	Bateman, James E.
URI:	https://cronfa.swan.ac.uk/Record/cronfa56947
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first_indexed	2021-05-24T09:46:28Z
last_indexed	2021-05-25T03:28:06Z
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spelling	2021-05-24T11:52:52.1634530 v2 56947 2021-05-24 Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics cf74d57adc25af60a7fc1a571ee1cb48 CHRISTOPHER DAWSON CHRISTOPHER DAWSON true false 2021-05-24 In levitated optomechanics, nano-scale objects are optically trapped so that their motion can be studied. These trapped nanoparticles are held in a 3D quadratic potential and act as damped harmonic oscillators; they are thermally and mechanically decoupled from the apparatus and their position is measured interfer-ometrically to picometre accuracy. These systems are well suited to sensing and metrology applications, as any external disturbance of the particle can be observed using the scattered trapping light.When examining the motion of a levitated nanoparticle, it’s position is recorded and used to estimate a power spectral density (PSD), from which state parameters can be estimated. In this thesis an experi-mental setup is presented, optimised for maximum collection of particle position information in 1D, using a ﬁbre-based parabolic mirror trap and heterodyne measurement system in order to produce spectra with minimal noise and unwanted artefacts.A novel application of the Middleton expansion from RF engineering is used to generate a complete power spectrum that depends on the physical parameters of the system. This method treats the particle as a stochastic harmonic oscillator, phase modulated by a Gaussian random process with known PSD. We reproduce the PSD of intensity at a detector, a quantity that is sinusoidally dependent on particle posi-tion. This technique generates a single, full PSD using modiﬁed Bessel functions, and does not depend on assumptions about the relative phases of the interfered ﬁelds, highlighting the non-linear dependence of measured signal on position. Theoretical spectra are ﬁtted to a measured PSD and the phase modulation depth is extracted; this is used to calculate the particle oscillation amplitude and, by an equipartition ar-gument, the centre of mass temperature to mass ratio. State parameters are tracked as environmental conditions change and an increase in centre of mass temperature as a function of decreasing background gas pressure is observed. E-Thesis Swansea Optomechanics, Levitated Optomechanics, Fibre optics, Signal Processing, Optics, Photonics, Motion control, Spectral Analysis 1 3 2020 2020-03-01 10.23889/SUthesis.56947 COLLEGE NANME COLLEGE CODE Swansea University Bateman, James E. Doctoral Ph.D College of Science 2021-05-24T11:52:52.1634530 2021-05-24T10:43:07.3407442 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics CHRISTOPHER DAWSON 1 56947__19975__0bd3afe44dc446fcbf2f4d2489c4ae5b.pdf Dawson_Christopher_PhD_Thesis_Final_Redacted_Signature.pdf 2021-05-24T11:49:19.9667543 Output 42015616 application/pdf E-Thesis – open access true Copyright: The author, Christopher Dawson, 2020. true eng
title	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics
spellingShingle	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics CHRISTOPHER DAWSON
title_short	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics
title_full	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics
title_fullStr	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics
title_full_unstemmed	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics
title_sort	Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics
author_id_str_mv	cf74d57adc25af60a7fc1a571ee1cb48
author_id_fullname_str_mv	cf74d57adc25af60a7fc1a571ee1cb48_***_CHRISTOPHER DAWSON
author	CHRISTOPHER DAWSON
author2	CHRISTOPHER DAWSON
format	E-Thesis
publishDate	2020
institution	Swansea University
doi_str_mv	10.23889/SUthesis.56947
college_str	Faculty of Science and Engineering
hierarchytype
hierarchy_top_id	facultyofscienceandengineering
hierarchy_top_title	Faculty of Science and Engineering
hierarchy_parent_id	facultyofscienceandengineering
hierarchy_parent_title	Faculty of Science and Engineering
department_str	School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str	1
active_str	0
description	In levitated optomechanics, nano-scale objects are optically trapped so that their motion can be studied. These trapped nanoparticles are held in a 3D quadratic potential and act as damped harmonic oscillators; they are thermally and mechanically decoupled from the apparatus and their position is measured interfer-ometrically to picometre accuracy. These systems are well suited to sensing and metrology applications, as any external disturbance of the particle can be observed using the scattered trapping light.When examining the motion of a levitated nanoparticle, it’s position is recorded and used to estimate a power spectral density (PSD), from which state parameters can be estimated. In this thesis an experi-mental setup is presented, optimised for maximum collection of particle position information in 1D, using a ﬁbre-based parabolic mirror trap and heterodyne measurement system in order to produce spectra with minimal noise and unwanted artefacts.A novel application of the Middleton expansion from RF engineering is used to generate a complete power spectrum that depends on the physical parameters of the system. This method treats the particle as a stochastic harmonic oscillator, phase modulated by a Gaussian random process with known PSD. We reproduce the PSD of intensity at a detector, a quantity that is sinusoidally dependent on particle posi-tion. This technique generates a single, full PSD using modiﬁed Bessel functions, and does not depend on assumptions about the relative phases of the interfered ﬁelds, highlighting the non-linear dependence of measured signal on position. Theoretical spectra are ﬁtted to a measured PSD and the phase modulation depth is extracted; this is used to calculate the particle oscillation amplitude and, by an equipartition ar-gument, the centre of mass temperature to mass ratio. State parameters are tracked as environmental conditions change and an increase in centre of mass temperature as a function of decreasing background gas pressure is observed.
published_date	2020-03-01T04:12:18Z
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score	11.012678

Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics / CHRISTOPHER DAWSON

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