Synchronisation of nanomechanical oscillators

Cudmore, Peter (2017). Synchronisation of nanomechanical oscillators PhD Thesis, School of Mathematics and Physics, The University of Queensland. doi:10.14264/uql.2017.462

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Author Cudmore, Peter
Thesis Title Synchronisation of nanomechanical oscillators
School, Centre or Institute School of Mathematics and Physics
Institution The University of Queensland
DOI 10.14264/uql.2017.462
Publication date 2017-03-27
Thesis type PhD Thesis
Supervisor Catherine. A. Holmes
Cecilia González-Tokman
Joseph Grotowski
Total pages 101
Total colour pages 19
Total black and white pages 82
Language eng
Subjects 0102 Applied Mathematics
0101 Pure Mathematics
0104 Statistics
Formatted abstract
Cavity optomechanics is an exciting new quantum technology that involves coupling an optical field to mechanical vibrational modes, and has applications in weak force measurement, quantum computing and the exploration of deep quantum phenomena, such as entanglement. In such systems an external driving force, often a laser, excites an electromagnetic field in a resonant optical cavity containing mechanical elements. Radiation pressure inside the cavity causes mechanical components to oscillate, and these in turn modulate the optical resonances, allowing the exchange of optical and vibrational energy.

There has been recent interest in optomechanical systems consisting of many vibrational components interacting with a single optical field, which have already shown improvements in measurement accuracy, and could potentially lead to new and interesting applications. In this situation, the interaction between optical and mechanical components couples each vibrational mode to the others and allows for the emergence of collective vibrational motion despite natural variations between individual oscillators. This phenomenon is called synchronisation, and has been shown to occur in coupled oscillator systems in biology, chemistry, engineering and physics.

In this thesis we consider the semiclassical dynamics of optomechanical systems described by the standard optomechanical Hamiltonian, with many mechanical vibrational modes, or resonators, with different frequencies. We show that this system has a natural separation of time scales: the fast-time dynamics of the optical component which, is slowly modulated by the mechanical subsystem; and the slow-time behaviour of mechanical subsystem.

The slow-time dynamics of the mechanical system is described by a type of coupled oscillator system that is not well understood; in particular here the oscillators are linear, and the coupling is nonlinear. To better understand this phenomenon, we develop a theory of synchronisation for linear oscillators with nonlinear all-to-all coupling, showing the existence and stability of synchronised states. We show that the conditions for synchronisation can be expressed in terms of coupling strength and frequency heterogeneity. This is in agreement with findings in previously studied models of synchronisation.

Applying our theory to recent optomechanical experiments in the resolved sideband regime, we produce estimates on experimental parameters above which synchronisation should occur. In a related scenario, we show how our results can be used to construct a bi-stable latch that is robust to variations in natural frequency.

Finally, we investigate how synchronisation of the mechanical system affects statistical properties of the fast-time optical system. In particular, we show that the optical system is asymptotic to a periodically correlated process, and how time-frequency analysis can aid in the detection of synchronised states.
Keyword Synchronisation
Coupled oscillators
Dynamical systems
Emergent dynamics
Additional Notes Colour Pages: 1, 25, 32, 33, 48, 50, 54, 59, 62, 63, 65, 69, 70, 73, 75, 76, 90-92

Document type: Thesis
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UQ Theses (RHD) - Open Access
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Created: Sun, 19 Mar 2017, 10:25:34 EST by Peter Cudmore on behalf of Learning and Research Services (UQ Library)