Quantum Nanomechanics: State Engineering and Measurement

Matthew Woolley (2010). Quantum Nanomechanics: State Engineering and Measurement PhD Thesis, School of Mathematics & Physics, The University of Queensland.

       
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Author Matthew Woolley
Thesis Title Quantum Nanomechanics: State Engineering and Measurement
School, Centre or Institute School of Mathematics & Physics
Institution The University of Queensland
Publication date 2010-09
Thesis type PhD Thesis
Total pages 208
Total colour pages 35
Total black and white pages 173
Subjects 02 Physical Sciences
Abstract/Summary Recently, there has been a great deal of interest in the study of mechanical systems near the quantum limit. That is, if one treats a macroscopic mechanical resonator as a damped harmonic oscillator, it is natural to ask about the quantum mechanics of such an oscillator. Can one cool the macroscopic mechanical degree of freedom to its quantum ground state, and can one monitor this degree of freedom with a sensitivity approaching the level of its quantum fluctuations? A number of experiments with a wide variety of mechanical system sizes and resonance frequencies have now approached quantum limits. Hence, one may consider the possibility of engineering quantum states of the mechanical mode. Of course, one must also detect such states, and so explicitly address the subtleties of quantum measurement in such systems. These topics are the subject of this thesis. One system that has been studied for the purpose of cooling and measurement of a mechanical resonator is a driven coplanar superconducting microwave cavity with an embedded, capacitively-coupled nanomechanical resonator. The steady-state entanglement between the mechanical mode and the microwave cavity mode, quantified through the logarithmic negativity, was calculated for driving of the cavity on the blue and red sideband of its resonance, detuned by the mechanical resonance frequency. It is shown that the steady-state entanglement persists with experimentally accessible parameters, though its verification is problematic. By adding parametric driving to the nanomechanical resonator, meaning modulation of its effective spring constant, it is possible to generate a squeezed state of the mechanical mode. In the adiabatic limit, where the cavity is effectively slaved to the mechanical mode, and under driving on the blue, red, and blue and red sideband driving of the microwave cavity, the output microwave field spectrum is calculated. The conditions under which one can infer squeezing of the mechanical motion through the observation of squeezing of a component of the output microwave field, are derived. This condition could be satisfied with the red sideband drive, which is compatible with resolved sideband cooling of the mechanical mode. To generate a highly non-classical state such as a Fock state (or number state), a highly nonlinear element must be added to the system. This could be provided by a Cooper pair box configured as a charge qubit. A Cooper pair box may be read-out using a microwave cavity, forming a circuit QED system. If the nanomechanical resonator is also dispersively coupled to the Cooper pair box, then a quantum non-demolition measurement of Fock states of a nanomechanical resonator via feedback control of the coupled circuit QED system is possible. Simulations of the measurement dynamics of such a system are performed. Projection onto Fock states of the nanomechanical resonator, and quantum jumps between these states, are observed. Beyond fundamental quantum mechanical experiments with macroscopic degrees of freedom, nanomechanical resonators may be applied for ultra-sensitive measurement. In the context of quantum metrology, the sensitivity with which some parameter may be estimated scales inversely with the number of quanta available for its measurement; this is known as the Heisenberg limit. In a nonlinear system, super-Heisenberg scalings of the parameter sensitivity are possible. The nonlinear regime is readily accessible in nanomechanical resonators. We consider the mechanical analogue of a nonlinear interferometer, formed by two electrostatically-coupled nanomechanical resonators with a Duffing nonlinearity. It is shown that the super-Heisenberg scaling of the sensitivity with which one can estimate the strain-dependent nonlinearity is achievable, and maintained in the presence of realistic levels of dissipation.
Keyword Quantum optics, quantum states, quantum measurement, nanoelectromechanical systems, cavity optomechanics, nanomechanical resonators, superconducting qubits, circuit QED, nonlinear metrology, quantum parameter estimation.
Additional Notes Colour pages: 26, 27, 29, 36, 40, 62, 67, 70, 71, 73, 78, 79, 81, 83, 85, 87, 90, 103, 104, 110, 123, 126, 127, 134, 135, 137, 144, 145, 146, 150, 159, 163, 164, 167, 168 Recent theses that I have seen have simply printed "UQ PhD Thesis" on the spine. I would prefer to have the title of the thesis and the author on the spine; ie. "Quantum Nanomechanics M. J. Woolley".

 
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Created: Wed, 26 Jan 2011, 23:22:03 EST by Mr Matthew Woolley on behalf of Library - Information Access Service