Quantum Mechatronics

Charles Meaney (2011). Quantum Mechatronics PhD Thesis, School of Mathematics and Physics, The University of Queensland.

       
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Author Charles Meaney
Thesis Title Quantum Mechatronics
School, Centre or Institute School of Mathematics and Physics
Institution The University of Queensland
Publication date 2011-07
Thesis type PhD Thesis
Supervisor Prof Gerard Milburn
Prof Ross McKenzie
Total pages 164
Total colour pages 46
Total black and white pages 118
Language eng
Subjects 100704 Nanoelectromechanical Systems
020404 Electronic and Magnetic Properties of Condensed Matter; Superconductivity
020604 Quantum Optics
Abstract/Summary This thesis studies and finds correspondences between the steady state and entanglement present in the quantum description of a dissipative nonlinear system, and the bifurcations of attractors in the steady state of the corresponding semi-classical model. The stable steady states of the semi-classical models include fixed points, single limit cycles, and multi-stability with many stable limit cycles. We show quantum signatures of bifurcations of these semi-classical steady states in the full quantum dissipative systems. Furthermore, we show that these quantum systems are realisable experimentally as nano-electromechanical devices. Recent progress in the fields of circuit quantum electrodynamics (circuit QED) and nano-mechanics means that their fabrication is possible. This thesis introduces the necessary mathematical and physical tools in Chapter 2, and introduces the experimental contexts of circuit QED and nano-mechanics in Chapter 3. The following chapters then study various nano-electromechanical devices. In Chapter 4, we consider a quarter wave coplanar microwave cavity terminated to ground via a superconducting quantum interference device. By modulating the flux through the loop, the cavity frequency is modulated. The flux is varied at twice the cavity frequency implementing a parametric driving of the cavity field. The cavity field also exhibits a large effective nonlinear susceptibility modelled as an effective Kerr nonlinearity, and is also driven by a detuned linear drive. We show that the semi-classical model corresponding to this system exhibits a fixed point bifurcation at a particular threshold of parametric pumping power. We show the quantum signature of this bifurcation in the dissipative quantum system. We further linearise about the below threshold classical steady state and consider it to act as a bifurcation amplifier, calculating gain and noise spectra for the corresponding small signal regime. Furthermore, we use a phase space technique to analytically solve for the exact quantum steady state. We use this solution to calculate the exact small signal gain of the amplifier. In Chapter 5, we consider the steady states of a harmonic oscillator coupled so strongly to a two-level system (a qubit) that the rotating wave approximation cannot be made. The Hamiltonian version of this model is known as the ExB Jahn-Teller model. The semi-classical version of this system exhibits a fixed point bifurcation, which in the quantum model leads to a ground state with substantial entanglement between the oscillator and the qubit. We show that the dynamical bifurcation survives in a dissipative quantum description of the system, amidst an even richer bifurcation structure. We propose an experimental implementation of this model based on a superconducting cavity: a superconducting junction in the central conductor of a coplanar waveguide. In Chapter 6, we consider a theoretical model for a nonlinear nano-mechanical resonator coupled to a superconducting microwave resonator. The nano-mechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nano-mechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented. In Chapter 7, using amplitude equations, we describe the classical dynamics of N nano-mechanical resonators inside a single co-planar microwave cavity. The nano-mechanical resonators are not directly coupled to one another, but an effective all-to-all coupling is mediated through their capacitive coupling to a common field mode of the microwave cavity. The coupling of each nano-mechanical resonator shifts the frequency of the cavity field proportional to the displacement of each resonator. We show that groups of identical nano-mechanical oscillators synchronise to form a single mechanical mode which couples to the microwave cavity with a strength dependent on the square sum of the individual mechanical-microwave couplings. Classically this system has a rich local and global bifurcation structure dominated by periodic orbits which, when analysed using amplitude equations, can be shown to exhibit multi-stability. Further we show that if the nano-mechanical oscillators are nonidentical the mechanism by which synchronisation is lost resembles that for large amplitude forcing which is not of the Kuramoto form.
Keyword quantum physics
superconductivity
nano-mechanics
nano-electromechanical systems
dynamical systems
quantum entanglement
bifurcations
nonlinear
semi-classical
Additional Notes Colour pages: 23, 24, 25, 26, 27, 28, 34, 35, 77, 78, 79, 80, 83, 84, 85, 86, 87, 89, 90, 99, 100, 102, 103, 104, 105, 106, 107, 120, 121, 122, 123, 124, 125, 126, 127, 128, 138, 139, 142, 143, 144, 147, 148, 149, 150, 152.

 
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Created: Tue, 08 May 2012, 12:39:30 EST by Mr Charles Meaney on behalf of Library - Information Access Service