Quantum Transport and Dynamics of Phonons in Mesoscopic Systems

Citation

Santamore, Deborah Hannah (2003) Quantum Transport and Dynamics of Phonons in Mesoscopic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/E62V-PR26. https://resolver.caltech.edu/CaltechETD:etd-05272003-152136

Abstract

Recent advances in nanotechnology have shrunk the size of mesoscopic structures. This allows us to investigate the quantum mechanics of mechanical oscillators. In this thesis we focus on two aspects.

In Part I, an individual discrete mode structure of an oscillator and its effect to thermal conductance have been thoroughly examined: Specifically, we investigated the reduction in the thermal conductance in the quantum limit due to phonon scattering by surface roughness, first using scalar waves, then using full three dimensional elasticity theory for an elastic beam with a rectangular cross section. At low frequencies, we find power laws for the scattering coefficients that are strongly mode dependent, and different from the results deriving from Rayleigh scattering of scalar waves, that is often assumed. The scattering gives temperature dependent contributions to the reduction in thermal conductance with the same power laws. At higher frequencies, the scattering coefficient becomes large at the onset frequency of each mode due to the flat dispersion. We use our results to attempt a quantitative understanding of the suppression of the thermal conductance from the universal value observed in experiment.

As individual phonon energy becomes comparable to or greater than the thermal energy, the individual phonon dynamics within each mode can be resolved. In Part II, we examine a possibility of detecting individual quanta of a system: We investigate a scheme that makes a quantum non-demolition measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two bending modes of an elastic beam. The non-linear coupling between the two modes shifts the resonant frequency of the readout oscillator proportionate to the excitation of the system oscillator. This frequency shift may be detected as a phase shift of the readout oscillation when driven on resonance. We show that in an appropriate regime this measurement approaches a quantum non-demolition measurement of the phonon number of the system oscillator. As a result it should be possible to monitor jumps between Fock states caused by the coupling of the system to the thermal reservoirs.

Thesis Files