Differential conductance of a ballistic quantum wire in the presence of Rashba spin-orbit and Zeeman interactions : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Theoretical Condensed Matter Physics at Massey University

This thesis calculates the theoretical differential conductance of a ballistic quantum wire semiconductor nanostructure in the presence of Rashba spin-orbit and Zeeman interactions. In semiconductor heterostructures the Rashba spin-orbit interaction arises due to structure inversion asymmetry and couples the spin of the electron to its orbital momentum. In our work Zeeman interaction is induced by application of external magnetic fields in directions transverse, parallel, and perpendicular to the wire axis. Differential conductance is defined as the rate of change of current with respect to a voltage which is applied between two contacts, one on the left (source) and the other on the right (drain) side of the nanostructure. The dispersion relations of the wire are obtained and from these differential conductance is calculated. Differential conductance is presented for zero and strong spin-orbit interaction situations and for magnetic fields applied in the various directions. The wire is studied under two specific regimes, namely normal and full Rashba mediated by the Rashba spin-orbit Hamiltonian. In the normal Rashba regime the wire is modelled without Rashba intersubband coupling while the full Rashba model includes this coupling. Spin-orbit interaction and the direction of applied magnetic field significantly modifies dispersions and have drastic effects on the differential conductance profile. The application of magnetic field in directions parallel (and perpendicular) to the wire in the normal regime in the strong Rashba limit results in the formation of energy gaps. The presence of these gaps drastically reduces conductance. These gaps are suppressed in the full Rashba model of the wire in the strong Rashba limit and therefore reduction in conductance is not observed in the parallel and perpendicular field directions. In the normal Rashba regime in the strong Rashba limit conductance is enhanced for a greater range of source-drian bias voltages at low fields, especially for fields applied in the parallel (and perpendicular) directions. Whereas, in the full Rashba regime in the strong Rashba limit conductance is enhanced up to mid range fields and voltages for all field directions. In both Rashba regimes in the strong Rashba limit the overall conductance is reduced at low fields and voltages for all field directions. Hence, it is concluded that weak Zeeman and weak spin-orbit effects at low bias voltages favours electron transmission in ballistic quantum wires

Ultra-low vibration pulse-tube cryocooler stabilized cryogenic sapphire oscillator with 10^-16 fractional frequency stability

A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the world's most stable microwave oscillator employing a cryocooler. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is sigma_y = 1 x 10^-15 tau^-1/2 for integration times 1 < tau < 10 s with a minimum sigma_y = 3.9 x 10^-16 at tau = 20 s. The long term frequency drift is less than 5 x 10^-14/day. From the measured power spectral density of phase fluctuations the single side band phase noise can be represented by L_phi(f) = 10^-14.0/f^4+10^-11.6/f^3+10^-10.0/f^2+10^-10.2/f+ 10^-11.0 for Fourier frequencies 10^-3<f<10^3 Hz in the single oscillator. As a result L_phi approx -97.5 dBc/Hz at 1 Hz offset from the carrier.Comment: 8 pages, 10 figures, presented at European Frequency and Time Forum, ESTEC, Noordwijk, Netherland, April 11-16th 2010 accepted in IEEE Trans. on Micro. Theory & Technique

Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators with 1 x 10^-16 frequency instability

Two nominally identical ultra-stable cryogenic microwave oscillators are compared. Each incorporates a dielectric-sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a low-vibration pulse-tube cryocooler. The phase noise for a single oscillator is measured at -105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability is characterized in terms of Allan deviation by 5.3 x 10^-16 tau^-1/2 + 9 x 10^-17 for integration times 0.1 s < tau < 1000 s and is limited by a flicker frequency noise floor below 1 x 10^-16. This result is better than any other microwave source even those generated from an optical comb phase-locked to a room temperature ultra-stable optical cavity.Comment: 4 pages, 5 figure

Cryogenic Sapphire Oscillator using a low-vibration design pulse-tube cryocooler: First results

A Cryogenic Sapphire Oscillator has been implemented at 11.2 GHz using a low-vibration design pulse-tube cryocooler. Compared with a state-of-the-art liquid helium cooled CSO in the same laboratory, the square root Allan variance of their combined fractional frequency instability is $\sigma_y = 1.4 \times 10^{-15}\tau^{-1/2}$ for integration times $1 < \tau < 10$ s, dominated by white frequency noise. The minimum $\sigma_y = 5.3 \times 10^{-16}$ for the two oscillators was reached at $\tau = 20$ s. Assuming equal contributions from both CSOs, the single oscillator phase noise $S_{\phi} \approx -96 \; dB \; rad^2/Hz$ at 1 Hz offset from the carrier.Comment: 5 pages, 5 figures, accepted in IEEE Trans on Ultrasonics, Ferroelectrics and Frequency Contro

Hyperparametric effects in a whispering-gallery mode rutile dielectric resonator at liquid helium temperatures

We report the first observation of low power drive level sensitivity, hyperparametric amplification, and single-mode hyperparametric oscillations in a dielectric rutile whispering-gallery mode resonator at 4.2 K. The latter gives rise to a comb of sidebands at 19.756 GHz. Whereas, most frequency combs in the literature have been observed in optical systems using an ensemble of equally spaced modes in microresonators or fibers, the present work represents generation of a frequency comb using only a single-mode. The experimental observations are explained by an additional 1/2 degree-of-freedom originating from an intrinsic material nonlinearity at optical frequencies, which affects the microwave properties due to the extremely low loss of rutile. Using a model based on lumped circuits, we demonstrate that the resonance between the photonic and material 1/2 degree-of-freedom, is responsible for the hyperparametric energy transfer in the system.Comment: 9 pages, 10 figure

Automated Multi-Disciplinary Optimization (MDO) Process Development and Application on Vehicle Program

This paper presents a highly automated process for Multi-Disciplinary Optimization (MDO) of a vehicle program to achieve weight reduction while balancing the performance for Crash, Body NVH, Full vehicle NVH and Durability attributes. The Full vehicle automated MDO process development resulted in tools and techniques that provided a significant time reduction compared to the conventional process resulting in a 8 week execution time. The activity of an automated process development was based on the foundation of scalability and modularity. The focus was to create an automated process that could cut down the amount of resources that need to be engaged on full-time basis for executing an MDO project. The emphasis was to capitalize on the existing technologies for both software and hardware, to enhance the technology as needed and to integrate different tools to fully automate the Ford MDO process. This process was developed to be highly scalable by maintaining the modularity of the software tools and enable seamless integration into Ford&apos;s Product Development Process. In order to test the efficacy of this automated process and to fine tune its requirements, the MDO process was implemented on a production vehicle program. This process relied on CAE models to cut down significant time as it is always easier to incorporate changes at CAE level as compared to CAD. The disciplines identified were Vehicle NVH, Body NVH, Safety and Durability. The decision was made to address only the structural needs of the vehicle and not consider the airflow etc. As a first step, the CAE models from these attributes were unified and synchronized using DEP&apos;s Meshworks. Critical shapes and sections at A, B, C, &amp; D pillars, roof header and rocker, weld pitch at key locations and 60 BIW component gages were included as parameters and applied directly on the crash model. These parameters were then automatically transposed on to the NVH and Durability models. A DOE matrix spanning the design space defined by the ranges of the design variables was created using the &apos;Optimal Latin Hypercube&apos; technique in Isight. The DOE matrix was used to automatically generate designs using DEP&apos;s Meshworks. The generated designs were evaluated using the High Performance Computing (HPC) facility at FORD. The load cases evaluated included NCAP, LINCAP, IIHS, ROOF, Bending/Torsion Stiffness, Modal Evaluation, Dynamic Stiffness, NTF and VTF, Idle and Rough road load cases using LS-DYNA, NASTRAN as primary solvers along with some FORD&apos;s proprietary codes. Output responses were extracted automatically to generate an Input/Output table. Isight was used to create a Response Surface Model (RSM) fitting all the responses and several optimization scenarios were carried out using the RSM to arrive at a few optimal solutions. The automated MDO process enabled faster turn around to identify optimal designs which resulted in weight reduction while maintaining Crash, Body NVH, and Vehicle NVH performance targets

Adapting a Cryogenic Sapphire Oscillator for Very Long Baseline Interferometry

Extension of very long baseline interferometry (VLBI) to observing wavelengths shorter than 1.3mm provides exceptional angular resolution (~20 micro arcsec) and access to new spectral regimes for the study of astrophysical phenomena. To maintain phase coherence across a global VLBI array at these wavelengths requires that ultrastable frequency references be used for the heterodyne receivers at all participating telescopes. Hydrogen masers have traditionally been used as VLBI references, but atmospheric turbulence typically limits (sub) millimeter VLBI coherence times to ~1-30 s. Cryogenic Sapphire Oscillators (CSO) have better stability than Hydrogen masers on these time scale and are potential alternatives to masers as VLBI references. Here, We describe the design, implementation and tests of a system to produce a 10 MHz VLBI frequency standard from the microwave (11.2 GHz) output of a CSO. To improve long-term stability of the new reference, the CSO was locked to the timing signal from the Global Positioning System satellites and corrected for the oscillator aging. The long-term performance of the CSO was measured by comparison against a hydrogen maser in the same laboratory. The superb short-term performance, along with the improved long-term performance achieved by conditioning, makes the CSO a suitable reference for VLBI at wavelengths less than 1.3mm.Comment: 24 pages, 15 figure