Physics
http://hdl.handle.net/10523/98
Tue, 28 Apr 2015 02:04:11 GMT2015-04-28T02:04:11ZFrom Disordered Bosons to Dipolar Fermions - Theoretical Studies in Ultracold Atoms
http://hdl.handle.net/10523/5586
From Disordered Bosons to Dipolar Fermions - Theoretical Studies in Ultracold Atoms
2015
Towers, Joseph
We use numerical simulation to study ultracold, quantum degenerate, atomic gases. In the first part of the thesis we study the effects of disorder, introduced via a bichromatic optical lattice, in one and two dimensional systems. We employ the Aubry-Andr\'{e} model and use time-dependent numerical simulations to investigate the disorder dependent transition to strong localisation present in the model. Weak s-wave interactions are added to the model and we observe the interaction between localisation and interaction induced self-trapping. We then add a tilted lattice potential to the model. In the homogeneous model this induces Bloch oscillations. While one might expect that a strong enough force will break the strong localisation or self-trapping, within the bounds of the single-band model, the trapping effect of the Bloch oscillations reinforces both of the other effects leading to increased confinement, albeit lacking the clear single frequency oscillation signature of pure Bloch oscillations.
Along with the two dimensional bichromatic optical lattice we add a term to the Hamiltonian equivalent to that of a uniform external magnetic field on charged particles. Since the experimental realisation of this model would employ neutral atoms, the magnetic field is synthetic, the equivalent effect being produced by an appropriate set of lasers and magnetic fields. We show that in the ballistic regime (weak bichromatic disorder) the system displays positive magnetoresistance. Conversely in the strong localisation regime the system exhibits negative magnetoresistance.
In the latter part of the thesis we use density functional theory to calculate the ground-state density of a harmonically trapped dipolar Fermi gas. We then use these to calculate the lowest energy collective mode oscillation frequencies under the hydrodynamic approximation. We find that increasing the strength of the dipoles has the effect of increasing the mode frequencies. The increase saturates for large dipole strengths. We verify this analytically and show that such is due to the local nature of the two dimensional energy functional and not dependent on the specific equation of state.
We employ an average density approximation to construct an energy functional for the inhomogeneous, 2D degenerate Fermi gas. The ground-state densities for a cylindrically symmetric harmonic trap are compared to the Kohn-Sham results, showing extremely good agreement in the tail region and good agreement with the exact ground-state energy. We then do the same for higher order polynomial traps and obtain improved agreement for higher degree.
Sun, 29 Mar 2015 21:41:16 GMThttp://hdl.handle.net/10523/55862015-03-29T21:41:16ZImplementation and Applications of the Stochastic Projected Gross-Pitaevskii Equation
http://hdl.handle.net/10523/5460
Implementation and Applications of the Stochastic Projected Gross-Pitaevskii Equation
2015
Rooney, Samuel James
Providing a complete description of dissipative superfluid dynamics is one of the major challenges of many-body quantum field theory. In this thesis we make a fundamental step towards this goal by implementing the stochastic projected Gross-Pitaevskii equation (SPGPE) in complete form for the first time.
The SPGPE is a high-temperature theory of Bose-Einstein condensate dynamics, providing a classical-field description of a low-energy subspace in contact with a thermal reservoir. The reservoir interaction terms account for dissipation and noise from thermal interactions, and arise from two distinct processes described as number-damping and energy-damping. This work advances previous applications of the SPGPE theory, which have only included number-damping processes, by implementing the energy-damping processes. We describe the properties of the deterministic and noise terms corresponding to the energy-damping process, and develop a novel algorithm to accurately and efficiently evaluate the energy-damping terms in the SPGPE.
We apply the SPGPE to a range of experimentally accessible systems, considering both non-equilibrium and quasi-equilibrium dynamics. We model the experiment of Neely et al. [Phys. Rev. Lett. 111, 235301 (2013)], where stirring of a toroidally trapped Bose-Einstein condensate generates a disordered array of quantum vortices that decay, via thermal dissipation, to form a macroscopic persistent current. We perform numerical simulations of the experiment using the number-damping SPGPE and ab initio determined reservoir parameters. We quantitatively reproduce both the formation time and size of the persistent current, as measured in the experiment.
In the first application of the full SPGPE, we consider the non-equilibrium dynamics of a condensate excited into a large-amplitude breathing mode. We find that in such non-equilibrium regimes, the energy-damping dominates over the number-damping process, leading to qualitatively different system dynamics. In particular, energy damping causes the system to rapidly reach thermal equilibrium without greatly depleting the condensate, showing that energy damping provides a highly coherent dissipation mechanism.
Finally, we apply the SPGPE to the quasi-equilibrium dynamics of single-vortex decay. Energy-damping processes have previously been neglected for this system. SPGPE simulations show that in fact energy-damping has a dominant effect on the lifetime of a single vortex, with lifetimes less than half those predicted by the number-damping SPGPE. In contrast to the breathing mode decay, we observe little qualitative difference between the energy-damping and number-damping descriptions of vortex decay. Our findings show that while energy-damping processes are important to quantitatively describe quasi-equilibrium dynamics, the system behavior may be described by the number-damping SPGPE with a suitably modified dissipation rate.
Thu, 12 Feb 2015 22:06:45 GMThttp://hdl.handle.net/10523/54602015-02-12T22:06:45ZThe onset of Rayleigh and Marangoni interfacial instability and their effects on penetration mass transfer across a moving interface
http://hdl.handle.net/10523/5429
The onset of Rayleigh and Marangoni interfacial instability and their effects on penetration mass transfer across a moving interface
2006
Fahmy, Muthasim
Interfacial convection due to the Rayleigh effect and the Marangoni effect can enhance mass transfer rates between fluids and is of importance to industrial engineering applications such as gas-liquid absorption and desorption.
Many linear analyses of the Rayleigh effect and the Marangoni effect can be found in scientific literature. However, most linear analyses have been based on the assumption that the liquid phase is stagnant. In the present thesis, the effect of Rayleigh and Marangoni instabilities on solute transfer between a gas phase and a liquid phase which are in parallel, cocurrent, laminar, stratified flow between two rigid horizontal plates has been investigated theoretically and experimentally. Model equations that describe the critical parameters for the onset of cellular convection have been derived, which take into account the effect of surface convection, surface diffusion and surface viscosity in the Gibbs adsorption layer. A piece-wise linear approximation to the penetration theory concentration profile and the non-linear velocity profile of Byers and King (1967) have been used in the model. The classical assumption of a frozen concentration profile has not been made. However, the simplifying assumption of a non-deformable interface has been made. An eigenvalue problem has been formulated for the linearised system. The critical parameters (the eigenvalues) have been numerically computed using a variational principle and the Rayleigh-Ritz method, for a variety of operating conditions.
The critical Rayleigh, Marangoni and wave numbers are found to be functions of the ratio of gas velocity to liquid velocity; the ratio of gas diffusivity to liquid diffusivity; the ratio of gas layer thickness to liquid layer thickness; the ratio of liquid viscosity to gas viscosity; the ratio of mean gas velocity to mean liquid velocity; the gas-liquid equilibrium Henry constant and the dimensionless downstream location. The effects of these ratios on the critical parameters have been investigated numerically for the Bénard-Marangoni problem and Rayleigh-Bénard-Marangoni problem, and compared to the linear analysis of Sun and Fahmy (2006) which used the more general nonlinear penetration theory concentration profile. It was found that the piece-wise linear approximation was a useful approximation, predicting the same trends for critical parameters as predicted by the non-linear concentration profile. In particular the linear analysis predicts that the system stability can be either enhanced or suppressed by increasing the surface convection number and the surface viscosity number, depending on where the operation line is on the Ra-Nia plane. The linear stability analysis also showed that the system would first become unstable at the exit end of the gas-liquid contactor.
An experimental setup, which makes some improvements on the system used by Sun et al. (2002), was used to validate some of the predictions of the theoretical analysis. The experimental setup and methods are described in detail. Experimental results for four sets of experiments involving CO₂ absorption into or desorption out of methanol or toluene films, including schlieren images and video are presented. These results confirm the theoretical prediction that instability would start at the exit end of the gas-liquid contactor and travel upstream as the driving concentration difference is increased. Furthermore, the theoretical prediction that an increase in the ratio of the gas velocity to the liquid velocity would increase the stability of the system, has been confirmed experimentally.
By fitting mass transfer enhancement factor versus driving concentration difference data to a correlation of the form proposed by Sun (2006a), a critical concentration difference has been calculated for each set of experiments. It is found that the theoretically predicted critical parameters can be made close to experimentally measured parameters by a suitable estimate of the viscosity number Vi. For tests involving desorption of CO₂ from methanol, the choice of Vi = 0.43 gave a relative error between experiment and linear theory of less than 20%. It was found that a much larger viscosity number would be required to account for the discrepancy between the theory and experiment in the experiment involving absorption of CO₂ into a toluene film.
Tue, 20 Jan 2015 00:58:00 GMThttp://hdl.handle.net/10523/54292015-01-20T00:58:00ZA Radio Interferometer Operating in the GPS L1 Band
http://hdl.handle.net/10523/5121
A Radio Interferometer Operating in the GPS L1 Band
2014
Shaw, Charles Farquhar
The Transient Array Radio Telescope is a wide field synoptic synthesis array operating in the GPS L1 band. It is designed as platform for the development of new algorithms for radio astronomy. This thesis describes the development of this instrument.
Fri, 07 Nov 2014 00:53:15 GMThttp://hdl.handle.net/10523/51212014-11-07T00:53:15ZInvestigation of Monolithic Erbium-Doped Resonators for Application in Cavity Quantum Electrodynamics
http://hdl.handle.net/10523/5114
Investigation of Monolithic Erbium-Doped Resonators for Application in Cavity Quantum Electrodynamics
2014
Hogg, Mark Richard
In this thesis we investigate the potential of erbium ions coupled to crystalline whispering-gallery mode resonators as hardware for quantum information processing. Achieving strong coupling between the erbium ions and the cavity would be a significant breakthrough for multiple quantum computing applications. To this end, we fabricate millimetre-sized resonators made from 0.001% erbium-doped yttrium orthosilicate (Er 3+ :Y 2 SiO 5 ). We show that the mechanical fabrication procedure used in making the resonators does not significantly impact the coherence properties of the erbium dopants.
We find that strong coupling should be achievable using currently available technologies, so long as significant absorption in the Y 2 SiO 5 crystals is not present at the wavelength of the erbium transition.
Wed, 05 Nov 2014 20:01:45 GMThttp://hdl.handle.net/10523/51142014-11-05T20:01:45ZFluctuations in Spin-1 Bose-Einstein Condensates
http://hdl.handle.net/10523/5091
Fluctuations in Spin-1 Bose-Einstein Condensates
2014
Symes, Luke
Ultra-cold spinor Bose gases present rich physics due to the special combination of superfluidity and magnetism in a quantum system. This system was first realized in 1998 by confining a Bose-Einstein condensate in an all-optical trap.
In this thesis, we consider the fluctuations of observable quantities in a spin-1 Bose gas. Understanding how fluctuations arise due to the spin excitations of the condensate is important because it offers an insight into how measurement noise reveals the many-body physics of the system.
To begin, we present the mean-field and Bogoliubov theory of a uniform spin-1 Bose gas subject to a constant magnetic field, describing the condensate and its low-energy collective excitations.
We then develop a formalism to describe the fluctuations in a general density-like observable. We start from the two-point correlation function and cast it in the form of a generalised static structure factor determined by the three Bogoliubov quasiparticle excitation branches. We derive analytic results for the fluctuation amplitudes and the temperature-dependent static structure factors for observables of total density and the three spin densities.
For all four magnetic phases, we analyse the spinor order parameter and quasiparticle spectra while numerically mapping out the fluctuation amplitudes and static structure factors for the total and spin density operators.
We describe the fluctuations in experimental measurements made within finite cells, which is an important step to making meaningful predictions for experiments. We consider cylindrical cells and gaussian cells as two limiting cases. We apply this analysis to an experimentally realisable system of a quasi-2D spinor gas in a harmonic trap, comparing extensive numeric results with analytic limits.
Thu, 30 Oct 2014 02:50:17 GMThttp://hdl.handle.net/10523/50912014-10-30T02:50:17ZA Digital Frequency Source for Movement of Ultracold Atoms by Acousto-Optic Deflection
http://hdl.handle.net/10523/5036
A Digital Frequency Source for Movement of Ultracold Atoms by Acousto-Optic Deflection
2014
McKellar, Thomas
This thesis documents the development of a frequency source based on a field programmable gate array (FPGA) and a direct digital synthesiser (DDS). The source was used to drive the two inputs of a dual-axis acousto-optic deflector (AOD), an integral component in a steerable optical tweezer unit designed for use with ultracold 87Rb and 40K. By synchronously changing the frequencies of the paired inputs to the AOD, an optical beam was able to be moved in two dimensions. The frequency source was used to trap and smoothly move samples of ultracold 87Rb over several millimetres, and by quickly toggling the inputs between multiple pairs of frequencies, multiple clouds were confined and moved in time-averaged potentials. The utility of the FPGA/DDS unit is shown, most notably by simultaneously evaporating four independent clouds through the Bose-Einstein Condensate (BEC) phase transition.
Tue, 14 Oct 2014 20:00:37 GMThttp://hdl.handle.net/10523/50362014-10-14T20:00:37ZTechniques to Determine Quiet Day Curves for Subionospheric VLF Observations
http://hdl.handle.net/10523/5018
Techniques to Determine Quiet Day Curves for Subionospheric VLF Observations
2014
Cresswell-Moorcock, Alyson Kathleen Mary (Kathy)
The ionization rate of the upper atmosphere can be significantly increased by space weather events, examples being solar proton events (SPE), solar flares, and energetic electron precipitation from the radiation belts. An increase in the ionization rate leads to a lowering of the lower edge of the ionospheric D-region. To study the effect of space weather events on our atmosphere it is important 1) to be able to detect the events and also 2) to have some way of determining changes in the height of the D-region. Very low frequency (VLF) radio waves propagate in the waveguide between the surface of the Earth and the lower edge of the ionosphere (D-region). Changes in the height of the D-region lead to changes in the amplitude and phase of the VLF signal received at an antenna. To gain an accurate indication of the size of these changes we need to know what the undisturbed signal, known as a Quiet Day Curve (QDC), would have been if no space weather event had taken place.
High power narrow-band communications transmitters operated by multiple nations provide the VLF radio signals used in this technique. In this study we use VLF radio wave observations from the Antarctic-Arctic Radiation- belt Dynamic Deposition VLF Atmospheric Research Konsortia (AARDDVARK) receivers located at Edmonton, Canada and Scott Base, Antarctica.
The purpose of this study is to develop a technique for the automatic calculation of QDCs for long-period experimental subionospheric VLF data sets. To enable the quantitative evaluation of how well our QDC finding techniques identify the true QDC of a data set, we have created a suite of synthetic data layers with a known QDC and imposed perturbations similar to those seen in real VLF data. We present this evaluation and comparison between the techniques to allow determination of the best QDC finding technique from those developed.
We evaluate two techniques for determining a long-period QDC by algorithm. These are Principal Component Analysis (PCA) and 2-dimensional Discrete Fourier Transforms (DFT). We also evaluate an averaging technique that finds a combined daily curve as a baseline comparison to our techniques. We further evaluate several adjustments to these techniques, endeavouring to improve the resulting QDC. We determine that the best QDC technique for data sets longer than two years is an adjustment to the DFT technique, while, for data sets shorter than two years, the best technique is PCA applied to a smoothed data set.
We judge the success of our adjusted DFT technique from the finding that the typical difference between the QDC and the synthetic data background is 0.13~dB for day and 0.17~dB for night. These values are smaller than typical experimentally observed noise levels. We therefore conclude that this QDC finding technique is successful. The pre-smoothed PCA technique gives a typical difference between the QDC and the synthetic data background of 0.38~dB for day, 0.47~dB for night. We therefore conclude that this QDC finding technique is fairly successful, although not as conclusively as the DFT based technique is.
We then apply our chosen QDC finding techniques, according to the length of the data sets, to the VLF observations. We apply the adjusted DFT technique to our Scott Base data sets, which span 4 years of observations, i.e., 2,103,840 minutes. We find that the QDC finding technique appears to qualitatively extract the QDC from these real data sets. In particular during solar flares, the extraction looks sensible. We provide examples of the difference between the received VLF signal and the QDC for an example day during which 10 solar flares occurred. We apply the pre-smoothed PCA technique to our Edmonton data sets, which span 20 months of usable data, i.e., 915,840 minutes. We find that this technique appears to be working, but have less confidence in its ability to extract perturbations lasting longer than a few hours.
Mon, 06 Oct 2014 00:59:06 GMThttp://hdl.handle.net/10523/50182014-10-06T00:59:06Z