Physicshttp://hdl.handle.net/10523/982015-10-05T04:01:17Z2015-10-05T04:01:17ZC-Field Theory of Dynamics in One Dimensional Bose Gases: The Kibble-Zurek Mechanism and Bright Soliton ArrestMcDonald, Robhttp://hdl.handle.net/10523/58712015-09-08T14:02:10Z2015-09-08T03:56:11ZC-Field Theory of Dynamics in One Dimensional Bose Gases: The Kibble-Zurek Mechanism and Bright Soliton Arrest
2015
McDonald, Rob
A grand canonical C-field theory has been previously developed for modelling finite temperature Bose gases, the stochastic projected Gross-Pitaesvkii equation (SPGPE) [1]. Previous investigations have shown quantitative agreement between experiments and the SPGPE, with a fitted growth rate [2,3] or no fitted parameters at all [4]. These and other works [5,6] have used the number-damping SPGPE, a sub-theory of the SPGPE neglecting a scattering process between the coherent and incoherent regions that conserves the particle number of each region, known as energy-damping. The systems in these works were in quasi-equilibirium and as such a growth process, also known as number-damping, is thought to be dominant. Evidence suggests that energy-damping is significant when the system is far from equilibrium [7]; we may also postulate systems where energy-damping is the only allowed process. In this thesis we use the full SPGPE including the energy-damping reservoir interaction in systems where this process plays an important role in the dissipative evolution.
We model quenches of chemical potential across the Bose-Einstein condensation transition in a one dimensional Bose gas confined to a toroid. We use two different models; the full SPGPE and the number-damping SPGPE. The purpose of this is to test the results of our simulations against the predictions of the Kibble-Zurek mechanism (KZM), a theory of defect formation in second order phase transitions. We find that both models give results consistent with KZM, in that various measurable quantities obey a power law with respect to the quench time. The power law exponents are determined by critical exponents, which depend on the universality class of the phase transition. We find the number-damping SPGPE results are consistent with the critical exponents predicted by mean field theory. We are unable to find a universality class with critical exponents consistent with the results of the full theory, and in particular the dynamical critical exponent differs from that predicted by mean field theory.
We also use the SPGPE to simulate the motion of a bright soliton in a one dimensional attractive Bose gas confined to a toroid and in contact with a thermal cloud of a second component. The bright soliton is an analytical solution of the one-dimensional Gross-Pitaevskii equation for an attractive Bose-Einstein condensate, which can propagate in space without changing its functional form. We derive a stochastic differential equation for the soliton velocity, finding that the energy-damping reservoir interaction manifests as an Ornstein-Uhlenbeck process for velocity decay, affording a complete analytic solution for the damping and diffusion rates of the bright soliton. The results of simulating the bright soliton using the SPGPE are compared against the analytic solutions of the velocity stochastic differential equation, including the mean, variance, two-time correlations, and power spectra of the velocity. We find that the numerical and analytical solutions show excellent agreement for all these quantities, validating our procedure for obtaining the velocity equation of motion.
2015-09-08T03:56:11ZCavity Length Control System for the Investigation of Correlation Between two He-Ne Raman LasersMuir, Paulhttp://hdl.handle.net/10523/58302015-08-14T14:02:47Z2015-08-14T00:00:54ZCavity Length Control System for the Investigation of Correlation Between two He-Ne Raman Lasers
2015
Muir, Paul
A cavity length control scheme was developed in order to investigate correlation between the chaotic Raman lasing of two unidirectionally coupled Raman lasers for two Ne Raman lines, 603.0 (2p2 to 1s4) nm and 659.9 nm (2p2 to 1s1). The Raman lasers were standard internal mirror He-Ne lasers and were both pumped externally by 588.2 nm radiation from a single dye laser.
The cavity lengths of each He-Ne Raman laser were monitored via the beat frequencies between the modes in the standard 632.8 nm output and the 632.8 nm modes of a stabilised reference He-Ne laser. A software based PID feedback servomechanism actively controlled the cavity length by varying the current supplied to heating pads wrapped around each cavity, altering the thermal expansion/contraction.
2015-08-14T00:00:54ZSolar Powered Animal Tracking Tags with GSM TelemetryButler, Mark Davidhttp://hdl.handle.net/10523/56722015-05-19T22:26:13Z2015-05-19T22:25:05ZSolar Powered Animal Tracking Tags with GSM Telemetry
2015
Butler, Mark David
This thesis describes the development of a solar energy harvesting system for lightweight wildlife tracking tags that use GSM cellular communication for telemetry. An energy harvesting system was designed and implemented in combination with a replacement firmware solution that controls the whole tag at a minimised energy cost. The design was tested both in the lab, and during deployment on Northern Royal Albatross. The solar energy system and firmware significantly improved the tag lifetime allowing effectively indefinite deployment. This solution also allows a greater GPS fix frequency, enabling zoologists to obtain a more detailed understanding of a tagged animals’ behaviour.
2015-05-19T22:25:05ZFrom Disordered Bosons to Dipolar Fermions - Theoretical Studies in Ultracold AtomsTowers, Josephhttp://hdl.handle.net/10523/55862015-04-28T09:46:37Z2015-03-29T21:41:16ZFrom 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.
2015-03-29T21:41:16ZImplementation and Applications of the Stochastic Projected Gross-Pitaevskii EquationRooney, Samuel Jameshttp://hdl.handle.net/10523/54602015-02-12T22:08:10Z2015-02-12T22:06:45ZImplementation 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.
2015-02-12T22:06:45ZThe onset of Rayleigh and Marangoni interfacial instability and their effects on penetration mass transfer across a moving interfaceFahmy, Muthasimhttp://hdl.handle.net/10523/54292015-04-28T09:50:58Z2015-01-20T00:58:00ZThe 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.
2015-01-20T00:58:00ZA Radio Interferometer Operating in the GPS L1 BandShaw, Charles Farquharhttp://hdl.handle.net/10523/51212015-04-28T09:35:05Z2014-11-07T00:53:15ZA 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.
2014-11-07T00:53:15ZInvestigation of Monolithic Erbium-Doped Resonators for Application in Cavity Quantum ElectrodynamicsHogg, Mark Richardhttp://hdl.handle.net/10523/51142015-04-16T21:54:21Z2014-11-05T20:01:45ZInvestigation 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.
2014-11-05T20:01:45Z