Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Applied evolution: An integrated approach to studying life history traits in response to drug selection

The use of chemical control measures to reduce the impact of parasite and pest species has frequently resulted in the development of resistance. Thus, resistance management has become a key concern in human and veterinary medicine, and in agricultural production. Although it is known that factors such as gene flow between susceptible and resistant populations, drug type, application methods, and costs of resistance can affect the rate of resistance evolution, less is known about the impacts of density-dependent eco-evolutionary processes that could be altered by drug-induced mortality. The overall aim of this thesis was to take an experimental evolution approach to assess how life history traits respond to drug selection, using a free-living dioecious worm (Caenorhabditis remanei) as a model. In Chapter 2, I defined the relationship between C. remanei survival and Ivermectin dose over a range of concentrations, in order to control the intensity of selection used in the selection experiment described in Chapter 4. The dose-response data were also used to appraise curve-fitting methods, using Akaike Information Criterion (AIC) model selection to compare a series of nonlinear models. The type of model fitted to the dose response data had a significant effect on the estimates of LD50 and LD99, suggesting that failure to fit an appropriate model could give misleading estimates of resistance status. In addition, simulated data were used to establish that a potential cost of resistance could be predicted by comparing survival at the upper asymptote of dose-response curves for resistant and susceptible populations, even when differences were as low as 4%. This approach to dose-response modeling ensures that the maximum amount of useful information relating to resistance is gathered in one study. In Chapter 3, I asked how simulations could be used to inform important design choices used in selection experiments. Specifically, I focused on the effects of both within- and between-line variation on estimated power, when detecting small, medium and large effect sizes. Using mixed-effect models on simulated data, I demonstrated that commonly used designs with realistic levels of variation could be underpowered for substantial effect sizes. Thus, use of simulation-based power analysis provides an effective way to avoid under or overpowering a study designs incorporating variation due to random effects. In Chapter 4, I 3 investigated how Ivermectin dosage and changes in population density affect the rate of resistance evolution. I exposed replicate lines of C. remanei to two doses of Ivermectin (high and low) to assess relative survival of lines selected in drug-treated environments compared to untreated controls over 10 generations. Additionally, I maintained lines where mortality was imposed randomly to control for differences in density between drug treatments and to distinguish between the evolutionary consequences of drug treatment versus ecological processes affected by changes in density-dependent feedback. Intriguingly, both drug-selected and random-mortality lines showed an increase in survivorship when challenged with Ivermectin; the magnitude of this increase varied with the intensity of selection and life-history stage. The results suggest that interactions between density-dependent processes and life history may mediate evolved changes in susceptibility to control measures, which could result in misleading conclusions about the evolution of heritable resistance following drug treatment. In Chapter 5, I investigated whether the apparent changes in drug susceptibility found in Chapter 4 were related to evolved changes in life-history of C. remanei populations after selection in drug-treated and random-mortality environments. Rapid passage of lines in the drug-free environment had no effect on the measured life-history traits. In the drug-free environment, adult size and fecundity of drug-selected lines increased compared to the controls but drug selection did not affect lifespan. In the treated environment, drug-selected lines showed increased lifespan and fecundity relative to controls. Adult size of randomly culled lines responded in a similar way to drug-selected lines in the drug-free environment, but no change in fecundity or lifespan was observed in either environment. The results suggest that life histories of nematodes can respond to selection as a result of the application of control measures. Failure to take these responses into account when applying control measures could result in adverse outcomes, such as larger and more fecund parasites, as well as over-estimation of the development of genetically controlled resistance. In conclusion, my thesis shows that there may be a complex relationship between drug selection, density-dependent regulatory processes and life history of populations challenged with control measures. This relationship could have implications for how resistance is monitored and managed if life histories of parasitic species show such eco-evolutionary responses to drug application.