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.

Graphic satire and the rise and fall of the First British Empire: political prints from the Seven Years' War to the Treaty of Paris, c. 1756-1783

This thesis examines the early stages of the transformation of emblematic political prints into political caricature from the beginning of the Seven Years' War (1756) to the Treaty of Paris, which ended the American Revolutionary War (1783). Both contextual and iconographical issues are investigated in relation to the debates occasioned by Britain's imperial project, which marked a period of dramatic expansion during the Seven Years' War, and ended with the loss of the American colonies, consequently framing this thesis as a study of political prints during the rise and fall of the so-called 'First British Empire'. Previous studies of eighteenth-century political prints have largely ignored the complex and lengthy evolutionary process by which the emblematic mode amalgamated with caricatural representation, and have consequently concluded that political prints excluded emblems entirely by the end of the 1770s. However, this study emphasizes the significance of the Wilkite movement for the promotion and preservation of emblems, and investigates how pictorial political argument was perceived and received in eighteenth-century British society, arguing that wider tastes and opinions regarding the utilization of political prints gradually shifted to accept both modes of representation. Moreover, the marketplace, legal status, topicality, and manufacturing methods of political prints are analyzed in terms of understanding the precarious nature of their consumption and those that endeavoured to engage in political printmaking. The evolution, establishment, and subsequent appropriation of pictorial tropes is discussed from the early modern period to the beginning of the so-called Golden Age of caricature, while tracing the adaptation of representational models in American colonial prints that employed emblems already entrenched in British pictorial political debate. Political prints from the two largest print collections, the British Museum and the Lewis Walpole Library at Yale are consulted, along with a number of eighteenth-century newspapers and periodicals, to develop the earlier research by M. Dorothy George, Charles Press, Herbert Atherton, Diana Donald, Amelia Rauser, and Eirwen Nicholson.

Evangelical young women, contemporary Christianity, and an empowering self- understanding: a study into how contemporary women of faith understand themselves and God in relation to Dei, Holy Scripture and Christian mission

This thesis combines historical reflection with qualitative research to examine how Christian young women from Evangelical traditions are developing religious self- understanding in empowering ways. It seeks to establish connections between the ways in which historians and feminist theologians have responded to forces of restriction and limitation in Christian women’s past, and the strategies of self-empowerment adopted by Evangelical young women today. This study approaches Christian history and the present condition of female self-understanding through three central questions: How do young women understand themselves in relation to the imago Dei? How do young women understand themselves in relation to the Bible? How do young women understand themselves in relation to Christian mission? The first chapter addresses the ways in which young women are responding to historic denials of woman as the imago Dei and concepts of female inferiority or especial guilt by reclaiming possession of the divine image. The next section discusses how young women are relating to the Bible in empowering ways, both by adopting similar strategies to those utilised throughout Christianity’s past, and through the development of their own patterns of interpretation. Finally, this thesis draws attention to Christian mission as a space of empowerment, examining how young women develop life-enriching knowledge of God and self through involvement with mission. This thesis proposes that as young women continue to develop strategies that enable them to understand themselves and their faith in empowering ways, knowledge of their innate dignity and potential will inspire them — and those who come after them — to witness to God freely and fully in all contexts.