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.

Business model evolution and firm performance of entrepreneurial companies

This research explores the business model (BM) evolution process of entrepreneurial companies and investigates the relationship between BM evolution and firm performance. Recently, it has been increasingly recognised that the innovative design (and re-design) of BMs is crucial to the performance of entrepreneurial firms, as BM can be associated with superior value creation and competitive advantage. However, there has been limited theoretical and empirical evidence in relation to the micro-mechanisms behind the BM evolution process and the entrepreneurial outcomes of BM evolution. This research seeks to fill this gap by opening up the ‘black box’ of the BM evolution process, exploring the micro-patterns that facilitate the continuous shaping, changing, and renewing of BMs and examining how BM evolutions create and capture value in a dynamic manner. Drawing together the BM and strategic entrepreneurship literature, this research seeks to understand: (1) how and why companies introduce BM innovations and imitations; (2) how BM innovations and imitations interplay as patterns in the BM evolution process; and (3) how BM evolution patterns affect firm performances. This research adopts a longitudinal multiple case study design that focuses on the emerging phenomenon of BM evolution. Twelve entrepreneurial firms in the Chinese Online Group Buying (OGB) industry were selected for their continuous and intensive developments of BMs and their varying success rates in this highly competitive market. Two rounds of data collection were carried out between 2013 and 2014, which generates 31 interviews with founders/co-founders and in total 5,034 pages of data. Following a three-stage research framework, the data analysis begins by mapping the BM evolution process of the twelve companies and classifying the changes in the BMs into innovations and imitations. The second stage focuses down to the BM level, which addresses the BM evolution as a dynamic process by exploring how BM innovations and imitations unfold and interplay over time. The final stage focuses on the firm level, providing theoretical explanations as to the effects of BM evolution patterns on firm performance. This research provides new insights into the nature of BM evolution by elaborating on the missing link between BM dynamics and firm performance. The findings identify four patterns of BM evolution that have different effects on a firm’s short- and long-term performance. This research contributes to the BM literature by presenting what the BM evolution process actually looks like. Moreover, it takes a step towards the process theory of the interplay between BM innovations and imitations, which addresses the role of companies’ actions, and more importantly, reactions to the competitors. Insights are also given into how entrepreneurial companies achieve and sustain value creation and capture by successfully combining the BM evolution patterns. Finally, the findings on BM evolution contributes to the strategic entrepreneurship literature by increasing the understanding of how companies compete in a more dynamic and complex environment. It reveals that, the achievement of superior firm performance is more than a simple question of whether to innovate or imitate, but rather an integration of innovation and imitation strategies over time. This study concludes with a discussion of the findings and their implications for theory and practice.