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.

Interaction techniques with novel multimodal feedback for addressing gesture-sensing systems

Users need to be able to address in-air gesture systems, which means finding where to perform gestures and how to direct them towards the intended system. This is necessary for input to be sensed correctly and without unintentionally affecting other systems. This thesis investigates novel interaction techniques which allow users to address gesture systems properly, helping them find where and how to gesture. It also investigates audio, tactile and interactive light displays for multimodal gesture feedback; these can be used by gesture systems with limited output capabilities (like mobile phones and small household controls), allowing the interaction techniques to be used by a variety of device types. It investigates tactile and interactive light displays in greater detail, as these are not as well understood as audio displays. Experiments 1 and 2 explored tactile feedback for gesture systems, comparing an ultrasound haptic display to wearable tactile displays at different body locations and investigating feedback designs. These experiments found that tactile feedback improves the user experience of gesturing by reassuring users that their movements are being sensed. Experiment 3 investigated interactive light displays for gesture systems, finding this novel display type effective for giving feedback and presenting information. It also found that interactive light feedback is enhanced by audio and tactile feedback. These feedback modalities were then used alongside audio feedback in two interaction techniques for addressing gesture systems: sensor strength feedback and rhythmic gestures. Sensor strength feedback is multimodal feedback that tells users how well they can be sensed, encouraging them to find where to gesture through active exploration. Experiment 4 found that they can do this with 51mm accuracy, with combinations of audio and interactive light feedback leading to the best performance. Rhythmic gestures are continuously repeated gesture movements which can be used to direct input. Experiment 5 investigated the usability of this technique, finding that users can match rhythmic gestures well and with ease. Finally, these interaction techniques were combined, resulting in a new single interaction for addressing gesture systems. Using this interaction, users could direct their input with rhythmic gestures while using the sensor strength feedback to find a good location for addressing the system. Experiment 6 studied the effectiveness and usability of this technique, as well as the design space for combining the two types of feedback. It found that this interaction was successful, with users matching 99.9% of rhythmic gestures, with 80mm accuracy from target points. The findings show that gesture systems could successfully use this interaction technique to allow users to address them. Novel design recommendations for using rhythmic gestures and sensor strength feedback were created, informed by the experiment findings.