This thesis is a dissemination of the experimental work I have carried out in the last three and a half years, under supervision of Prof. Miles Padgett and Dr. Sonja Franke-Arnold. Presented within are seven unique experiments investigating the orbital angular momentum (OAM) states of light, and the associated spatial modes. Six of these experiments relate to measurements on quantum-entangled photon pairs produced in down-conversion. The first chapter of my thesis is a brief review of the some of the contributions made to the field of research of OAM, both involving classical and quantum states of light. This chapter introduces some of the hallmark experiments within the subject, from which my experimental work reported in this thesis is inspired. The second chapter details the set up of the down conversion experiment, and the experimental techniques used to design a fully functioning quantum measurement system. Most importantly, this includes the holographic techniques used to measure the spatial states of the photon pairs. In addition to holographic measurements, a system to holographically auto-align the down-conversion experiment was developed. Due to the sensitive nature of the experiments presented, this automated system has been crucial to the success of all of the single photon experiments presented within this document. The experimental results are split into three separate categories. The first (Chapter 3) describes measurements investigating the Fourier relationship between OAM and angular position states, both at the classical and quantum levels. The following chapter (Chapter 4) consists of four experiments designed to quantify the degree of entanglement of states of OAM and angular position. This includes the first demonstration of the historic EPR (Einstein-Podolsky-Rosen) paradox for OAM and angle states, violation of a Bell-type inequality for arbitrary OAM states, and characterisation of the density matrices for a range of OAM state-spaces. The final chapter (Chapter 5) reports a new type of ghost imaging using down-converted photon pairs. In this experiment, we violate a Bell inequality within a ghost image, demonstrating the entangled nature of our system and contributing a new element to the long standing contention over quantum vs. classical features within ghost imaging. These experiments have seen a wide range of collaboration. The experimental work on the Fourier relation on single photons was carried out in collaboration with Dr. Anand Kumar Jha (University of Rochester). The work on ghost imaging was performed with collaboration with Prof. Monika Ritsch-Marte (Innsbruck Medical University), and the angular EPR paradox work was carried out in collaboration with Prof. Robert Boyd (Univ. of Rochester) and Prof. David Ireland (Univ. of Glasgow). The work I present here is experimental, however any theoretical developments are in a large part due to the support of Dr. Sonja Franke-Arnold and Prof. Steve Barnett (Univ. of Strathclyde).
This thesis is a dissemination of the experimental work I have carried out in the last three and a half years, under supervision of Prof. Miles Padgett and Dr. Sonja Franke-Arnold. Presented within are seven unique experiments investigating the orbital angular momentum (OAM) states of light, and the associated spatial modes. Six of these experiments relate to measurements on quantum-entangled photon pairs produced in down-conversion. The first chapter of my thesis is a brief review of the some of the contributions made to the field of research of OAM, both involving classical and quantum states of light. This chapter introduces some of the hallmark experiments within the subject, from which my experimental work reported in this thesis is inspired. The second chapter details the set up of the down conversion experiment, and the experimental techniques used to design a fully functioning quantum measurement system. Most importantly, this includes the holographic techniques used to measure the spatial states of the photon pairs. In addition to holographic measurements, a system to holographically auto-align the down-conversion experiment was developed. Due to the sensitive nature of the experiments presented, this automated system has been crucial to the success of all of the single photon experiments presented within this document. The experimental results are split into three separate categories. The first (Chapter 3) describes measurements investigating the Fourier relationship between OAM and angular position states, both at the classical and quantum levels. The following chapter (Chapter 4) consists of four experiments designed to quantify the degree of entanglement of states of OAM and angular position. This includes the first demonstration of the historic EPR (Einstein-Podolsky-Rosen) paradox for OAM and angle states, violation of a Bell-type inequality for arbitrary OAM states, and characterisation of the density matrices for a range of OAM state-spaces. The final chapter (Chapter 5) reports a new type of ghost imaging using down-converted photon pairs. In this experiment, we violate a Bell inequality within a ghost image, demonstrating the entangled nature of our system and contributing a new element to the long standing contention over quantum vs. classical features within ghost imaging. These experiments have seen a wide range of collaboration. The experimental work on the Fourier relation on single photons was carried out in collaboration with Dr. Anand Kumar Jha (University of Rochester). The work on ghost imaging was performed with collaboration with Prof. Monika Ritsch-Marte (Innsbruck Medical University), and the angular EPR paradox work was carried out in collaboration with Prof. Robert Boyd (Univ. of Rochester) and Prof. David Ireland (Univ. of Glasgow). The work I present here is experimental, however any theoretical developments are in a large part due to the support of Dr. Sonja Franke-Arnold and Prof. Steve Barnett (Univ. of Strathclyde).
Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
Entanglement in higher dimensions is an attractive concept that is a chal- lenge to realise experimentally. To this end, the entanglement of the orbital angular momentum (OAM) of photons holds promise. The OAM state-space is discrete and theoretically unbounded. In the work that follows, we investi- gate various aspects of OAM entanglement. We show how the correlations in OAM and its conjugate variable, angular position, are determined by phase- matching and the shape of the pump beam in spontaneous parametric down- conversion. We implement tests of quantum mechanics which have been previously done for other variables. We show the Einstein-Podolsky-Rosen paradox for OAM and angle, supporting the incompatibility of quantum me- chanics with locality and realism. We demonstrate violations of Bell-type inequalities, thereby discounting local hidden variables for describing the correlations we observe. We show the Hardy paradox using OAM, again highlighting the nonlocal nature of quantum mechanics. We demonstrate violations of Leggett-type inequalities, thereby discounting nonlocal hidden variables for describing correlations. Lastly, we have looked into the entan- glement of topological vortex structures formed from a special superposition of OAM modes and show violations of Bell-type inequalities confined to a finite, isolated volume.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated
The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly 25 years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here, we explain the intuition that led to the first quantum experiment with OAM 15 years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps to applying these properties in novel quantum protocols. At the end, we identify several interesting open questions that could form the subject of future investigations with OAM.This article is part of the themed issue 'Optical orbital angular momentum'.
This dissertation deals with theoretical and experimental research on nonclassical, or entangled, states of atoms and photons. In the first part, I describe two approaches to the preparation of entangled states of a large number of atoms. The first approach is based on the transfer of quantum correlations from non-classical light to the atomic spins. I consider three different situations: (a) the atoms are placed in a loss-free cavity and no relaxation of any kind is present; (b) the atoms are placed in a cavity with input and output for the electromagnetic field and the atoms spontaneously decay from the upper state; (c) there is no cavity around the atoms and spontaneous emission is present. I show that in all three situations with judicious choice of parameters, entangled samples of atoms can be produced. The second approach is based on quantum-nondemolition (QND) measurements of collective atomic operators. I describe experiments with pulsed and cw light as the probe, that result in squeezed spin states of atoms. When a rf magnetic field is applied to the atomic sample, sub- shot noise performance of an atomic spin interferometer is demonstrated. In the second part of the thesis I describe investigations of phase properties of two-photon and single-photon states. These experiments make use of spontaneous type-II down-conversion in a nonlinear crystal. First, interferometric measurement of a phase shift at the Heisenberg limit for a two-photon state is described. Next, a violation of Bell-type inequalities in phase space is demonstrated for the quantum optical version of the Einstein-Podolsky-Rosen state. Finally, some recent work directed toward homodyning a single photon against a strong local oscillator field is described.