The bandwidth of any communication system, classical or quantum, is limited by the number of orthogonal states in which the information can be encoded. Quantum key distribution systems available commercially rely on the two-dimensional polarisation state of photons. Quantum computation has also been largely designed on the basis of qubits. However, a photon is endowed with other degrees of freedom, such as orbital angular momentum (OAM). OAM is an attractive basis to be used for quantum information because it is discrete and theoretically infinite-dimensional. This promises a higher information capacity per photon which can lead to more complex quantum computation protocols and more security and robustness for quantum cryptography. Entanglement of OAM naturally arises from spontaneous parametric down-conversion (SPDC). However, any practical experiment utilising the innately high-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. Only a finite subset of this space is accessible experimentally. Given such a constraint, we show that the number of measured, entangled OAM modes in photon pairs generated by SPDC can be increased by tuning the phase-matching conditions in the SPDC process. We achieve this by tuning the orientation angle of the nonlinear crystal generating the entangled photons.
The bandwidth of any communication system, classical or quantum, is limited by the number of orthogonal states in which the information can be encoded. Quantum key distribution systems available commercially rely on the two-dimensional polarisation state of photons. Quantum computation has also been largely designed on the basis of qubits. However, a photon is endowed with other degrees of freedom, such as orbital angular momentum (OAM). OAM is an attractive basis to be used for quantum information because it is discrete and theoretically infinite-dimensional. This promises a higher information capacity per photon which can lead to more complex quantum computation protocols and more security and robustness for quantum cryptography. Entanglement of OAM naturally arises from spontaneous parametric down-conversion (SPDC). However, any practical experiment utilising the innately high-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. Only a finite subset of this space is accessible experimentally. Given such a constraint, we show that the number of measured, entangled OAM modes in photon pairs generated by SPDC can be increased by tuning the phase-matching conditions in the SPDC process. We achieve this by tuning the orientation angle of the nonlinear crystal generating the entangled photons.
Any practical experiment utilizing the innate D-dimensional entanglement of the orbital angular momentum (OAM) of photons is subject to the generation capacity of the entangled photon source and the modal capacity of the detection system. We report an experimental spontaneous parametric-down-conversion system able to generate and detect tunable high-dimensional OAM entanglement. By tuning the phase matching, we demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20. In terms of quantum mutual information capacity, this is an increase from 3.18 to 4.95 bits/photon. Furthermore, we measure correlations in the conjugate variable, angular position, and obtain concurrence values 0.96 and 0.90. The good entanglement measures in both OAM and angular position bases indicate bipartite, D-dimensional entanglement where D is tunable.
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.
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.
The generation of paired photons entangled in orbital angular momentum (OAM), provides a new degree of freedom that is increasingly being used as a source of quantum states. Elucidation of the OAM spectrum of OAM spectrum of the generated photons is of paramount importance, since quantum information applications require the ability to generate arbitrary entangled states with the appropriate OAM correlations. Here we discuss the OAM spectrum of the photon generated via SPDC in two complementary scenarios. On one hand, we should consider the whole geometry of the nonlinear process, taking into account azimuthal variations of the nonlinear coefficient or the phase matching conditions. On the other hand, all relevant experiments reported to date detect only a small section of the full down-conversion cone. In this scenario, the measured OAM correlations depend of the emission angle of the photons and the strength of the Poynting vector walk-off. We will present experiments in SPDC where this dependence is clearly revealed.
Photon pairs entangled in high-dimensional orbital angular momentum (OAM) degrees of freedom (DOF) have been widely regarded as a possible source for improving the capacity of quantum information processing. The generation of a high-dimensional maximally entangled state in the OAM DOF is therefore much desired. In this work, we demonstrate a simple method to generate a broader and flatter OAM spectrum, i.e., a larger spiral bandwidth (SB), of entangled photon pairs generated through spontaneous parametric down-conversion by modifying the pump beam profile. By investigating both experimentally and theoretically, we find that an exponential pump profile that is roughly the inverse of the mode profiles of the single-mode fibers used for OAM detection will provide a much larger SB compared to a Gaussian-shaped pump.
Introduction Although the orbital angular momentum (OAM) of light is often quantified in terms of ℓℏ per photon, one should recognise that this result can be derived directly from Maxwell's equations and is most certainly not an exclusively quantum property. Following the recognition of optical OAM in 1992 [1], the immediate thrust of experimental work was to observe OAM transfer to microscopic objects. These exciting experiments by Rubinsztein- Dunlop [2, 3] and others established that the predicted angular momentum was truly mechanical, but did not provide insight on OAM at the level of single photons. Laguerre- Gaussian modes were identified as being a natural basis set for describing beams with OAM, where their phase terms describe the helical phasefronts corresponding to an OAM of ℓℏ per photon. The polarisation of light has played an important historical role in the experimental investigation of quantum entanglement, quantum gate operations and quantum cryptography. A potential advantage of OAM is that it resides in a higher-dimensional state space which, as follows from the theory, is infinite-dimensional. One of the experimental challenges is to access a large number of these dimensions. In quantum communication, the most obvious advantage of high n -dimensional systems is the increased bandwidth [4], but qunits also lead to stronger security [5, 6]. An increase in the number of entangled quantum modes has also been shown to improve measures of nonlocality [7], to allow quantum computation with better fault tolerance [8] and to simplify quantum logic structures [9].