An important problem in the practical application of high-dimensional two-photon orbital angular momentum (OAM) entanglement generated by spontaneous down conversion is a lower degree of entanglement, where the amplitudes of modes are not uniformly distributed. In contrast to the previously raised entanglement concentration protocol, we here report on an experimental scheme that addresses this problem by tuning the two-photon quantum angular position correlation. An opaque mask with N evenly distributed angular slits having a radius r is inserted in the two-photon down-conversion light path. The number N should be such that the separation of adjacent angular slits is larger than the scale of the two-photon angular position correlation. The OAM entanglement for the two-photon state after the opaque mask is cast into a set of folded subbands with a dimension of N, owing to the reduction of rotational symmetry from continuous invariance to discrete invariance. Almost maximum OAM entanglement can be realized by properly setting the width of the angular slits.
An important problem in the practical application of high-dimensional two-photon orbital angular momentum (OAM) entanglement generated by spontaneous down conversion is a lower degree of entanglement, where the amplitudes of modes are not uniformly distributed. In contrast to the previously raised entanglement concentration protocol, we here report on an experimental scheme that addresses this problem by tuning the two-photon quantum angular position correlation. An opaque mask with N evenly distributed angular slits having a radius r is inserted in the two-photon down-conversion light path. The number N should be such that the separation of adjacent angular slits is larger than the scale of the two-photon angular position correlation. The OAM entanglement for the two-photon state after the opaque mask is cast into a set of folded subbands with a dimension of N, owing to the reduction of rotational symmetry from continuous invariance to discrete invariance. Almost maximum OAM entanglement can be realized by properly setting the width of the angular slits.
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.
We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing N angular slits placed in the path of twin photons define a qudit space of dimension N2, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical results for the Concurrence as a function of the angular aperture size for the case of high-dimensional OAM entanglement and for the case of high-dimensional path entanglement, produced by N × M angular slits. Our results provide additional means for preparation and characterization of entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.
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.
High-dimensional quantum entanglement is an important resource for fundamental research and quantum technological application. Recently, the orbital angular momentum (OAM) of light has received much attention to realize high-dimensional quantum systems, and generating and manipulating the OAM entanglement has become an important topic. Here, we propose an inverse design technique to manipulate the OAM entanglement of the photon pair generated through spontaneous parametric down-conversion. The proposed technique directly tailors the OAM states of entangled photon pairs by shaping the incident pump beam. In particular, we construct a physics-informed model by leveraging the backpropagation algorithm and adhering to the overlap integral relation. Our model automatically optimizes diffractive masks, allowing the structured pump to quantitatively modulate the OAM distribution. The generation of maximally entangled states in different dimensions is demonstrated numerically and experimentally.