Spatially incoherent light can result from nonlinear processes where a group of photons are emitted in entangled states of spatial modes, which results in an incoherent mixture of constituting spatial modes when the photons are assessed one by one. In this paper we explore a method which uses a tilted lens to probe the orbital angular momentum (OAM) spectrum of such a mixture. We examine the general case where the photons are in mixtures of both different OAM and radial modes, resulting in a 2-dimensional random distribution that creates a more difficult challenge compared to mixtures of OAM only.
Spatially incoherent light can result from nonlinear processes where a group of photons are emitted in entangled states of spatial modes, which results in an incoherent mixture of constituting spatial modes when the photons are assessed one by one. In this paper we explore a method which uses a tilted lens to probe the orbital angular momentum (OAM) spectrum of such a mixture. We examine the general case where the photons are in mixtures of both different OAM and radial modes, resulting in a 2-dimensional random distribution that creates a more difficult challenge compared to mixtures of OAM only.
The angular profile and the orbital angular momentum of a light mode are related by Fourier transform. Any modification of the angular distribution, e. g. via diffraction off a suitably programmed spatial light modulator, influences the orbital angular momentum spectrum of the light. This holds true even at the single photon level. We observe the influence of various angular masks on the orbital angular momentum spectrum, both in the near and the far field, and describe the resulting patterns in terms of angular diffraction. If photons are entangled in their orbital angular momentum, diffraction of one photon affects the orbital angular momentum spectrum of its partner photon, and angular ghost diffraction can be measured in the coincidence counts. We highlight the role of the angular Fourier relationship for these effects.
The orbital angular momentum of light (OAM) is a fundamental property of light. Beams with OAM have a helical wave front that carries quantized orbital angular momentum L hbar per photon, where L is any integer. This unbounded Hilbert space can increase information capacity of both classical and quantum communications and also improve and extend qubit and qudit quantum algorithms. Additionally, the use of the OAM modes allows for novel imaging techniques to directly observe and measure various topological properties of objects ranging from defects in semiconductors to rotating black holes and extrasolar planets. However, measuring such higher dimensional OAM states is fundamentally important, albeit challenging, in order to use this rich degree of freedom. In the work that follows, I present two novel OAM to time mapping schemes and an application using the higher dimensionality of OAM to non-destructively probe quantum states. These are the first OAM measuring schemes to use the temporal degree of freedom to measure OAM. The use of the novel loop nature allows for high fidelity and high speed measurements of a large number of OAM states without significant increase in experimental resources. The first scheme experimentally demonstrates a compact and practical device to measure the OAM spectrum. I report a fidelity of -21.3 dB for 5 different OAM states. The second scheme extends the first, but uses non-demolition measurements to iteratively test for specific OAM values. While this increases experimental complexity, it allows for the detection of an arbitrarily large OAM value from a single photon. I also discuss details of each technique investigate the affects of misalignment on the OAM spectrum. In the remaining part, I discuss my novel generalized quantum Zeno interrogation. The original quantum Zeno interrogation is limited to the two-dimensional state of a single object; while the generalized version has the ability to non-destructively probe the quantum state a set of objects, and deterministically imprint that information onto a single photon using the OAM 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.
We study the high-dimensional orbital angular momentum OAM) entanglement contained in the spatial profiles of two quantum-correlated photons. For this purpose, we use a multi-mode two-photon interferometer with an image rotator in one of the interferometer arms. By measuring the two-photon visibility as a function of the image rotation angle we measure the azimuthal Schmidt number, i.e., we count the number of OAM modes involved in the entanglement; in our setup this number is tunable from 1 to 8.
Abstract In this work, we investigate the orbital angular momentum (OAM) spectrum of photons generated via spontaneous parametric down-conversion (SPDC) and study how shaping the transverse profile of the pump beam influences the resulting spectrum. Using a perfect optical vortex (POV) mode as the pump, we show that the OAM spectrum narrows significantly, leading to purer OAM states. We further examine the entanglement between the down-converted photons in the OAM basis, finding that Laguerre–Gaussian (LG) pumped photons exhibit increased higher-dimensional entanglement at the expense of mode purity.
Uncertainty relations are core to both classical and quantum physics, and lend themselves to tests across many degrees of freedom, with structured light emerging as a vibrant tool to harness these degrees of freedom. Here, we test Popper's conjecture by replacing the traditional spatial and momentum states with angular position and orbital angular momentum (OAM) states of photons, showing that the OAM spectrum for an entangled photon passing through a virtual slit differs from that of a photon passing through a physical slit. To achieve this, we produce two OAM entangled photons, one of which is sent to a slit encoded as a digital hologram, thereby localising its angular position, all the while measuring the OAM of the other. We show that the measured OAM spectrum is limited to that of the initial SPDC photons, independent of the OAM encoded into the slit, consistent with Popper's viewpoint. Our approach allows us to overcome prior limitations imposed by physical slits and linear momentum, and offers a versatile toolbox for further probes of quantum systems.