Abstract Photons carrying orbital angular momentum (OAM) are excellent qudits and are widely used in several applications, such as long distance quantum communication, d -dimensional teleportation and high-resolution imaging and metrology. All these protocols rely on quantum tomography to characterise the OAM state, which currently requires complex measurements involving spatial light modulators and mode filters. To simplify the measurement and characterisation of OAM states, here we apply a recent tomography protocol [Asadian et al , Phys. Rev. A 94 010301 (2016)]. Our scheme for OAM tomography in d dimensions requires only a set of measurements on a path qubit, i.e., a two-dimensional system. This replaces the current complexity of OAM measurements by the ability to perform generalized Pauli operators X d , Z d on OAM states. Our scheme can be adapted in principle to other degrees of freedom, thus opening the way for more complex qudit tomography.
Abstract Photons carrying orbital angular momentum (OAM) are excellent qudits and are widely used in several applications, such as long distance quantum communication, d -dimensional teleportation and high-resolution imaging and metrology. All these protocols rely on quantum tomography to characterise the OAM state, which currently requires complex measurements involving spatial light modulators and mode filters. To simplify the measurement and characterisation of OAM states, here we apply a recent tomography protocol [Asadian et al , Phys. Rev. A 94 010301 (2016)]. Our scheme for OAM tomography in d dimensions requires only a set of measurements on a path qubit, i.e., a two-dimensional system. This replaces the current complexity of OAM measurements by the ability to perform generalized Pauli operators X d , Z d on OAM states. Our scheme can be adapted in principle to other degrees of freedom, thus opening the way for more complex qudit tomography.
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) of light is a promising degree of freedom for quantum communication and quantum computation. However, efficient methods to transform and measure OAM modes are still not available readily. Here, we propose a method for full quantum state tomography for arbitrary OAM states of light. The key component in our scheme is the helicity sorter, a device that can sort OAM modes of a light beam based on their Helicity. We present two setups to implement the Helicity sorted, one requires O(N) number of optical elements for 2N OAM modes, and the other uses spatial light modulators and is independent of the number of OAM modes. Ours is the first method to provide the efficient and scalable full quantum state tomography of the OAM modes and can be extremely important for quantum communication and quantum computation.
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.
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
Abstract Electromagnetic waves have both spin momentum and orbital angular momentum (OAM). Light carrying OAM has broad applications in micro-particle manipulation, high-precision optical metrology, and potential high-capacity optical communications. In the concept of quantum information, a photon encoded with information in its OAM degree of freedom enables quantum networks to carry much more information and increase their channel capacity greatly compared with those of current technology because of the inherent infinite dimensions for OAM. Quantum memories are indispensable to construct quantum networks. Storing OAM states has attracted considerable attention recently, and many important advances in this direction have been achieved during the past few years. Here we review recent experimental realizations of quantum memories using OAM states, including OAM qubits and qutrits at true single photon level, OAM states entangled in a two-dimensional or a high-dimensional space, hyperentanglement and hybrid entanglement consisting of OAM and other degree of freedom in a physical system. We believe that all achievements described here are very helpful to study quantum information encoded in a high-dimensional space.
The physical properties of a quantum system, whether pure or mixed, are described fully by its density matrix. Recovery of the density matrix through projective measurements -- referred to as quantum state tomography -- is a cornerstone of quantum optics and metrology. The implementation of this approach in transmission electron microscopy, in particular for the characterisation of an electron beam after inelastic scattering, has remained a longstanding challenge as a result of the complexity of scanning high-dimensional phase spaces, with the number of required measurements growing quadratically with space dimensionality. Here, we introduce a simplified approach by restricting tomography to the electron orbital angular momentum (OAM) subspace. By using an electron optical device known as an OAM sorter, we discretise the phase space into a finite set of measurable states, thus significantly reducing the experimental and computational burden. The resulting measurements suffice to probe essential features of inelastic scattering. We demonstrate the technique by studying the inelastic scattering of a structured electron probe exciting volume plasmons in a carbon film. The combined use of a structured beams and OAM-resolved quantum tomography reveals symmetry-breaking effects and offers insight into the coherence and evolution of the scattered quantum states. Analysis of the diagonalised density matrices further reveals the nature of the induced state transitions, demonstrating the power of the approach for quantum tomography of electron scattering.