Unitary transformations of spatial modes for quantum experiments

Spatial modes have attracted a lot of attention in the quantum optics community because of their possible application in high-dimensional quantum bits, i.e. qudits. One crucial task in quantum communication and computation applications, is the ability to perform unitary transformations on these qudits. However, arbitrary unitary transformations between full-field spatial modes have not been realized so far. Thus, in order to bring spatial modes closer to communication and computation applications, methods for performing these transformations need to be devised. In this thesis, we introduce a method for generating these unitary transformations. The method is based on multi-plane light conversion (MPLC), where the spatial structure of light is transformed through multiple consecutive transverse-phase modulations. The method we use for generating these task specific phase-modulations is called wavefront matching (WFM). This thesis consists of three main sections. First, we will introduce some necessary theory behind high-dimensional quantum-states and single photons. We will also explore some theory behind the generation of single photons and introduce light's spatial modes in more detail. Second, we will introduce WFM along with other methods we needed for testing the unitary transformations experimentally. Finally, we will experimentally test the mode transformations in a spatial mode filter and in multi-mode transformations. We apply the mode filter in quantum key distribution (QKD) and quantum state tomography (QST) measurements, and we implement different high-dimensional quantum gates using the multi-mode transformations. Additionally, we introduce a method of potentially observing two-photon interference with these unitary transformations. With the mode filter, we achieved error rates below five percent and in the QKD application we measured a theoretical data transmission rate of 1.98 bits per measured photon. With the quantum gates, we achieved accuracies of up to 98\% in all mutually unbiased bases (MUBs). The results shown in this thesis demonstrate the efficiency and unitarity of WFM in a broad set of different tasks. All the shown tasks are important in high-dimensional quantum communication and computation, and hence we believe that WFM will become an important tool in high-dimensional quantum information processing. We also give an outlook on how WFM could potentially be improved, and list some additional tasks, in which WFM could be useful. We believe that the broad applicability of WFM will enable some unexplored quantum information or photonics applications

High-dimensional two-photon interference effects in spatial modes

Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides implementing the analogue of the Hong-Ou-Mandel interference using a two-dimensional spatial-mode splitter, we extend the scheme to observe coalescence and anti-coalescence in different three and four-dimensional spatial-mode multiports. The operation within spatial modes, along a single beam-path, lifts the requirement for interferometric stability and opens up new pathways of implementing linear optical networks for complex quantum information tasks.Comment: 14 pages, 12 figure

Near-perfect measuring of full-field transverse-spatial modes of light

Along with the growing interest in using the transverse-spatial modes of light in quantum and classical optics applications, developing an accurate and efficient measurement method has gained importance. Here, we present a technique relying on a unitary mode conversion for measuring any full-field transverse-spatial mode. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We experimentally test the technique using a single spatial light modulator and achieve an average error of 4.2% for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. Moreover, as the method can also be used to measure any complex superposition state, we demonstrate its potential in a quantum cryptography protocol and in high-dimensional quantum state tomography.Comment: 7 pages, 4 figure

Photonic angular super-resolution using twisted N00N states

The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100$\,\hslash$, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular super-sensitivity and accessible generation of N00N states between any transverse light fields.Comment: 12 pages, 8 figure

High-efficiency interface between multi-mode and single-mode fibers

Multi-mode fibers (MMFs) and single-mode fibers (SMFs) are widely used in optical communication networks. MMFs are the practical choice in terms of cost in applications that require short distances. Beyond that, SMFs are necessary because of the modal dispersion in MMFs. Here, we present a method capable of interfacing an MMF with an SMF using a re-programmable multi-plane light conversion scheme (MPLC). We demonstrate that only 3-phase modulations are necessary to achieve MMF-to-SMF coupling efficiencies from 30\% to 70\% for MMF's with core diameters up to 200 microns. We show how the obtained coupling efficiency can be recovered if the output field of the MMF changes entirely, e.g. through strong deformation of the fiber, by simple monitoring of the field. Furthermore, we test the influence of the resolution of both essential devices (field reconstruction and MPLC) on coupling efficiencies. We find that commercially available devices with increased speed and efficiency, such as wavefront sensors and deformable mirrors, are sufficient for establishing an MMF to SMF interface which auto-corrects any decoupling in the kHz regime

High-order aberrations of vortex constellations

When reflected from an interface, a laser beam generally drifts and tilts away from the path predicted by ray optics, an intriguing consequence of its finite transverse extent. Such beam shifts manifest more dramatically for structured light fields, and in particular for optical vortices. Upon reflection, a field containing a high-order optical vortex is expected to experience not only geometrical shifts, but an additional splitting of its high-order vortex into a constellation of unit-charge vortices, a phenomenon known as topological aberration. In this article, we report on the first direct observation of the topological aberration effect, measured through the transformation of a vortex constellation upon reflection. We develop a general theoretical framework to study topological aberrations in terms of the elementary symmetric polynomials of the coordinates of a vortex constellation, a mathematical abstraction which we prove to be the physical quantity of interest. Using this approach, we are able to verify experimentally the aberration of constellations of up to three vortices reflected from a thin metallic film. Our work not only deepens the understanding of the reflection of naturally occurring structured light fields such as vortex constellations but also sets forth a potential method for studying the interaction of twisted light fields with matter.Comment: Main: 6 pages, 3 figures. Supplementary: 6 pages, 2 figure

High-dimensional quantum gates using full-field spatial modes of photons

Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g. wave plates for polarisation. However for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations when the number of phase modulation planes is comparable to the number of modes. More importantly, we experimentally implement several high-dimensional quantum gates for up to 5-dimensional states encoded in the full-field mode structure of photons. In particular, we realise cyclic and quantum Fourier transformations, known as Pauli $\hat{X}$-gates and Hadamard $\hat{H}$-gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect "unitarity" by means of quantum process tomography unveiling a process purity of 99%. Lastly, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e. azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation and sensing schemes

Observation of the quantum Gouy phase

Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.publishedVersionPeer reviewe

Spectral Vector Beams for High-Speed Spectroscopic Measurements

Structured light harnessing multiple degrees of freedom has become a powerful approach to use complex states of light in fundamental studies and applications. Here, we investigate the light field of an ultrafast laser beam with a wavelength-depended polarization state, a beam we term spectral vector beam. We demonstrate a simple technique to generate and tune such structured beams and demonstrate their spectroscopic capabilities. By only measuring the polarization state using fast photodetectors, it is possible to track pulse-to-pulse changes in the frequency spectrum caused by, e.g. narrowband transmission or absorption. In our experiments, we reach read-out rates of around 6 MHz, which is limited by our technical ability to modulate the spectrum and can in principle reach GHz read-out rates. In simulations we extend the spectral range to more than 1000 nm by using a supercontinuum light source, thereby paving the way to various applications requiring high-speed spectroscopic measurements.Comment: 11 pages, 12 figure

Talbot self-imaging and two-photon interference in ring-core fibers

Wave propagation on the surface of cylinders exhibits interferometric self-imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a higher-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-core fiber, our findings open the door to applications in optical telecommunications as a compact beam multiplexer as well as in quantum information processing tasks as a scalable realization of a linear optical network.publishedVersionPeer reviewe