The central topic of the Thesis concerns light scattering experiments with entangled photons. Specifically, we study the effect of scattering processes on polarization-entanglement of twin-photons. The main idea is that scattering generally couples polarization and spatial degrees of freedom of photons. The details of this coupling depend on the characteristics of the scattering medium. Such coupling, in turn, can reduce the entanglement of twin-photons, if the photon pairs are detected in a momentum-insensitive way. We have investigated a broad range of optical scattering media ranging from milk to polymer fibers. By manipulating the parameters of these samples we were able to generate a broad range of quantum states, proving for the first time that scattering processes are a substantial tool for mixed-state engineering. This is of great importance for quantum information since any real-world application thereof has to deal with mixed (as opposed to pure) states.
The central topic of the Thesis concerns light scattering experiments with entangled photons. Specifically, we study the effect of scattering processes on polarization-entanglement of twin-photons. The main idea is that scattering generally couples polarization and spatial degrees of freedom of photons. The details of this coupling depend on the characteristics of the scattering medium. Such coupling, in turn, can reduce the entanglement of twin-photons, if the photon pairs are detected in a momentum-insensitive way. We have investigated a broad range of optical scattering media ranging from milk to polymer fibers. By manipulating the parameters of these samples we were able to generate a broad range of quantum states, proving for the first time that scattering processes are a substantial tool for mixed-state engineering. This is of great importance for quantum information since any real-world application thereof has to deal with mixed (as opposed to pure) states.
Understanding the complex interactions of the quantum light with different media provides valuable insights into potential applications in quantum tomography, microscopy, circuit and network design, and imaging. This thesis investigates quantum light interaction with two types of media: I. Random media entailing multiple scattering (Chapters 2-5), and II. Structured media, specifically designed to control quantum interferences (Chapters 6 and 7). In the first part of the thesis, and through solving the Lippmann-Schwinger equation for collections of small scatterers, a first principle scalar model for multiple scattering in finite-sized random media is developed. This efficient numerical model serves as the basis for investigating the coherent backscattering, a manifestation of weak localization in random media, for several bounded random media and various illuminations. Through employing mode expansion, next, the developed model is adapted to a general class of quantum-optical studies and quantum correlations are successfully derived and analyzed in scattering from finite disordered structures as well as systems of few scatterers. In multiple scattering of two-photon states in weak localization regime, the emergence of coherent two-photon backscattering is presented for the first time in coincidence detection, and it is demonstrated that quantum correlations can be used as a probe of entanglement dimensionality. Multiple scattering of two-photon states results in granular patterns known as speckle patterns. The statistical properties of single- and two-photon speckle patterns in scattering of different states are numerically calculated and the speckle visibilities and relevant parameters are derived. Specifically, the deviation of the probability density functions from negative exponential distributions, traditionally recognized as Rayleigh statistics in classical scattering, is identified, and shown to significantly depend on the presence of entanglement. Lastly, a different numerical implementation (based on COMSOL Multiphysics package) is used to consolidate our findings by incorporating the polarization effects. Coherent backscattering and coherent two-photon backscattering are observed for co-polarized fields in scattering from synthesized disordered media. It is demonstrated that depending on the particle exchange symmetry in polarization entangled excitation, the photons can exhibit statistical tendency to bunch together in the same mode, appear in separate modes (antibunching), or show a mixed response after multiple scattering. These bosonic-, fermionic-, and anyonic-like behaviors are studied in connection with coherent backscattering phenomenon, and it is demonstrated that the degree of enhancement in backscattering depends on the exchange symmetries. The simplicity and effectiveness of the implemented scattering analysis and the significance of the consequent conclusions suggest our approach as a promising platform for ‘numerical experiments’ without the limitations of analytical or semi-analytical models, and a practical tool prior to experiments. In the second part of the thesis, the random media operating as multimode platforms are replaced with engineered surfaces, i.e., metasurfaces, to realize targeted quantum interferences. First, a design roadmap for general lossy, asymmetric, and unbalanced coupling networks is presented, allowing to achieve maximum programmability in two-photon interferences. Next, two switchable metasurface-based coupling networks are designed to control nonclassical two-photon interferences via thermally driven crystallographic phase transitions. Numerical simulations confirm smooth transition between coalescence and anti-coalescence, aiming to address the current need in quantum optics for free-space compact devices creating tunable quantum interferences and acting as fast modulators for the second order quantum correlations. Our proposed compact and rapidly controllable devices pave the way towards new quantum applications as well as improving the current free-space quantum systems.
Light, which is composed of discrete quanta, or photons, is one of the most fundamental concepts in physics. Being an elementary entity, the behaviour of photons is governed by the rules of quantum mechanics. The ability to create, manipulate and measure quantum states of light is not only useful in foundational tests of quantum theory, but also in a wide range of quantum technologies – which aim to utilize non-classical properties of quantum systems to perform tasks not possible with classical resources. Only recently has it been possible to control the properties of number states of light, which have a fixed photon-number. Two-photon states are central to testing fundamental physical theories (such as locality and reality) and the implementation of quantum information technologies. The versatility of photon-pair states is en- abled by the potential entanglement properties it can posses. Thus controlling the correlations between photons is crucial to both pure and applied physics. To produce a single photon, a photon-pair state can be used. Detection of one photon indicates its twin’s existence. Many applications, such as optical quantum computation, require pure indistinguishable single photons. Heralding single pho- tons from a photon-pair will, in general, produce single photons in a mixed quantum state due to correlations within the pair. A common approach to creating photon-pairs is through the nonlinear sponta- neous four-wave mixing interaction in optical fibres. This thesis presents a theoreti- cal and experimental implementation of a scheme to tailor the spectral correlations within the pairs. Emphasis is placed on engineering the two-photon state such that they are completely uncorrelated. Spatial entanglement is naturally avoided due to the discrete nature of the optical fibre modes. Spectral correlations are eliminated by careful choice of dispersion characteristics and conditions. The purity of the photons generated by this scheme is demonstrated by means of two-photon inter- ference from independent sources. We measure a purity of (85.9 ± 1.6)% with no spectral filtering, exhibiting the usefulness of this source for quantum technologies and applications.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated
Quantum optics, the study of light at the level of its building blocks, \nhas been one of the frontiers of science. The arena of quantum optics \nhas been fruitful for investigations of a wide range of interesting questions, \nfrom those on the fundamental structures in driven dissipative \nsystems to those on applications of quantum information processing \nand quantum communication. \nThe first part of this thesis is concerned with one of the holy grails \nof quantum optics: an efficient transfer of energy (coupling) between \nsingle photons and matter degrees of freedom. From a certain point \nof view, the problem of efficient coupling is purely geometrical. The \nefficiency of coupling between an atom and light is difficult because \nit is difficult to shape the wavefunction of a single photon such \nthat it overlaps perfectly with the matter degree of freedom (emitter). \nThe first contribution of this thesis is addressing this issue by considering \nan emitter which perfectly matches the single photon plane-wave. \nMoreover, luckily, such an emitter is already realized in nature in the \nform of a two-dimensional crystal. We show that a new generation \nof two-dimensional semiconductors, transition metal dichalcogenide \n(TMD) monolayers, have especially favorable characteristics for allowing \nhighly efficient coupling between photons and matter degrees \nof freedom. \nOne of the most important goals in realizing an efficient coupling \nbetween photons and matter degrees of freedom is that unlike photons, \nmatter excitations interact with each other. Hence, if we would \nlike to have photons which act as if they interact, one possible way \nis to first convert them into matter excitations, and then transfer the \ncorrelations due matter interactions back to photons. As the second \ncontribution of this thesis, we demonstrate that TMD monolayers placed \nwithin a cavity can help us create photons which avoid each other \nas if they interact. The effect can be simply understood as the TMD \nmonolayer acting as a filter for photons, such that it only allows the \npassage of one photon at a time. \nBesides being the fundamental building block of light, photons also \nserve as mediators of interactions between charged particles. In a \nsense, two positive charges repel each other because there is always \na photon which lets them know that they are close to one another. \nOn the other hand, systems of many interacting particles behave in \na completely different way then when they are alone. It may even be \nargued that all physical phenomena at some level emerge from the \nbehavior of many interacting constituents. Given this point of view, \nit is crucial to find ways to control photons in order to control the \ninteractions that they mediate between matter degrees of freedom. \nAs the third contribution of this thesis, we analyze an experimental \nscheme where the control of photonic degrees of freedom can allow \nan experimentalist to modify the strength and range of interactions \nbetween matter. In particular, we propose squeezed photon states as \na resource to control such interactions. \nThe second part of this thesis is concerned with the emergent phenomena \narising in a system of many interacting particles. In particular, \nthe fourth contribution of this thesis considers the combination \nof two fascinating phenomena which emerges such condensed matter \nsystems: superconductivity and geometric effects in lattice band \nstructures. Separately, both superconductivity and the non-trivial geometrical \neffects in lattice systems are well-established subfields of condensed \nmatter physics. Yet only more recently, the combination of \nthese two phenomena were investigated in the context of topological \nsuperconductors, as well as other superconducting states which emerge \non top of band structures with non-trivial geometry. In our study, \nwe attempt at clarifying one of the ways that the non-trivial geometry \nassociated with the lattice band structure may affect the dynamics of \nan emergent superconducting state. Surprisingly, our analysis shows \nthat one of the most robust characteristics of the superconductor, vortices \nenclosing a quantum of magnetic flux, can be modified due to \ngeometrical effects.
Polarization-entangled photons are routinely produced using complex nonlinear media. In using such systems to produce polarization-entangled photons, it is assumed that the entanglement effects are not altered by such nonlinear media. However, this assumption is generally accepted but there remains the need to ensure that the nonlinear media do not alter the entanglement of the photons. To address the polarization entanglement of photons in the absence of a complex nonlinear medium, such as a nonlinear crystal or an atomic system, this paper calculates branching ratios of entangled and unentangled photons from the fundamental process of photon–photon scattering in vacuum as opposed to in a complex nonlinear medium. Herein, the Dyson–Feynman formalism of quantum electrodynamics is used to examine selected entanglement effects manifested in the well-known process of photon–photon scattering in vacuum. Based on known partial scattering amplitudes for processes where two photons of specified polarizations interact via an intermediate fermion loop to form a final state of two photons with allowed polarization states, polarization-entangled photon affects are analyzed for cases where both initial and final states are described by specific entangled states, extending previous analyses. The current analysis compares the cases where unentangled photons scatter in a vacuum into final states of (a) unentangled photons, (b) maximally entangled photons (symmetric Bell state), and (c) antisymmetric Bell state. This comparison reveals that the probability of scattering into a state of maximally entangled polarization-entangled states is of the same order as that of scattering into unentangled final-state photons.