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Two-photon interference : spatial aspects of two-photon entanglement, diffraction, and scattering

Wouter H. J. Peeters

Published Dec 21, 2010• 0 citations
OpenAlex

Abstract

This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical process of spontaneous parametric down-conversion. These entangled photons are then passed through different optical systems to study various aspects of two-photon interference. Firstly, an experimental analysis is made of the high-dimensional entanglement that is present in the orbital angular momentum of the photons. Secondly, we present a comprehensive description of two-photon quantum interference behind a double slit. We demonstrate how to control the quantum correlations and present the first observations of complete two-photon diffraction patterns behind a double slit. Finally, we present pioneering experiments on spatially entangled two-photon states that are scattered of random media. We have observed and theoretically analyzed the structure in the random two-photon interference patterns called two-photon speckle patterns. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments also demonstrate a two-photon interference phenomenon that survives averaging over different realizations of disorder. The latter results are closely related to bosonic, fermionic, and anyonic particle exchange symmetries.

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This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical process of spontaneous parametric down-conversion. These entangled photons are then passed through different optical systems to study various aspects of two-photon interference. Firstly, an experimental analysis is made of the high-dimensional entanglement that is present in the orbital angular momentum of the photons. Secondly, we present a comprehensive description of two-photon quantum interference behind a double slit. We demonstrate how to control the quantum correlations and present the first observations of complete two-photon diffraction patterns behind a double slit. Finally, we present pioneering experiments on spatially entangled two-photon states that are scattered of random media. We have observed and theoretically analyzed the structure in the random two-photon interference patterns called two-photon speckle patterns. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments also demonstrate a two-photon interference phenomenon that survives averaging over different realizations of disorder. The latter results are closely related to bosonic, fermionic, and anyonic particle exchange symmetries.
We report the observation of speckle patterns in quantum correlations within light that is scattered by a disordered medium. The random medium is illuminated with spatially entangled photon pairs, and fourth-order speckle patterns are spatially resolved by two independently scanning detectors. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments demonstrate that two-photon speckle from a surface scatterer and a volume scatterer look entirely different.
We report a two-photon double-slit interference experiment. Two correlated photons, generated by spontaneous parametric downconversion and traveling in different directions, are made to pass through a double slit in such a way that the path of one photon can be identified with that of the other photon. No single-photon interference pattern is observed even if the path is not actually identified, but a spatial interference pattern appears in the joint detection counting rates of the photon pairs. It can easily be shown that these nonlocal phenomena cannot be exhibited by any kind of classical field.
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞)\left[0,\infty\right)[0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.
Full text: We present two experiments on single- and two-particle interference. In the single-photon interference experiment, photons from a spontaneous parametric down-conversion (SPDC) source are send through a double slit. An interference pattern is built up frame by frame from shots obtained with an EMCCD camera behind the slit. Each frame contains on average less than one photon, thus demonstrating true single-photon sensitivity of the camera. The build-up of the interference pattern nicely demonstrates the concept of wave-particle duality. In a next step, we describe the Heisenberg's lens experiment and present the conditions required to analyse and investigate the spatial correlations of momentum entangled photons produced by SPDC. The occurrence of double-slit interference now depends on the experimental arrangement for the second photon of the pair, for example: interference can only occur if the second photon is also passing a double slit. We present an analysis of such a double-double-slit experiment. (author)
This paper demonstrates the engineering of spatially entangled two-photon states behind a double slit by tailoring the incident pure two-photon state. We experimentally characterize many different two-photon states by measuring their complete two-photon interference patterns in the far field of the double slit. Spatial entanglement right behind the double slit can reside in either the modulus or the phase of the two-photon field. The balance between these two types of entanglement is fully controlled by experimentally utilizing the phase-front curvatures of the pump beam and the phase-matching profile. We project either a far-field image or a magnified near-field image of the two-photon source onto the double slit. Our theoretical analysis shows how the two-photon interference pattern behind the double slit effectively acts as a phase-sensitive probe of the incident two-photon field profile. We thus present phase-sensitive measurements of the generated two-photon field profile probed in an image plane of the two-photon source.
We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern produced by an object changes from a quantum (perfectly correlated) case to a classical (uncorrelated) one. The observed diffraction and interference patterns are accurately reproduced by Fourier-optical analysis taking into account the quantum spatial correlation. We show that the relation between the spatial correlation and the object size plays a crucial role in the formation of both one- and two-photon diffraction-interference patterns.