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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum imaging and orbital angular momentum

Jonathan Leach, Barry Jack, Jacquiline Romero, David G. Ireland, Sonja Franke‐Arnold, Steve Barnett, Miles J. Padgett

Published Feb 6, 2010• 3 citations
Publisher

Abstract

We report a violation of the CHSH inequality for ghost-images. This is achieved by using two spatially separated phase modulators within the context of a two-photon parametric down-conversion experiment. We obtain edge enhanced images as a direct consequence of the quantum correlations in the orbital angular momentum (OAM) of the down-converted photon pairs. For phase objects, with differently orientated edges, we show a violation of the CHSH Bell-type inequality for an OAM subspace, thereby unambiguously revealing the quantum nature of our ghost-imaging arrangement.

DOI
10.1117/12.845250

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We report a violation of the CHSH inequality for ghost-images. This is achieved by using two spatially separated phase modulators within the context of a two-photon parametric down-conversion experiment. We obtain edge enhanced images as a direct consequence of the quantum correlations in the orbital angular momentum (OAM) of the down-converted photon pairs. For phase objects, with differently orientated edges, we show a violation of the CHSH Bell-type inequality for an OAM subspace, thereby unambiguously revealing the quantum nature of our ghost-imaging arrangement.
We demonstrate the contrast enhancement of images within a ghost-imaging system by use of nonlocal phase filters. We use parametric down-conversion as the two-photon light source and two separated phase modulators, in the signal and idler arms which represent different phase filters and objects, respectively. We obtain edge enhanced images as a direct consequence of the quantum correlations in the orbital angular momentum (OAM) of the down-converted photon pairs. For phase objects, with differently orientated edges, we show a violation of a Bell-type inequality for an OAM subspace, thereby unambiguously revealing the quantum nature of our ghost-imaging arrangement.
This thesis is a dissemination of the experimental work I have carried out in the last three and a half years, under supervision of Prof. Miles Padgett and Dr. Sonja Franke-Arnold. Presented within are seven unique experiments investigating the orbital angular momentum (OAM) states of light, and the associated spatial modes. Six of these experiments relate to measurements on quantum-entangled photon pairs produced in down-conversion. The first chapter of my thesis is a brief review of the some of the contributions made to the field of research of OAM, both involving classical and quantum states of light. This chapter introduces some of the hallmark experiments within the subject, from which my experimental work reported in this thesis is inspired. The second chapter details the set up of the down conversion experiment, and the experimental techniques used to design a fully functioning quantum measurement system. Most importantly, this includes the holographic techniques used to measure the spatial states of the photon pairs. In addition to holographic measurements, a system to holographically auto-align the down-conversion experiment was developed. Due to the sensitive nature of the experiments presented, this automated system has been crucial to the success of all of the single photon experiments presented within this document. The experimental results are split into three separate categories. The first (Chapter 3) describes measurements investigating the Fourier relationship between OAM and angular position states, both at the classical and quantum levels. The following chapter (Chapter 4) consists of four experiments designed to quantify the degree of entanglement of states of OAM and angular position. This includes the first demonstration of the historic EPR (Einstein-Podolsky-Rosen) paradox for OAM and angle states, violation of a Bell-type inequality for arbitrary OAM states, and characterisation of the density matrices for a range of OAM state-spaces. The final chapter (Chapter 5) reports a new type of ghost imaging using down-converted photon pairs. In this experiment, we violate a Bell inequality within a ghost image, demonstrating the entangled nature of our system and contributing a new element to the long standing contention over quantum vs. classical features within ghost imaging. These experiments have seen a wide range of collaboration. The experimental work on the Fourier relation on single photons was carried out in collaboration with Dr. Anand Kumar Jha (University of Rochester). The work on ghost imaging was performed with collaboration with Prof. Monika Ritsch-Marte (Innsbruck Medical University), and the angular EPR paradox work was carried out in collaboration with Prof. Robert Boyd (Univ. of Rochester) and Prof. David Ireland (Univ. of Glasgow). The work I present here is experimental, however any theoretical developments are in a large part due to the support of Dr. Sonja Franke-Arnold and Prof. Steve Barnett (Univ. of Strathclyde).
We utilise the position and orbital angular momentum (OAM) correlations between the signal and idler photons generated in the down-conversion process to obtain ghost images of a phase object. By using an OAM phase filter, which is non-local with respect to the object, the images exhibit isotropic edge-enhancement. This imaging technique is the first demonstration of a full-field, phase-contrast imaging system with non-local edge enhancement, and enables imaging of phase objects using significantly fewer photons than standard phase-contrast imaging techniques.
Orbital angular momentum entangled photons emitted by a down-conversion source are shown to be in higher dimensional entangled states. This is experimentally confirmed by demonstrating a violation of Clauser-Horne-Shimony-Holt-type Bell inequalities. The experiment is performed in two steps. First, the two-photon two-dimensional entanglement is demonstrated for orbital angular momentum states by violating the usual CHSH Bell inequality. In a second step the setup is extended in order to show that the entanglement also holds in three dimensions. By using a generalized type of the CHSH Bell inequality, a violation of more than 18 standard deviations is achieved. Higher dimensional entangled states thus allow the realization of new types of quantum communication protocols. They also provide a more secure quantum cryptography scheme.
The chained CHSH inequality is of paramount importance in quantum information science, demonstrating superiority over the CHSH inequality in some quantum information tasks. Hitherto, experimental verification was rarely considered to verify the chained CHSH inequality, as previous experimental efforts primarily focused on the CHSH inequality. Here, by employing two-photon orbital angular momentum (OAM) entanglement, we experimentally demonstrate the chained CHSH across multiple settings. In theory, we demonstrate a geometrical connection of optimal measurement vectors and establish that the optimal measurement vectors reside in a circle through the center of the Bloch sphere. This allows us to construct multiple sets of optimal measurement vectors on different circles. In the experiment, we typically choose circles in the XOY, XOZ, and YOZ planes to observe violations of the chained CHSH inequality. Our experimental results indicate that the maximum violation increases with setting k , underscoring the dependence of the maximum violation on the measurement angles.