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Physical Review A

Quantum image control through polarization entanglement in parametric down-conversion

D. P. Caetano, P. H. Souto Ribeiro, J. T. C. Pardal, Antonio Zelaquett Khoury

Published Aug 14, 2003• 34 citations
Publisher

Abstract

We demonstrate both theoretically and experimentally the manipulation of quantum entangled images, using the coupling between polarization entanglement and the entanglement for the transverse degrees of freedom. Starting from a two-crystal bright source of polarization-entangled photons, we arrive at a configuration in which we are able to prepare superposition states for the down-converted angular spectrum while the polarization superposition state is preserved. This scheme allows us to select the detected quantum image by performing projections onto polarization subspaces. We also demonstrate the potential of the system for applications to quantum cryptography of images.

DOI
10.1103/physreva.68.023805

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We demonstrate both theoretically and experimentally the manipulation of quantum entangled images, using the coupling between polarization entanglement and the entanglement for the transverse degrees of freedom. Starting from a two-crystal bright source of polarization-entangled photons, we arrive at a configuration in which we are able to prepare superposition states for the down-converted angular spectrum while the polarization superposition state is preserved. This scheme allows us to select the detected quantum image by performing projections onto polarization subspaces. We also demonstrate the potential of the system for applications to quantum cryptography of images.
We discuss how it is possible to manipulate quantum spatial properties of light beams by using the transfer of the angular spectrum. Twin beams from the parametric down-conversion can be prepared in a state that carries two different quantum images. At the same time, the twin photons can be entangled in polarization. This preparation allows the selection between the detection of each one of the images at a time or a mixture by performing proper projections onto polarization sub-spaces. As another example, we show how to produce a light beam presenting spatial anti-bunching through the control of the entangled angular spectrum and reflections.
Maximally entangled photon pairs with a spatial degree of freedom is a potential way for realizing high-capacity quantum computing and communication. However, methods to generate such entangled states with high quality, high brightness, and good controllability are needed. Here, a scheme is experimentally demonstrated that generates spatially maximally entangled photon pairs with an orbital angular momentum degree of freedom via spontaneous parametric down-conversion in a nonlinear crystal. Compared with existing methods using postselection, the technique can directly modulate the spatial spectrum of down-converted photon pairs by engineering the input pump beam. In addition, the relative phase between spatially entangled photon pairs can be easily manipulated by preparing the relative phase of input pump states.
The two-photon state generated by spontaneous parametric down-conversion (SPDC) exhibit spatial entanglement embedded in the corresponding mode function. The control of the spatial characteristics of the generated two-photon state is an issue of paramount importance. For example, the spatial entanglement of the two down converted photons forms the basis of quantum imaging, and entanglement in orbital angular momentum has opened a new scenario for implementing multidimensional Hilbert spaces. We put forward several techniques to engineer the spatial structure of entangled two-photon states generated in SPDC. The first strategy we consider for spatial control of the quantum state makes use of the direct manipulation of the pump beam. This technique makes feasible to prepare arbitrary engineered entangled states in any d-dimensional Hilbert space. The second strategy is based on the proper preparation of the down-converting crystal itself, namely quantum state manipulation by quasi-phase-matching (QPM) engineering. We use properly designed transversely varying QPM gratings in nonlinear crystals.
We suggest and demonstrate a novel source of two-photon multipartite entangled states which exploits the transverse spatial structure of spontaneous parametric down-conversion together with a programmable spatial light modulator (SLM). The one-dimensional SLM is used to perform polarization entanglement purification and to realize arbitrary phase gates between polarization and momentum degrees of freedom of photons. We experimentally demonstrate our scheme by generating two-photon three-qubit linear cluster states with high fidelity using a diode laser pump with a limited coherence time and power on the crystal as low as  2.5~2.5 2.5 mW.