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Conference on Lasers and Electro-Optics

Quasi-phase matching engineering for spatial control of entangled two-photon states

Juan P. Torres, Silvia Carrasco, Lluís Torner

Published Jan 1, 2004• 0 citations
Publisher

Abstract

We show that properly transverse engineering of quasi-phase-matched geometries can be used to tailor the spatial mode function that describes the quantum state of photon pairs generated in spontaneous parametric down-conversion.
DOI
10.1364/iqec.2004.ithg4

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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.
By making use of the spatial shape of paired photons, parametric down-conversion allows the generation of two-photon entanglement in a multidimensional Hilbert space. How much entanglement can be generated in this way? In principle, the infinite-dimensional nature of the spatial degree of freedom renders unbounded the amount of entanglement available. However, in practice, the specific configuration used, namely, its geometry, the length of the nonlinear crystal, and the size of the pump beam, can severely limit the value that could be achieved. Here we show that the use of quasi-phase-matching engineering allows one to increase the amount of entanglement generated, reaching values of tens of ebits of entropy of entanglement under different conditions. Our work thus opens a way to fulfill the promise of generating massive spatial entanglement under a diverse variety of circumstances, some more favorable for its experimental implementation.
The ability to engineer the properties of quantum optical states is essential for quantum information processing applications. Here, we demonstrate tunable control of spatial correlations between photon pairs produced by spontaneous parametric down-conversion. By shaping the spatial pump beam profile in a type-I collinear configuration, we tailor the spatial structure of coincidences between photon pairs entangled in high dimensions, without effect on intensity. The results highlight fundamental aspects of spatial coherence and hold potential for the development of quantum technologies based on high-dimensional spatial entanglement.