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

Quantum state engineering for spatial control of entangled photon pairs

Juan P. Torres, Lluís Torner

Published Mar 14, 2005• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.588624

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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.
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Quasi-phase-matching (QPM) technique has been successfully applied in nonlinear optics, such as optical frequency conversion. Recently, remarkable advances have been made in the QPM generation and manipulation of photon entanglement. In this paper, we review the current progresses in the QPM engineering of entangled photons, which are finished mainly by our group. By the design of concurrent QPM processes insides a single nonlinear optical crystal, the spectrum of entangled photons can be extended or shaped on demand, also the spatial entanglement can be transformed by transverse inhomogeneity of domain modulation, resulting in new applications in path-entanglement, quantum Talbot effects, quantum imaging etc. Combined with waveguide structures and the electro-optic effect, the entangled photons can be generated, then guided and phase-controlled within a single QPM crystal chip. QPM devices can act as a key ingredient in integrated quantum information processing.
Discretizing transverse linear momentum of photon pairs, generated by spontaneous parametric down conversion (SPDC), is one of the simplest methods for producing bipartite entangled states in high dimensions. So far, it has been employed only to prepare states in dimensions $m\ifmmode\times\else\texttimes\fi{}m$. In this work, we study the generalization for engineering entangled states in dimensions $m\ifmmode\times\else\texttimes\fi{}n$. Our approach relies on the manipulation of the pump beam transverse profile and the phase-matching function of the SPDC process to prepare, behind an mmm- and nnn-slit aperture, different $m\ifmmode\times\else\texttimes\fi{}n$ spatial entangled states. We demonstrate the technique experimentally for some $2\ifmmode\times\else\texttimes\fi{}3$ states. Compared to previous approaches in producing $2\ifmmode\times\else\texttimes\fi{}n$ photonic entanglement, which require either more than two photons or hybrid entanglement, our scheme is less demanding and simpler since we employ only two photons and a single degree of freedom to encode the states.