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

Three-photon entangled states generated by spontaneous parametric down-conversion in a cavity

А. А. Калачев, Ulia Z. Fattakhova

Published Mar 3, 2008• 0 citations
Publisher

Abstract

The possibility of generation of three-photon correlated states (triphotons) by spontaneous parametric down-conversion in a cubic nonlinear medium which is placed in a cavity is analyzed. It is shown that the number of generated photons per mode is proportional to the square cavity finesse and to the number of longitudinal cavity modes which satisfy the condition of triple resonance. The number of photons per mode and the counting rate of a detector are estimated for typical experimental conditions.

DOI
10.1117/12.801591

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The possibility of generation of three-photon correlated states (triphotons) by spontaneous parametric down-conversion in a cubic nonlinear medium which is placed in a cavity is analyzed. It is shown that the number of generated photons per mode is proportional to the square cavity finesse and to the number of longitudinal cavity modes which satisfy the condition of triple resonance. The number of photons per mode and the counting rate of a detector are estimated for typical experimental conditions.
We consider the quantum state of light produced via direct parametric decay of pump photons into photon triples in a medium with cubic nonlinearity. For this state generated in the near-collinear frequency-degenerate regime, the third- and second-order Glauber's correlation functions are calculated and the intensity distribution over frequency and wave vector is found. It is shown that the number of photons generated into a single mode via the three-photon down-conversion is proportional to the width of the frequency-angular intensity distribution for the corresponding two-photon phase matching (spontaneous parametric down-conversion). The intensity of three-photon parametric down-conversion is shown to have an extremely broad frequency spectrum, even for a fixed angle of scattering.
We investigate the third-order spontaneous parametric down-conversion process in a nonlinear media with inversion centers. Specifically, we analyze in details the three-photon differential count rate in unit frequency and angular regions, total count rate and measurement time for rutile and calcite crystals which have comparatively large cubic susceptibilities. Special attention is given to consideration of limited frequency and angular detection ranges in order to calculate experimentally available detection rate values.
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We propose two interesting methods of generating the four-photon WWW state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon WWW state, the three-photon Greenberger-Horne-Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general nnn-photon WWW state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.