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arXiv:1508.03291 · Laser Physics Letters

Three-photon generation by means of third-order spontaneous parametric down-conversion in bulk crystals

N A Borshchevskaya, Konstantin G. Katamadze, S P Kulik, M V Fedorov

Published Oct 16, 2015• 31 citations
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Abstract

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.

DOI
10.1088/1612-2011/12/11/115404

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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 study the third-order spontaneous parametric down-conversion (TOSPDC) process, as a means to generate entangled photon triplets. Specifically, we consider thin optical fibers as the nonlinear medium to be used as the basis for TOSPDC in configurations where phase matching is attained through the use of more than one fiber transverse modes. Our analysis in this paper, which follows from our earlier paper [Opt. Lett. 36, 190--192 (2011)], aims to supply experimentalists with the details required in order to design a TOSPDC photon-triplet source. Specifically, our analysis focuses on the photon triplet state, on the rate of emission, and on the TOSPDC phase-matching characteristics for the cases of frequency-degenerate and frequency nondegenerate TOSPDC.
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 propose a general scheme to investigate photon triplet generation (PTG) via third-order spontaneous parametric downconversion (TOSPDC) in χ (3) nonlinear structures. Our approach leverages the quantum-classical correspondence between TOSPDC and its reverse classical process, three-wave sum-frequency generation (TSFG), to efficiently estimate the PTG rate. We apply this framework to nonlinear metasurfaces supporting quasi-bound states in the continuum (qBICs) in the optical range. From numerical analysis of noncollinear TSFG with degenerate input waves at qBIC wavelengths, we predict wavelength-tunable three-photon emission with spatio-angular correlations. These findings establish a novel method for modeling TOSPDC and also highlight the potential of nonlinear resonant metasurfaces as compact free-space photon triplet sources with quantum state control.
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.