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Physical Review A

Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium

Maria V. Chekhova, Olga A. Ivanova, V. Berardi, Augusto Garuccio

Published Aug 19, 2005• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.023818

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Physical Review A•Jul 20, 2007•33 citations
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.
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 report the complete measurement of the spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion pumped by a cw laser in both the collinear and the noncollinear regimes. The measurement includes the single-photon spectra as well as the two-photon joint spectra. Our results reveal interesting yet subtle differences between the collinear and the noncollinear regimes of frequency-degenerate type-I spontaneous parametric down-conversion. The single-photon and two-photon spectral measurements are in good agreement with the numerical simulation taking into account the tuning curve and the experimental geometry.
We investigate production of three-photon states in cascaded parametric down-conversion (PDC). The analysis includes preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. Considering cascaded optical parametric oscillator (OPO) driven by a sequence of laser pulses with Gaussian time-dependent envelopes, we investigate quantum statistical properties of high intensity mode generated in intracavity three-photon splitting. Calculating the normalized third-order correlation function below-and at the generation threshold, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.
Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion are studied theoretically and experimentally. For monochromatic pumping, the joint spectral intensity function for the photon pair is found to be symmetric even though each photon has a different central wavelength. The single-photon (first-order) interference shows the familiar triangular interferogram, usually associated with the cw-pumped frequency-degenerate type-II spontaneous parametric down-conversion. For broadband (ultrafast) pumping, on the other hand, the joint spectral intensity function is shown to be asymmetric, similar to the case of ultrafast-pumped frequency-degenerate type-II spontaneous parametric down-conversion. The spectral studies reported here are expected to play an important role in developing ultrabright two-color entangled photon sources.
We have studied the space-time entangled Stokes-anti-Stokes photons generated from a three-level system. In the presence of counterpropagating pump and control lasers, paired Stokes and anti-Stokes fields are spontaneously emitted into opposite directions. The two-photon wave packet is generally a convolution of the phase matching and the third-order nonlinear susceptibility and the feature of the joint temporal correlation is determined by either of them. When the phase matching plays a major role in determining the spectral width of biphotons, the two-photon interference exhibits as conventional type-II spontaneous parametric down-conversion (SPDC). However, if the spectral width of paired photons is determined by the third-order nonlinear susceptibility, two types of four-wave mixings (FWMs) destructively interfere and contribute to the two-photon coincidences. In such a case, the coincidence counting rate appears as a damped Rabi oscillation and exhibits the photon antibunching. The oscillation frequency is equal to the effective Rabi frequency. We have also discussed polarization-entanglement generation in a three-state case. It is found that if the phase matching is crucial in determining the properties of paired Stokes and anti-Stokes photons, the generated state is the same as the degenerate type-II SPDC. However, if the spectral width is mainly controlled by the resonant linewidths in the third-order nonlinearity, one can select one FWM to produce polarization-entangled biphotons, but paired photons from the other FWM process is nonpolarization entangled.