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Quantum Electronics

Generation of triphotons upon spontaneous parametric down-conversion in a resonator

А. А. Калачев, Yu Z Fattakhova

Published Dec 31, 2007• 7 citations
Publisher

Abstract

The possibility of generating correlated three-photon states of light (triphotons) during spontaneous parametric down-conversion of light in a cubic medium in a resonator is analysed. It is shown that the number of photons per mode of the three-photon field is proportional to the square of the resonator finesse and the number of longitudinal resonator modes satisfying the triple resonance condition.

DOI
10.1070/qe2007v037n12abeh013671

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The possibility of generating correlated three-photon states of light (triphotons) during spontaneous parametric down-conversion of light in a cubic medium in a resonator is analysed. It is shown that the number of photons per mode of the three-photon field is proportional to the square of the resonator finesse and the number of longitudinal resonator modes satisfying the triple resonance condition.
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.
The problem of generating a narrow-band biphoton field during spontaneous parametric down conversion of light in a quadratic nonlinear medium in a cavity is discussed. It is shown that, in the case of double resonance (for signal and idle fields), the form of the single-photon wave packet is biexponential and has a half-width determined by the photon life time in the cavity. An experiment is carried out on the generation of narrow-band biphotons in a crystal of lithium iodine with I-type matching in a frequency degenerate collinear regime. The second-order correlation function of the cavity-enhanced biphotons is measured using the electric nanosecond time delay line.
We experimentally demonstrate how the two-photon field generated by spontaneous parametric down-conversion contains an intriguing fine structure associated with the positional spread within the photon pair. The obtained results provide a three-dimensional picture of the near-field correlations, which are determined by the phase-matching conditions. These correlations are compared with previous results on second-harmonic generation, spatial antibunching, and transverse entanglement in parametric down-conversion.
Creation of entangled photon pairs is one of the key topics in contemporary quantum optics. In the present article, we theoretically describe the generation of photon pairs in the process of spontaneous parametric down-conversion of light by a resonant spherical nanoparticle made of a dielectric material with bulk ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}}^{(2)}$ nonlinearity. We consider the nanoparticle size that satisfies the condition of excitation of resonant eigenmodes described by Mie theory. We demonstrate that a highly directional photon pair generation can be observed utilizing the nonlinear Kerker-type effect, and that this regime provides useful polarization correlations between the emitted photons.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the regime in which stimulation occurs at the single-photon level has hitherto remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by a weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we observe a clear enhancement that cannot be accounted for by spontaneous processes or accidental coincidences alone, and is consistent with stimulation involving the seed and the generated photon pair. These results provide time-domain evidence of seed-induced three-photon correlations and suggest new ways to engineer and probe multi-photon states for quantum imaging, sensing, and information processing.