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Annual Meeting Optical Society of America

Intensity correlations in parametric downconversion

Stephen R. Friberg, C. K. Hong, L. Mandeļ

Published Jan 1, 1985• 0 citations
Publisher

Abstract

When a laser beam interacts with a nonlinear crystal, some of the incident photons fission into two lower frequency signal and idler photons through the process of spontaneous parametric downconversion. It is shown that, as a result of the strong positive correlation between signal and idler photons, the normalized intensity cross-correlation function λ12(τ) should be inversely proportional to the downconverted light intensity and ideally should be given by the inverse of the mean number of photons counted in the resolving time. This unusual relationship, which is a reflection of the quantum mechanical character of the downconverted optical field, has been confirmed in photoelectric counting measurements. The experiment makes use of the light from an argon-ion laser oscillating at 351.1 nm interacting with an 8-cm long crystal of KDP. The downconverted light is extracted at 633.5 and 788.0 nm in two directions that satisfy the phase-matching condition and is allowed to fall on two counting photomultipliers. The output pulses are fed to a time-to-digital converter that yields the cross-correlation function.

DOI
10.1364/oam.1985.tul4

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Journal of the Optical Society of America B•Feb 1, 1990•12 citations
When a laser beam interacts with a nonlinear crystal, some of the incident photons fission into two lower frequency signal and idler photons through the process of spontaneous parametric downconversion. It is shown that, as a result of the strong positive correlation between signal and idler photons, the normalized intensity cross-correlation function λ12(τ) should be inversely proportional to the downconverted light intensity and ideally should be given by the inverse of the mean number of photons counted in the resolving time. This unusual relationship, which is a reflection of the quantum mechanical character of the downconverted optical field, has been confirmed in photoelectric counting measurements. The experiment makes use of the light from an argon-ion laser oscillating at 351.1 nm interacting with an 8-cm long crystal of KDP. The downconverted light is extracted at 633.5 and 788.0 nm in two directions that satisfy the phase-matching condition and is allowed to fall on two counting photomultipliers. The output pulses are fed to a time-to-digital converter that yields the cross-correlation function.
A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.
Taking advantage of our previous experimental results and calculations that establish a new approach to the calibration of photo detectors using correlated photon pairs, we developed an experimental setup with a fast electronic control unit for the direct measurement of photon statistics. The most convenient source for generating such correlated photon pairs is a nonlinear optical process of spontaneous parametric down conversion (SPDC). When a photon of the pump beam is incident to a nonlinear crystal with phase matching condition, a pair of photons (signal and idler) is created at the same time. The photons are detected in the signal beam, and a controllable shutter is placed in the idler beam. When a detection event is made in the signal beam the fast optical shutter opens for a certain (pre-programmed) time. While the opening time of the shutter is adjustable with good time resolution, the time interval between the photons in the idler beam can be scanned, so the photon statistics can be determined.
We have investigated the question whether time delays between signal and idler photons produced in the parametric downconversion process depend on the length of the nonlinear medium. In an ideal fission process one might expect the correlation times to be independent of this length. Experiments were therefore carried out on KDP crystals of different lengths. The distribution of time delays was measured with the help of two microchannel plate photodetectors and a time-to-digital converter. Electronic transit time spreads in the detector were determined by use of a pulsed diode laser. As a major part of the observed spread of time delays (of the order of 100 ps) is due to the photomultipliers, length-dependent effects are derivable only from the difference between rather similar distributions. The derived time delay dispersion between signal and idler photons was found to be of the order of 100 ps in an 8-cm long crystal with 400-ps transit time, and there are indications that it is slightly smaller in a 1/2-cm long crystal of 25-ps transit time. The experimental results are compared to theoretical calculations based on a parametric coupling Hamiltonian, which indicate that crystal length should play a very small role, of the order of 1 ps, and then only when the relative acceptance bandwidth Δω/ω is ~1 % or greater.
Using a multidimensional Gaussian approximation of the wave function for the signal and idler light generated by spontaneous parametric down-conversion, we derive analytical expressions for the second-order coherence function and the fourth-order coherence function (which is proportional to the signal-idler photon coincidence rate). The magnitudes of these functions are expressed as products of Gaussian functions of the azimuthal angles, the polar angles, and the time delay. Their widths determine six parameters: the coherence angles and coherence time, and the entanglement angles and entanglement time. We show how these parameters are governed by the pump-beam waist, the pump spectral width, and the crystal length. We thereby derive relations analogous to the van Cittert--Zernike theorem and the Siegert relation for thermal light. We show that the normalized photon coincidence rate decreases sharply as the signal and idler apertures become mismatched or misaligned. We experimentally confirm this latter prediction by using parametrically down-converted light obtained from a LiIO3{\mathrm{LiIO}}_{3}LiIO3​ crystal pumped by Kr+{\mathrm{Kr}}^{+}Kr+-ion laser radiation at 413 nm. \textcopyright{}1996 The American Physical Society.
Measurements have been made of the rate at which signal photons are produced in a nonlinear crystal in the process of parametric downconversion, when a coherent light beam from a He:Ne laser is injected into the crystal in the direction of the conjugate-idler photons. The latter provides a stimulating field for the downconversion. When the phase matching condition inside the nonlinear medium is satisfied, the rate of downconversion is enhanced by the presence of the He–Ne laser beam by a factor of the form 1 + βIi, where li is the intensity of the He:Ne laser beam. The effect of defocusing either the pump beam or the He–Ne idler beam is investigated. Possible use of this phenomenon to study the photon amplifier with single-photon input will be discussed.
We investigate the theory of the process in which an idler photon emitted spontaneously from a nonlinear crystal in the process of parametric downconversion serves as idler input to a second downconverter. The signal photon from this second crystal is then detected in coincidence with the signal photon from the first crystal, which provides the time reference. We show that the first idler photon can induce a stimulated downconversion in the second crystal, which serves as a photon amplifier, and we calculate the ratio of the stimulated to the spontaneous emission probability.