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Physical Review Letters

Measurement of Time Delays in the Parametric Production of Photon Pairs

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

Published May 6, 1985• 201 citations
Publisher

Abstract

The spread in time intervals between the two photons produced in the process of spontaneous parametric down-conversion in a potassium dihydrogen phosphate crystal has been measured with a time resolution of the order of 100 psec. The correlation time is found to be independent of the coherence time of the pump photons or of the propagation time through the crystal, consistent with recent theoretical predictions.

DOI
10.1103/physrevlett.54.2011

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The spread in time intervals between the two photons produced in the process of spontaneous parametric down-conversion in a potassium dihydrogen phosphate crystal has been measured with a time resolution of the order of 100 psec. The correlation time is found to be independent of the coherence time of the pump photons or of the propagation time through the crystal, consistent with recent theoretical predictions.
We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.
In the process of spontaneous parametric down-conversion, photons from a pump field are converted to signal and idler photon pairs in a nonlinear crystal. The reversed process, or up-conversion of these pairs back to single photons in a second crystal, is also possible. Here, we present experimental measurements of the up-conversion rate with a controlled time delay introduced between the signal and idler photons. As a function of delay, this rate presents a full width at half maximum of 27.9 fs under our experimental conditions, and we further demonstrate that group delay dispersion of the photon pairs broadens this width. These observations are in close agreement with our calculations, thus demonstrating an ultrafast, nonclassical correlation between the signal and idler waves.
The quantum mechanical description of parametric fluorescence is the splitting of a single photon into two photons. This description has been verified by observing coincidences between photons emitted by an ammonium dihydrogen phosphate crystal pumped by a 325-nm He-Cd laser. The coincidence rate RC{R}_{C}RC​ decreases to the calculated accidental rate [<0.03RC(max)<0.03{R}_{C}(max)<0.03RC​(max)], unless the two detectors are arranged to satisfy energy and momentum conservation and have equal time delays.
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.
It was shown by Riedmatten et al. [J. Mod. Opt. 51 1637 (2004)] that two different four-photon states could be generated according to the relation between the duration time of the pump laser T and the coherence time t of the single photon from spontaneous parametric down-conversion (SPDC). In this paper, using four photons generated by the SPDC in a Periodically Poled Potassium Titanyl Phosphate (PPKTP), we experimentally observe the four-photon interference in a Michelson interferometer. All experimental results can be explained by the product of two independent two-photon interferences. Our experimental condition corresponds to the case of T ≫ t. This experiment clearly confirms the theory given by Riedmatten et al.
In spontaneous parametric down-conversion, pairs of photons are known to be created coherently and with equal probability over the entire length of the crystal. Then, there is no particular position in the crystal where a photon pair is created. We make the seemingly contradictory observation that the time delay between the photons in the pair depends on the distance from the crystal to the collection lens, as if the photons were actually collected preferentially from a particular position in the crystal. We resolve this contradiction by showing that the spatio–temporal correlations critically affect the temporal properties of the pair of photons. The theoretical model we present matches all our experimental results. We expect this to have important implications for experiments that require indistinguishable photons.