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Annual Meeting Optical Society of America

Effect of crystal length on the correlation times of downconverted photons

C. K. Hong, Z. Y. Ou, L. Mandeļ

Published Jan 1, 1986• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1986.tum8

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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.
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.
We present a theoretical and experimental analysis of the joint effects of the transverse electric field distribution and of the nonlinear crystal characteristics on the properties of photon pairs generated by spontaneous parametric downconversion (SPDC). While it is known that for a sufficiently short crystal the pump electric field distribution fully determines the joint signal–idler properties, for longer crystals the nonlinear crystal properties also play an important role. In this paper we present experimental measurements of the angular spectrum (AS) and of the conditional angular spectrum (CAS) of photon pairs produced by SPDC, carried out through spatially resolved photon counting. In our experiment we control whether or not the source operates in the short-crystal regime through the degree of pump focusing, and explicitly show how the AS and CAS measurements differ in these two regimes. Our theory provides an understanding of the boundary between these two regimes and also predicts the corresponding differing behaviors.
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.
In the process of spontaneous parametric downconversion, photons from a pump field are converted to signal and idler photon pairs in a nonlinear crystal. The reversed process, or upconversion of these pairs back to single photons in a second crystal, is also possible. Here, we present experimental measurements of the upconversion 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[1].
This chapter discusses two reported experiments in which the interference between signal and idler photons generated in the process of parametric down-conversion were investigated. Although two-photon interference effects have been treated theoretically before, it analyzes the two experiments in some detail to show how differences between the predictions of classical and quantum theories appear. The chapter compares the predictions of classical and quantum theories with the experimental results obtained. As practically all detectors of light rely on the photoelectric effect, in which a free electron is produced at the expense of a photon, the photon annihilation operator plays a key role in describing the measurement of light in the quantum theory. The time correlation between signal and idler photons produced in the parametric down-conversion process was first measured with a resolving time of about 10 nanoseconds. The interference effect can be made the basis of a measurement of the length of a photon wave packet with femtosecond time resolution.