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Frontiers in Optics

Time-Resolved Upconversion of Entangled Photon Pairs

Kevin A. O’Donnell, Alfred B. U’Ren

Published Jan 1, 2009• 2 citations
Publisher

Abstract

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].

DOI
10.1364/fio.2009.pdpa8

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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].
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 process of upconversion in a nonlinear crystal involves the annihilation of two photons and the generation of a single photon with frequency given by the sum of the incident photon frequencies. In this paper we discuss recent work where we exploit the upconversion of two photonic modes, each of them generated by the process of spontaneous parametric downconversion, either from the same or different crystals. On the one hand, we describe an experiment where we exploit upconversion for the temporal characterization of photon pairs. On the other hand, we describe an experimental technique, which relies on the detection of an upconverted photon from two distinct photon-pair sources, which permits two photons that never interacted to become entangled in frequency.
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.
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.
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 present a simple treatment of the phenomenon of spontaneous parametric downconversion consisting of the coherent scattering of a single pump photon into an entangled photon pair inside a nonlinear crystal. The energy and momentum entanglement of the quantum state of the generated twin photons are seen as a consequence of the fundamental indistinguishability of the time and the position in which the photon pair is created inside the crystal. We also discuss some consequences of photon entanglement.