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arXiv:0909.2007 · Physical Review Letters

Time-Resolved Up-Conversion of Entangled Photon Pairs

Kevin A. O’Donnell, Alfred B. U’Ren

Published Sep 18, 2009• 60 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.103.123602

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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].
Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.
Summary form only given. Entangled photons are the workhorse of quantum information technology and cryptography. So far, the emphasis has been on entanglement of the polarization state (for type II down conversion), or of the wave vectors of the degenerate signal and idler pair (for type I down conversion). A subject of current interest is entanglement in the spatial domain, i.e. nontrivial, spatially extended, correlation between signal and idler. A prime example of this being the discussion regarding the conservation and entanglement of orbital angular momentum in spontaneous parametric down conversion. We report our very first measurements of the signal-idler correlation in type I down conversion, employing a frequency-doubled femtosecond Ti:sapphire laser as our source of pump photons, and a fourth generation intensified CCD as our "multi-element single-photon detector" With pump pulses at /spl lambda/ = 400 nm of approximately 2 nJ energy and 250 fs duration directed at a 0.5 mm long BBO crystal we detect roughly one pair in every four frames.
An experimental study of the dispersion cancellation occurring in frequency-entangled photon pairs is presented. The approach uses time-resolved up-conversion of the pairs, which has temporal resolution at the femtosecond level, and group-delay dispersion sensitivity of $\ensuremath{\approx}20\text{ }\text{ }{\mathrm{fs}}^{2}$ under experimental conditions. The cancellation is demonstrated with dispersion stronger than $\ifmmode\pm\else\textpm\fi{}{10}^{3}\text{ }\text{ }{\mathrm{fs}}^{2}$ in the signal ($\ensuremath{-}$) and idler (+++) modes.
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.
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.