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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Parametric down-conversion with coherent pulse pumping and quantum interference between independent fields

Z. Y. Ou

Published Aug 1, 1997• 60 citations

Abstract

The process of parametric down-conversion pumped by a short coherent pulse is analysed. The coherence properties of the down-converted field are investigated. It is found that the spectrum of the down-conversion is mostly determined by the nonlinear medium and is independent of the width of the short pumping pulse and that it is impossible to realize a transform-limited two-photon state. Fourth-order interference between a weak coherent pulse and the down-converted pulse is considered. It is found that high visibility near 100% is achievable by means of narrow optical filtering. It is shown that by gating the detection on one of the down-converted photons, a transform-limited single-photon pulse is achievable in the other conjugate field, but its pulse width is shorter than that of the down-converted pulse and its peak position is uncertain within the pulse width of the down-converted light. However, with narrow optical filtering on the gating detection process, a transform-limited single-photon state can be obtained in the gated field with its peak position synchronized to the pump pulse. The possibility for the realization of a multi-photon interference experiment is explored for the quantum state measurement of the single-photon state.

DOI: 10.1088/1355-5111/9/4/009

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Theory and experiment of two-photon

lquot

direct

rquot

interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump

Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young’s double-slit experiment. In this experiment, a short focal length lens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.

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.

The generation of entangled states of three or more photons through the nonlinear process of spontaneous parametric down-conversion requires the use of a femtosecond pump to provide an indistinguishability of photon pairs generated from different nonlinear crystals. We demonstrate experimentally that the quantum interference between two photons generated in each of the nonlinear crystals will degrade significantly as the duration of the femtosecond pump pulse becomes shorter than the coherence time of the signal and idler photons. Spectral postselection using narrow-band filters compensates this effect at the expense of the photon flux available for detection.

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We present a theory for fourfold quantum interference of photons generated from independent spontaneous parametric down-conversion processes. Closed-form expressions for fourfold quantum interference patterns and visibility are found. The theoretical result for fourfold quantum interference patterns is in good agreement with experimental data reported. Detailed numerical calculations for the dependence of fourfold quantum interference visibility on experimentally controllable parameters are carried out. It is found out that higher visibility can be achieved for small biphoton width, short pump pulse coherence time, and narrow bandwidth of spectral filters. The optimal condition for obtaining at the same time higher fourfold interference visibility and intensity is also discussed.