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Journal of Optics B Quantum and Semiclassical Optics

Double-slit interference of biphotons generated in spontaneous parametric downconversion from a thick crystal

Ayman F. Abouraddy, Bahaa E. A. Saleh, Alexander V. Sergienko, Malvin Carl Teich

Published Feb 1, 2001• 18 citations
Publisher

Abstract

In this paper we investigate the fourth-order coherence of biphoton beams from spontaneous parametric downconversion resulting from a nonlinear crystal as exemplified in a double-slit interference configuration where the signal and idler beams both pass through the same double slits. We find that the angle of the crystal optical axis and the crystal length are important factors, along with the double-slit separation and system bandwidth, in determining the nature of the fourth-order interference pattern obtained behind the slits. Only careful planning of system parameters and understanding of the tuning curves of the downconversion will illuminate the obtained coincidence patterns.

DOI
10.1088/1464-4266/3/1/359

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In this paper we investigate the fourth-order coherence of biphoton beams from spontaneous parametric downconversion resulting from a nonlinear crystal as exemplified in a double-slit interference configuration where the signal and idler beams both pass through the same double slits. We find that the angle of the crystal optical axis and the crystal length are important factors, along with the double-slit separation and system bandwidth, in determining the nature of the fourth-order interference pattern obtained behind the slits. Only careful planning of system parameters and understanding of the tuning curves of the downconversion will illuminate the obtained coincidence patterns.
Fourth-order interference patterns of biphotons generated by type-I spontaneous parametric downconversion are examined for beams with partial angular and spectral entanglement, both for degenerate and nondegenerate constituent photons. Two-beam configurations using a single beam-splitter interferometer and a Mach-Zehnder interferometer are explicitly studied, as are four-beam configurations using pairs of beam splitters and Mach-Zehnder interferometers. The interference pattern generally comprises a number of harmonic functions of the path-length difference with frequencies and visibilities that usually depend on direction, and may have a finite or infinite duration (fourth-order coherence length). The relation between the visibility and the spectral indistinguishability of the two beams is established. Certain components of the interference pattern are independent of direction so that they are not washed out by the use of apertures of finite size.
Induced coherence without induced emission has been obtained, in Mandel's group, through the alignment of the idler beams produced by two nonlinear crystals in parametric downconversion processes. The interference resulting between the two spontaneous signal beams emitted by the crystals is explained by the relationship between degree of coherence and degree of indistinguishability. Although the quantitative understanding of this interference has yet to be understood, the degree of visibility obtained from those interference patterns reflects the phase correlation established between the signal emission of the two crystals in the spontaneous downconversion process. Those experiments have explored this nonclassical phenomenon by inserting absorbers in the idler connection path between the two crystals, by insertion of optical delays, and even by a topological modification of the connection path by Pancharatnam's or Berry's phase in the optical domain. In all the experiments performed to date, the variations introduced in the connection path deliberately decreased the degree of indistinguishability and, consequently, the degree of coherence.
The main goal in Quantum Cryptography is high security and this can be achieved by using single photon sources. The present work is a theoretical analysis devoted to investigate the interference pattern of biphoton amplitude generated by spontaneous parametric down conversion (SPDC) in a nonlinear crystal (BBO) pumped by femtosecond optical pulses. We have studied the visibility as a function of Gaussion aperture width for different parameters, such as the crystal length. The best visibility can be obtained at crystal length of (1.5 mm) . In our results, patterns occur and increase with increase of crystal length and decreasing aperture diameter. When using slit aperture (vertical and horizontal direction), the coincident count is more symmetry in horizontal with dimension (1×7) mm. With double crystal and parallel direction,the visibility decreases dramatically with increase in the Gaussian aperture width, while at a distance between crystals equal to (3mm) the visibility vanishes slowly at crystal thickness (L=0.5mm).