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Journal of Al-Nahrain University-Science

Effect of Gaussian Aperture Width on Visibility for Different Crystal Length

Adawiya J. Haider, Muslm Fadhel J

Published Jun 1, 2011• 0 citations
Publisher

Abstract

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).

DOI
10.22401/jnus.14.2.14

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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).
The main goal in Quantum Cryptography is high security and this can be achieved by using single photon sources, thus we have studied the entangled photon source and how the coincident count rate and visibility could be affected by the optical elements of the system setup. 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 femto-second optical pulses. We have studied the visibility as a function of optical path delay for different parameters, such as the crystal length, aperture diameter, size and shape of the aperture The shape of interference pattern can be enhanced by using different shapes & sizes of aperture. So in the case of continuous wave ( CW )pumping, when using circular aperture the visibility is highest and symmetry shape occurs at lower aperture diameter (b=0.5mm). Asymmetry and wide dip pattern is occurred at larger aperture diameter (b=10mm), when using shifting ring, a negative peak was appeared. In case of pulsed pump asymmetry, 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 symmetric in horizontal with dimension (1x7) mm. All the results of this work are based on several numerical techniques and different programming codes. For example, adaptive Simpson quadrator method have been used to numerically evaluate the double integral in some equations. And adaptive Lobatto quadrator method has been used to numerically evaluate a single integrals. The later method is more efficient when required a high accuracy or a smooth integral
Summary form only given. By far the most efficient source of two-particle entangled state is spontaneous parametric downconversion (SPDC). Especially, cw laser pumped type-II SPDC has been widely treated as a good source of entangled photon pairs, since one can easily prepare a polarization Bell state. However, femtosecond pulse pumped type-II SPDC shows poor quantum interference visibility when a thick crystal is used. To restore the visibility, one has to use narrow-band spectral filters at the expense of available photon flux. We demonstrate a scheme for high-visibility two-photon interference with thick (3.4 mm.) type-II BaB/sub 2/O/sub 4/ (BBO) crystals in femtosecond pulse pumped SPDC. Polarization Bell states can be prepared using this method without spectral and amplitude post-selection.
We investigate quantum interference effects of entangled two-photon states generated in a nonlinear crystal pumped by femtosecond pulses. Attention is devoted to the effects of the pump-pulse profile (pulse duration and chirp) as well as those originating in second-order dispersion, both in the nonlinear crystal and in the optical elements through which the down-converted photons propagate. The characteristics of the pump pulse, along with the dispersion, influence on the visibility and the symmetry of the coincidence-count interference pattern. Nonlocal dispersion cancellation occurs in some cases.
We report on experimental measurements of coincidence and single particle spectral shapes of biphoton signals when frequency entangled states are generated by SPDC crystals pumped by short pulses.It is shown evidence for biphoton coincidence spectrum narrower and single-particle one wider than the pump spectrum, with a large contrast between coincidence and singles distributions.The investigation of biphoton correlations has been performed by fixing one monochromator at the maximal transmission wavelength on down-converted signal gate and scanning the one placed in the idler branch in order to observe the spectral distribution of single counts and coincidences.The degree of entanglement is evaluated by the ratio of the FWHM of single particle and coincidence distributions: the greater the ratio, the greater is the entanglement.The degree of entanglement in frequency variables can be very high: it increases linearly with the length of the crystal, and decreases with the growing pump pulse.
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.
Two spatially separated type-I nonlinear crystals are pumped by femtosecond laser pulses to create entangled photon pairs in the process of spontaneous parametric down-conversion. The two-photon entangled state exhibits high-visibility quantum interference for both polarization and space-time variables without the need of stringent spectral postselection by using narrow-band filters. The visibility is insensitive to the thickness of the crystals, unlike in the case of pulse pumped type-II parametric down-conversion; therefore the intensity can be easily increased by using thick nonlinear crystals. This method will be indispensable in experiments that require a pulsed source of entangled photon pairs, such as generation of multiphoton entangled states, quantum teleportation, and quantum communications.