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Effect of Aperture shape on Visibility of Quantum Cryptography System

Adawiya J. Haider, Azhar I. Hassan, Ali J. Addie

Published Mar 1, 2008• 0 citations
OpenAlex

Abstract

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

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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
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).
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.
Photon modes have an important role in characterizing the quantum sources of light. Proper coupling of various photon modes obtained in spontaneous parametric down conversion (SPDC) process in optical fibers is essential to generate an effective source of entangled photons. The two main pre-detection factors affecting the biphoton mode coupling in SPDC are the pump beam focusing parameter and the crystal thickness. We present the numerical and experimental results on the effect of pump focusing on conditional down-converted photon modes for a Type-I BBO crystal. We experimentally verify that biphoton coupling efficiency decreases asymptotically with pump beam focusing parameter. We attribute this behaviour to (a) the asymmetry in the spatial distribution of down-converted photons with the pump beam focusing parameter and (b) the ellipticity of biphoton modes introduced due to the focusing of the pump beam. We also show experimentally the ellipticity as well as quantify the asymmetry with the pump focusing parameter. These results may be useful in selecting optimum conditions in the down-conversion process for generating efficient sources of entangled photons for quantum information applications.
We have experimentally demonstrated two-photon interference between biphoton amplitudes arising from two well-separated pump pulses. It is important to note the following. 1) The pump pulse intensity was low enough so that single counting rates of the detectors were kept much smaller than pulse repetition rates: the probability of having one spontaneous parametric down conversion (SPDC) photon pair per pulse in our experiment is negligible. Hence the interference cannot be explained as two SPDC photons from two pump pulses (one SPDC photon pair from each pulse) interfering at the detectors. The two pump pulses simply provide two biphoton amplitudes which could result in coincidence counts, and interference occurs between these two biphoton amplitudes only when they are indistinguishable. 2) The BBO crystal in our experiment was only 100 /spl mu/m thick, so the two-pulse did not exist in BBO at the same time at any moment. 3) Due to the delays in the interferometer (/spl tau/ /spl tau//sub 1/), the signal-idler never met at the beamsplitter. Therefore, the existence of two-photon interference cannot be viewed as the interference between the signal and idler photons. These three points again emphasize the fact that it is the indistinguishability of the two-photon Feynman alternatives for the biphoton amplitudes which is responsible for the two-photon quantum interference effects.
Quantum computation and quantum communication require sources of entangled photons, especially from low-cost diode lasers. This study considered a polarization entangled photons pulse source produced via a spontaneous parametric down-conversion process in the type-I phase-matching of two nonlinear crystals, incorporating a continuous wave laser diode operating in pulse mode as a pump. The generated photons were measured based on visibility as a function of the pump frequency and collection apertures. A polarization correlation between photon pairs of approximately 93% and a Bell parameter S value of 2.56 ± 0.05 were obtained using the source described here.