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arXiv:quant-ph/0407113 · Physical Review A

Efficient fiber coupling of down-conversion photon pairs

Andrzej Dragan

Published Nov 12, 2004• 31 citations
arXivHTMLPDF

Abstract

We develop and apply an effective analytic theory of a noncollinear, broadband type-I parametric down-conversion to study a coupling efficiency of the generated photon pairs into single mode optical fibers. We derive conditions necessary for highly efficient coupling for single and double type-I crystal producing polarization entangled states of light. We compare the obtained approximate analytic expressions with the exact numerical solutions and discuss the results for a case of beta barium borate crystals.

DOI
10.1103/physreva.70.053814

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•Dec 7, 2016•0 citations
We develop and apply an effective analytic theory of a noncollinear, broadband type-I parametric down-conversion to study a coupling efficiency of the generated photon pairs into single mode optical fibers. We derive conditions necessary for highly efficient coupling for single and double type-I crystal producing polarization entangled states of light. We compare the obtained approximate analytic expressions with the exact numerical solutions and discuss the results for a case of beta barium borate crystals.
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A small, portable, high-flux correlated photon-pair source has been designed and constructed from simple opto-mechanical parts. Unique to this device is its straightforward alignment process, together with the direct coupling of signal and idler photons into polarization-maintaining single-mode optical fibers. Spontaneous parametric down-conversion is used to produce photon pairs in β-barium borate (BBO) at a center wavelength of 810 nm. Owing to the applied type-I phase-matching, coincident photons have identical polarization. The estimated fiber-coupling efficiency is 51%, the measured photon and coincidence flux are 636 and 130 kHz/mW, respectively, normalized to pump power (44 mW). The source has an extremely wide wavelength spectrum of 202-nm FWHM, measured at the fiber output, which limits the actual heralding ratio to 20%.
Sources of photon pairs based on the spontaneous parametric down-conversion process are commonly used for long-distance quantum communication and quantum information processing. The key feature for improving the range of transmission is engineering their spectral properties. Our analysis shows the way for full control of spectral correlation within a fiber-coupled photon pair. The result of extensive numerical simulations allows us to specify the settings for the generation of pairs featuring positive-energy correlation, which can potentially improve the signal-to-noise ratio in practical implementation of quantum communication protocols. We analytically and numerically analyze the characteristics of a source based on a $\ensuremath{\beta}$-barium borate crystal cut for type-II phase matching at the degenerated frequencies $755\phantom{\rule{4pt}{0ex}}\mathrm{nm} \ensuremath{\rightarrow}1550\phantom{\rule{4pt}{0ex}}\mathrm{nm}+1550\phantom{\rule{4pt}{0ex}}\mathrm{nm}$. The presented framework is general and can be applied to other crystals.
There are several problems that must be solved in order to increase the distance of quantum communication protocols based on photons as an information carriers. One of them is the dispersion, whose effects can be minimized by engineering spectral properties of transmitted photons. In particular, it is expected that positively correlated photon pairs can be very useful. We present the full characterization of a source of single photon pairs at a telecom wavelength based on type II spontaneous parametric down conversion (SPDC) process in a beta-barium borate (BBO) crystal. In the type II process, a pump photon, which is polarized extraordinarily, splits in a nonlinear medium into signal and idler photons, which are polarized perpendicularly to each other. In order for the process to be efficient a phase matching condition must be fulfilled. These conditions originate from momentum and energy conservation rules and put severe restrictions on source parameters. Seemingly, these conditions force the photon pair to be negatively correlated in their spectral domain. However, it is possible to achieve positive correlation for pulsed pumping. The experimentally available degrees of freedom of a source are the width of the pumping beam, the collected modes’ widths, the length of the nonlinear crystal and the duration of the pumping pulse. In our numerical model we use the following figures of merit: the pair production rate, the efficiency of photon coupling into a single mode fiber, the spectral correlation of the coupled photon pair. The last one is defined as the Pearson correlation parameter for a joint spectral distribution. The aim here is to find the largest positive spectral correlation and the highest coupling efficiency. By resorting to the numerical model Ref. [1] we showed in Ref. [2], that by careful adjustment of the pump’s and the collected modes’ characteristics, one can optimize any of the source's parameters. Our numerical outcomes conform to the experimental results presented in Refs [3,4]. Here we investigate typical, experimentally available source parameters: the widths of the pump beam and collected modes ranging from 20μm to 500m, the crystal length ranging from 1mm to 7.5mm while the pulse duration is set to 50fs, 100fs or 150fs. We achieve the correlation coefficient value as high as approximately 0.8, or – for different values of parameters – coupling efficiency equal to 0.76.