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arXiv:1511.04159

The thick-crystal regime in photon pair sources

Brigitta Septriani, James A. Grieve, Kadir Durak, Alexander Ling

Published Nov 13, 2015• 1 citation
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Abstract

We present comprehensive measurement data on the pump and collection beam parameters necessary to achieve high collection efficiency ($89.0 \pm 1.7 \%$) together with high brightness when a single $β$-Barium Borate crystal is operated in the thick-crystal regime and pumped with a narrow linewidth laser source. Spectral analysis of the collinear, non-degenerate photons suggest that the effective interaction length within the crystal is dominated by the collection beam mode and the use of longer crystals with increased spatial walk-off does not necessarily lead to a reduced collection efficiency. This result is an important consideration for optical designers who seek to develop practical photon pair sources.

DOI
10.48550/arxiv.1511.04159

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We present comprehensive measurement data on the pump and collection beam parameters necessary to achieve high collection efficiency (89.0±1.7%89.0 \pm 1.7 \%89.0±1.7%) together with high brightness when a single βββ-Barium Borate crystal is operated in the thick-crystal regime and pumped with a narrow linewidth laser source. Spectral analysis of the collinear, non-degenerate photons suggest that the effective interaction length within the crystal is dominated by the collection beam mode and the use of longer crystals with increased spatial walk-off does not necessarily lead to a reduced collection efficiency. This result is an important consideration for optical designers who seek to develop practical photon pair sources.
The workhorse technique for generating correlated pairs of photons is based on spontaneous parametric downconversion in nonlinear crystals. These photon pair sources are usually designed with relatively short crystal lengths, in the belief that this is necessary to attain good performance. We show, contrary to common practice, that concurrent high brightness and efficiency are also available to longer crystals. We present comprehensive measurement data on the pump and collection beam parameters necessary to achieve high collection efficiency (89.0%±1.7% and 81.9%±3.7% for signal and idler) together with high brightness when a single thick β-barium borate crystal (15.76 mm) is pumped with a narrow linewidth laser. Spectral analysis of the collinear, nondegenerate photons suggests that the effective interaction length within the crystal is dominated by the collection beam mode, and the use of longer crystals with increased spatial walk-off does not necessarily lead to reduced collection efficiency. This surprising result is an important consideration for optical designers who seek to develop practical photon pair sources.
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.
Both correlated-mode coupling efficiency and photon pair flux (brightness) of spontaneous parametric down-conversion (SPDC) coupled into single-mode fibers are key parameters for various quantum information science applications. We present an experimental investigation on the optimization of the correlated-mode coupling efficiency and the brightness of frequency-degenerated SPDC photon pairs into single-mode optical fibers. Using photon pairs generated from a type-I phase-matched bulk $\ensuremath{\beta}$-barium borate crystal pumped by a continuous-wave laser, we carefully evaluated both the correlated-mode coupling efficiency and the brightness of SPDC light coupled to a single-mode optical fiber, while continuously changing the focusing of the pump and collection modes, experimenting with Rayleigh lengths from 3 to 280 (for the pump) and 0.2 to 20 (for the collection) times the crystal length. The measured data suggest that the correlated-mode coupling efficiency can be close to unity for any pump focus, however, the optimal Rayleigh length of the collection mode depends on the pump focus parameter, and the brightness can be increased by tightening the pump focus, provided that the Rayleigh length of the collection mode is precisely adjusted. A maximal correlated-mode coupling efficiency of $99.0\ifmmode\pm\else\textpm\fi{}1.3%$ was experimentally achieved. These results will be useful for photonic quantum science and technology using SPDC sources with high heralding efficiencies.
We present an optical design where polarization-entangled photon pairs are generated within two β\betaβ-Barium Borate crystals whose optical axes are parallel. This design increases the spatial mode overlap of the emitted photon pairs enhancing single mode collection without the need for additional spatial walk-off compensators. The observed photon pair rate is at least 65000 pairs/s/mW with a quantum state fidelity of 99.37±0.13%99.37\pm0.13\%99.37±0.13% when pumped with an elliptical spatial profile.