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Conference on Lasers and Electro-Optics

Spatial distinguishability of photons produced by parametric down-conversion with a focused pump

Ryan S. Bennink, Yun Liu, Duncan Earl, Warren P. Grice

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Focusing the pump in type-II SPDC not only increases the efficiency of photon collection with single-mode fibers, but also increases the spatial distinguishability of the photons, in some cases reducing the polarization entanglement.
DOI
10.1109/cleo.2006.4629147

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It is known that photons produced by spontaneous parametric down-conversion can be coupled into optical fibers more efficiently by focusing the pump field. We find that focusing the pump in type-II down-conversion causes photons of ordinary and extraordinary polarization to acquire very different angular spreads, which amounts to spatial information that distinguishes between the polarization states. Numerical studies predict that the photons collected by a detector or quantum channel will be of predominantly one polarization and that the degree of polarization entanglement will be lessened in some cases.
Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement. Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walk-off) of the two polarizations, along with a strong correlation between wavelength and emission direction. We also examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be accomplished by properly focusing the pump.
The challenge of optimizing the emission into single spatial modes of photons from spontaneous parametric down-conversion is addressed from the perspective of spatial entanglement. It is shown that single-mode coupling is most efficient in the absence of entanglement. Evidence of the relationship between spatial entanglement and pump focusing is revealed through experimental results, and numerical simulations show that spatial entanglement and single-mode coupling are optimized under nearly identical pump parameters.
We investigate the methods to obtain maximum correlated photon pairs generated in Type I spontaneous parametric down conversion (SPDC) with focused pump beam. We study the effect of pump focusing on the photon collection efficiency of signal and idler modes. The correlated photon pair collection efficiency decreases asymptotically with input pump beam focusing parameter [1]. The results obtained here are expected to be useful in designing appropriate optical fibers for generating efficient entangled photon sources for quantum information applications.