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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spectral and spatial effects in spontaneous parametric down-conversion with a focused pump

Warren P. Grice, Ryan S. Bennink, Zhi Gao Zhao, Kent A. Meyer, William Barclay Whitten, R. Shaw

Published Aug 1, 2008• 3 citations
Publisher

Abstract

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.

DOI
10.1117/12.795102

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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.
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.
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.
Spontaneous parametric down-conversion (SPDC) is a reliable and robust source of photons for quantum information applications. For applications that involve operations such as entanglement swapping or single-photon heralding, two-photon states are required to be factorable (uncorrelated) in their spectral and spatial degrees of freedom. We report the design and experimental characterization of an SPDC source that has been optimized for high spectral and spatial purity. The source is pumped by the 776 nm output of a mode-locked Ti:Sapphire laser and consists of a periodically-poled Potassium Titanyl Phosphate (PPKTP) crystal phase-matched for collinear type-II SPDC. The dispersive properties of PPKTP at these wavelengths is such that it is possible to minimize the spectral entanglement by matching the widths of the pump to the spectral phase-matching function. The spatial entanglement is minimized through careful control of the pump focus, yielding nearly single-mode emission. An advantage of this approach is that the emission rate into the collection modes is very high, resulting in a very bright SPDC source. We also report a scheme that employs the output of collinear sources such as these to produce polarization-entangled photon pairs. The scheme, which requires only simple polarization elements, can be scaled to N-photon GHZ states.
Optimizing the brightness of a spontaneous parametric down-conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wave function, generalizing previous known results, by considering collinear and noncollinear emission. We present analytical expressions for our results in the thin-crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is 1/21/\sqrt{2}1/2​ for collinear degenerate emission and approaches 1/21/21/2 for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\ensuremath{\beta}$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin-crystal regime.