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Physical Review A

Spatial-to-spectral mapping in spontaneous parametric down-conversion

Silvia Carrasco, Juan P. Torres, Lluís Torner, Alexander V. Sergienko, Bahaa E. A. Saleh, Malvin Carl Teich

Published Oct 21, 2004• 42 citations
Publisher

Abstract

We put forward an approach for manipulating the spectral profile of entangled photon pairs. Such spectral properties are mediated by the geometry of noncollinear spontaneous parametric down-conversion and by selecting the appropriate spatial profile of the pump laser radiation. We show that one can translate spatial features imprinted in the pump beam into desired spectral profiles of the generated entangled-photon state. Particular configurations suitable for generating entangled pairs with ultranarrow spectral width and with multiple-peaked spectra are demonstrated.

DOI
10.1103/physreva.70.043817

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We put forward an approach for manipulating the spectral profile of entangled photon pairs. Such spectral properties are mediated by the geometry of noncollinear spontaneous parametric down-conversion and by selecting the appropriate spatial profile of the pump laser radiation. We show that one can translate spatial features imprinted in the pump beam into desired spectral profiles of the generated entangled-photon state. Particular configurations suitable for generating entangled pairs with ultranarrow spectral width and with multiple-peaked spectra are demonstrated.
We experimentally demonstrate an approach for manipulating the spectral profiles of entangled-photon pairs. The spectral properties are determined by selecting both the appropriate spatial profile of the pump laser radiation and the geometry of the noncollinear spontaneous parametric downconversion. Both spectra, the spectrum of the individual signal and idler photons, and the joint spectrum of the entangled-photon pairs, can be modified at will over a substantial range of values. This technique is therefore expected to be useful for an array of quantum-optics applications.
We report a theoretical study of spatial and spectral profiles of twin photons generated with a pump beam having a partially spatially coherent nature. These profiles are simulated for both type-I and type-II spontaneous parametric down conversion in collinear and non-collinear configurations and found to be highly dependent on the choice of beam waist and transverse correlation length of the pump beam. It is found that by suitable selection of coherence length and size of the pump beam, the asymmetry in spatial geometry of down-converted photons and the spectral width can be modified. Owing to the partially spatially coherent nature, these biphoton beams might offer more robustness against losses compared to their fully coherent counterparts, and thus could yield a high success rate in free-space quantum communication and in quantum key distribution.
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.
In this work we study the transverse spatial correlation of the pair of photons generated via the process of spontaneous parametric frequency down-conversion, in periodically poled non-linear crystals illuminated by a pulsed laser beam. It is well known that the two-photon state generated in quasi-phase matching (QPM) configurations depends explicitly on the characteristics of the pump beam, on the crystal modulated non-linearity, and on the detection geometry. This has allowed the development of several techniques for controlling the biphoton spectral and spatial properties. Here we discuss another technique for implementing the spatial entanglement modification in QPM gratings. We show, theoretically and experimentally, that in nearly collinear geometries, the spatial shape modulation of the pump beam allows for the control of the biphoton transverse spatial correlation.