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arXiv:0710.2089 · Physical Review A

Tailoring polarization entanglement in anisotropy-compensated spontaneous parametric down-conversion

G. Brida, Marco Genovese, Maria V. Chekhova, Leonid A. Krivitsky

Published Jan 10, 2008• 7 citations
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Abstract

We show that the angular spectrum of type-II SPDC contains a continuum of maximally entangled states. For the realization of a bright source of entangled two-photon states, a standard technique is to compensate for the transverse walkoff in the production crystal. We demonstrate that polarization entangled states can be effectively engineered by generalizing this approach. Our method allows us to considerably enrich the set of generated entangled states with a controlled tailoring of them.

DOI
10.1103/physreva.77.015805

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We show that the angular spectrum of type-II SPDC contains a continuum of maximally entangled states. For the realization of a bright source of entangled two-photon states, a standard technique is to compensate for the transverse walkoff in the production crystal. We demonstrate that polarization entangled states can be effectively engineered by generalizing this approach. Our method allows us to considerably enrich the set of generated entangled states with a controlled tailoring of them.
We study the frequency-angular line shape for a phase-matched nonlinear process producing entangled states and show that there is a continuous variety of maximally entangled states generated for different mismatch values within the natural bandwidth. Detailed considerations are made for two specific methods of polarization entanglement preparation, based on type-II spontaneous parametric down-conversion (SPDC) and on SPDC in two subsequent type-I crystals producing orthogonally polarized photon pairs. It turns out that different Bell states are produced at the center of the SPDC line and on its slopes, corresponding to about half-maximum intensity level. These Bell states can be filtered out by either frequency selection or angular selection, or both. Our theoretical calculations are confirmed by a series of experiments, performed for the two above-mentioned schemes of producing polarization-entangled photon pairs and with two kinds of measurements: frequency selective and angular selective.
Spontaneous parametric down-conversion (SPDC) is one of the most widely used sources of polarization-entangled photon pairs, and understanding the generated biphoton state is essential for realizing high-brightness and high-purity entangled-photon sources. In particular, Type-II SPDC produces a biphoton wavefunction with a complex coupling between the spatial and polarization degrees of freedom owing to birefringence. In this study, we calculate the real-space distribution of the two-photon polarization state from the biphoton wavefunction of Type-II SPDC generated in a \b{eta}-barium borate (BBO) crystal. By identifying the spatial correlation direction between polarization and real-space coordinates, we designed aperture shapes that restrict the collection along this correlation direction. Through both numerical simulations and experiments, we demonstrate that such correlation-aligned apertures simultaneously achieve higher entanglement purity and improved photon collection efficiency. These results establish a practical design principle for optimizing aperture geometries based on the real-space biphoton wavefunction, providing a new approach to realizing high-purity and high-brightness SPDC entangled-photon sources.
We studied the broadband polarization entangled states generated within the linewidth of type-II spontaneous parametric down conversion (SPDC). Applying a complete quantum polarization tomography protocol at an arbitrary combination of frequency and angular sideband modes, we reveal the complex structure of non-degenerate non-collinear polarization-entangled states generated within the SPDC linewidth. We demonstrate that the simultaneous compensation of longitudinal and transverse walk-off leads to homogenization of the structure of polarization entanglement.