Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion
arXiv:quant-ph/0407216 · doi:10.1103/PhysRevA.71.053812
Abstract
We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and non-maximally entangled pure states of first order Hermite-Gaussian modes.
9 pages, 4 figures. Corrections made as per referee comments, references updated. Submitted PRA
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