Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion

S. P. Walborn, S. Pádua, C. H. Monken

Published 2004-07-27, updated 2005-02-22Version 2

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.