Partially coherent spontaneous parametric downconversion: Twisted Gaussian biphotons

Abstract

Partially coherent optical beams present phenomena that may not appear in perfectly coherent beams. In this regard, spontaneous parametric downconversion is an intriguing physical process, since the optical properties of the pump laser beam are transferred to the quantum properties of the down-converted photon pairs. Here, the authors study the transfer of twist phase, a novel property of the so-called twisted Gaussian Schell model beams, from a pump beam to down-converted photons. The authors show that a non-zero twist phase can lead to highly entangled yet highly mixed states. The correlations that appear in near/far-field intensity measurements, in the two-photon covariance matrix as well as in orbital angular momentum modes, are explored. The authors derive expressions for the purity of the two-photon state and relate it to the transverse spatial coherence of the pump beam. Their main results utilize a Wigner function formalism that can be applied to a number of scenarios involving partially coherent downconversion sources and contribute to the recent interest in spatially correlated photon pairs produced in mixed states, with possible applications in quantum communication and imaging.