Quantum States of Heralded Photons
D. B. Horoshko, Stephan De Bièvre, Giuseppe Patera, Mikhail I. Kolobov · 2019
Summary form only given. In the last decades much attention has been attracted to the photon heralding technique [1], which consists in generating a photon pair in two modes and detecting a photon of one (idler) mode, preparing thus the other (signal) mode in a single-photon state. In this work we consider spontaneous parametric downconversion (SPDC) as a source of photon pairs and find the density matrix of the signal mode conditioned by a photon detection in the idler one. We take into account three physical parameters of the scheme: the degree of two-mode squeezing r produced by SPDC, the transmittance of the idler channel η, which includes the quantum efficiency of the photodetector, and the transmittance of the signal channel μ, see Fig. 1(a). We show that the conditional state of the signal mode is a weighted difference of two thermal states ρ(-)(q,p,γ) = \mathscrN ([(ρth (q))/(1-q)] - γ[(ρth(q p))/(1-qp)] ) = \mathscrN Σ∞n=0 (dn- γ(qp)n) |n 〉〈n |, (1).