Exact theory for photon subtraction for fields from quantum to classical limit

Department of Biomedical Engineering and Computational Science, Helsinki University of Technology P.O. Box 9203, FIN-02015 HUT, Finland, EU

Corresponding author: tihayryn@lce.hut.fi

Received: 10 July 2009
Accepted: 7 August 2009

Abstract

Recently Parigi et al. (Science, 317 (2007) 1890) measured the statistics of a photon-subtracted and a photon-added thermal field. They showed that the measurements agree with the theoretical predictions of the beam splitter (BS) model. We show the equivalence of the quantum trajectory approach and the BS model in photon subtraction by deriving the BS model from the generalized photon counting operators. Our photon counting operators, corresponding to measurements using a resolving detector and a nonresolving detector, are generalization of the standard quantum jump approach. Our model is exact from weak quantum fields to the classical limit of strong fields. We show that our generalized photon counting operators reproduce exactly the results of the BS model when the reflection probability of the beam splitter is equated with the absorption probability of a photon in the standard quantum jump model of cavity field damping. Our theory can explain the recent experimental results of Parigi et al. and shows how similar experiments can be made to test the photon subtraction for the whole range of electromagnetic field intensities ranging from quantum to classical limit. We propose new experiments to test the generalized photon counting operators in the intermediate regime between the quantum and classical limits.