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MRS Proceedings

General Photon Counting Model for Beam Splitters and Optoelectronic Devices

Teppo Häyrynen, Jani Oksanen, Jukka Tulkki

Published Jan 1, 2009• 1 citation
Publisher
DOI
10.1557/proc-1229-ll05-10

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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.
The first experimental verification of the Tersoff-Bayer interstatistics transition theory has been reported.1-3 A novel difference photon-counting method of detection, which reveals the field's particle fluctuations, is used to gain information on the beam splitting process of a highly Bose degenerate chaotic (and coherent) photon beam emitted from an ultrastable He-Ne laser. The splitting device consists of an electrooptic Pockels cell which acts as a stationary beam splitter or a chaotic beam splitter depending on the output properties of a driving noise generator. We found that the quantum Bose statistics in a splitting (i.e., scattering) process corresponds to a fully stochastic splitting process. This conclusion has been experimentally verified for two-way splitting and for general multichannel scattering induced by microscopic particles.
We consider a single-mode optical cavity field with simultaneous dissipative and amplifying couplings to a reservoir via a two-state system. In previous works, the reservoir has either solely absorbed energy (detector setup) or added energy (amplifying setup) to the cavity. In this work, we allow both interactions simultaneously and derive a reduced dynamic model for the optical field. Our model includes four physical parameters: the field-two-state system coupling γ, the excitation and de-excitation couplings of the two-state system to the reservoir λA and λD, respectively, and the mirror losses of the cavity C. We show that, depending on the parameters, our setup can operate as a detector, a light-emitting diode or a laser. We also consider single-photon subtraction and addition schemes based on beam splitters and calculate the output fields and the probabilities of the subtraction and addition events. Furthermore, we discuss which are the parameter regimes in which our model is equivalent to beam splitter-based schemes.