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CRC Press eBooks

Nonclassical Effects in Parametric Downconversion

John Rarity, P. R. Tapster

Published Aug 12, 2020• 4 citations
Publisher

Abstract

In parametric downconversion the quantum effects arise because two photons are created from one pump photon. Detection of photons in one train can be used to modify the quantum statistics of the other train to produce antibunched and/or sub-poissonian light. This chapter reports on two experiments of this type. The first employs single photon detection techniques and a fast optical shutter to create antibunched and slightly sub-poissonian light. The second uses analogue detection and feedback to produce sub-poissonian light at picowatt power levels with a Fano factor of 0.78 over a limited bandwidth. Sub-poissonian light is potentially useful in finite dose transmission measurements and the high degree of temporal coincidence of the downconverted photon pairs can be exploited in absolute measurement of detector quantum efficiency. The detailed shape of the fourth order interference effect can be related to the fourier transform of the photon bandwidth determined by the phase matching uncertainty and aperture size.

DOI
10.1201/9781003069539-7

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In parametric downconversion the quantum effects arise because two photons are created from one pump photon. Detection of photons in one train can be used to modify the quantum statistics of the other train to produce antibunched and/or sub-poissonian light. This chapter reports on two experiments of this type. The first employs single photon detection techniques and a fast optical shutter to create antibunched and slightly sub-poissonian light. The second uses analogue detection and feedback to produce sub-poissonian light at picowatt power levels with a Fano factor of 0.78 over a limited bandwidth. Sub-poissonian light is potentially useful in finite dose transmission measurements and the high degree of temporal coincidence of the downconverted photon pairs can be exploited in absolute measurement of detector quantum efficiency. The detailed shape of the fourth order interference effect can be related to the fourier transform of the photon bandwidth determined by the phase matching uncertainty and aperture size.
Two novel methods of generating light with sub-Poissonian photon-counting statistics are described. Both methods are based on the use of parametric downconversion to generate two beams with simultaneously produced photons. By detecting the photons in one beam a knowledge of the time sequence of the photons in the other beam is obtained and used to modify the initially Poisson statistics. Expressions for the probability distribution functions of the two methods are derived and Fano factors are evaluated.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.
A two-photon state can be selected by coincidence detection of photon pairs created in parametric downconversion. We demonstrate a reduction in the coincidence-count rate when pairs of photons are combined in a beam splitter. This reduction occurs only when photon wave functions overlap and can permit accurate (subpicosecond) relative timing measurements. We relate the width of the coincidence reduction to the bandwidth of the downconverted light and thence to the detailed phase-matching conditions in the parametric downconversion crystal. We also demonstrate that the loss of coincidences is associated with an increased probability of detection of photon pairs in each output of the beam splitter.
Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.
The use of dead time effects to generate sub-Poissonion photo-electron counting statistics is discussed. An experiment is described in which dead times are introduced using an optical shutter triggered by photo-detection events. Although the triggering photo-electron train is sub-Poissonion and antibunched, the light sampled by a second detector gives rise to a super-Poissonion and bunched train of photo-elecrons. A second experiment is proposed which would generate truly sub-Poisson light (ie detector independent). This is based on the use of optical dead times in parametric fluorescence.