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Annual Meeting Optical Society of America

Observation of spatial beating at near optical frequencies in the interference of two photons

Z. Y. Ou, L. Mandeļ

Published Jan 1, 1988• 0 citations
Publisher

Abstract

An experiment has been performed in which signal and idler photons produced in the process of parametric downconversion are mixed at a beam splitter, and the mixed beam splitter outputs are directed to two photodetectors feeding a coincidence counter. Two optical filters with passbands centered at frequencies ω1, and ω2 are inserted just before the detectors. When the two-photon coincidence rate is measured as a function of the time delay δτ introduced between the two photons, it is found that the rate exhibits a cosine variation with δτ at the difference frequency |ω1− ω2|. The experimental results are consistent with a quantum analysis of the experiment but not with a classical treatment. We have observed a beat note with a period of 37 fs, which is several orders of magnitude shorter than the resolving time of the photodetectors. In principle a beat note should be observable at optical frequencies with this technique.

DOI
10.1364/oam.1988.ma6

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An experiment has been performed in which signal and idler photons produced in the process of parametric downconversion are mixed at a beam splitter, and the mixed beam splitter outputs are directed to two photodetectors feeding a coincidence counter. Two optical filters with passbands centered at frequencies ω1, and ω2 are inserted just before the detectors. When the two-photon coincidence rate is measured as a function of the time delay δτ introduced between the two photons, it is found that the rate exhibits a cosine variation with δτ at the difference frequency |ω1− ω2|. The experimental results are consistent with a quantum analysis of the experiment but not with a classical treatment. We have observed a beat note with a period of 37 fs, which is several orders of magnitude shorter than the resolving time of the photodetectors. In principle a beat note should be observable at optical frequencies with this technique.
When signal and idler photons produced in the process of parametric down-conversion are mixed together, and directed to two photodetectors that respond to nonoverlapping optical frequencies centered at ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$, it is found that the joint probability of two-photon detection exhibits a modulation of the form $cos({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})\ensuremath{\tau}$, where $c\ensuremath{\tau}$ is the path difference. The experimental results are well described by a simple quantum-mechanical analysis.
The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is observed in the correlation between the photodetections at the output ports of the beam splitter. The time dependence of the beat amplitude reflects the coherence properties of the photons. Most remarkably, simultaneous photodetections are never observed, so that a temporal filter allows one to obtain perfect two-photon coalescence even for nonperfect photons.
A new fourth-order interference experiment has been carried out and analyzed theoretically in classical and in quantum terms. Two photons produced in the process of parametric down-conversion provide the two inputs to a Mach-Zehnder type of interferometer, while two photodetectors coupled to a coincidence counter measure the output. The coincidence rate, after subtraction of accidentals, exhibits a cosine variation with the optical path difference, in agreement with quantum mechanics, but in disagreement with a classical analysis. By contrast, when two coherent light beams from a He:Ne laser are used as inputs to the interferometer, no fourth-order interference is observed.
Heterodyne interferometry uses beats produced by superposing two light waves with different frequencies at a photodetector. The output from the photodetector then contains a component at the beat frequency which can be processed to obtain information on changes in the optical path difference. We present experimental results which show that beats can be observed down to power levels at which the mean time interval between the arrival of photons at the photodetector is much greater than the transit time from the laser source to the detector and also when the mean time interval between photons is greater than the period of the beat. These results show that the beats are not due to the interference of one photon with another, but arise from a succession of single-photon events. It follows that measurements can be made even at extremely low photon fluxes by using homodyne detection and extending the integration time.
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.