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IEEE Journal of Quantum Electronics

A comparison of the information-gathering capacities of photon-correlation devices

H C Kelly

Published Dec 1, 1971• 17 citations
Publisher

Abstract

This paper will begin with a survey of the general problem of correlation spectroscopy. It will present a novel approach to the derivation of theN-time generating functions and will use these generating functions to compute the expected signals in four kinds of photon-correlation devices and the noise associated with these signals. The four devices treated are 1) the full digital correlator, 2) the gated digital correlator, 3) the multichannel analyzer, 4) the pulse-separation analyzer. We compare the information-gathering abilities of the four systems by showing how the quantity(1/T) (\Gamma/\sigma_{\Gamma})^{2}varies as a function of the number of channels used, the number of observed correlation times, the average count rate, and the gating levels. Here\Gammais the half-width of a Lorentz line,\sigma_{\Gamma}is the uncertainty in\Gammaas computed from a least-squares fit to the data, andTis the length of the experiment.

DOI
10.1109/jqe.1971.1076583

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This paper will begin with a survey of the general problem of correlation spectroscopy. It will present a novel approach to the derivation of theN-time generating functions and will use these generating functions to compute the expected signals in four kinds of photon-correlation devices and the noise associated with these signals. The four devices treated are 1) the full digital correlator, 2) the gated digital correlator, 3) the multichannel analyzer, 4) the pulse-separation analyzer. We compare the information-gathering abilities of the four systems by showing how the quantity(1/T) (\Gamma/\sigma_{\Gamma})^{2}varies as a function of the number of channels used, the number of observed correlation times, the average count rate, and the gating levels. Here\Gammais the half-width of a Lorentz line,\sigma_{\Gamma}is the uncertainty in\Gammaas computed from a least-squares fit to the data, andTis the length of the experiment.
Correlation between channels of the normalized photocount-rate correlation function g(2)(τ) becomes significant at high count rates and leads to a number of data-analysis problems. We derive an expression for channel correlation that is valid for a detector area of arbitrary extent and compare the theoretical predictions with measured values. A data-analysis procedure is demonstrated that employs the theoretical expression for channel correlation and provides a rigorous test of an assumed fitting function. The procedure facilitates the use of the cumulant method in determining the polydispersity of scatterers. An expression for the statistical bias of g(2)(τ) is also derived and compared with measured values.
An adequate analysis of photon correlation data requires knowledge about the statistical accuracy of the measured data. For the model of gamma-distributed intensities, that is including the effect of a finite intercept, the full covariance matrix is calculated for all the channels of the photon autocorrelation functions. A thorough discussion of multiple sample time correlation illuminates the importance of temporal averaging effects at large lag times. A practical estimation scheme is given for the noise in photon correlation data from a multiple sample time measurement.
Q uantum entanglement refers to the nonclassical dependency of physically separated quantum systems. It is an essential resource that must be freely available for implementing many of the novel functions of quantum information processing, such as database searching, clock synchronization, teleportation, computing and cryptography.1 The efficient generation and transmission of quantum entanglement is therefore of prime importance. With the ubiquitous standard optical fiber serving as the transmission medium and the widespread availability of efficient active and passive fiber devices, technological synergy between the generation and propagation components of the overall quantum network can be achieved by deploying sources of entanglement that rely on the nonlinearity of the fiber itself. Such fiber-based sources of quantum entanglement would also have the advantage of modal purity over their crystal counterparts,2,3 which is very important for realizing complex networks that involve many quantum operations. In our quest to develop fiber-based devices for quantum information processing, we have recently demonstrated an allfiber source of quantum-correlated photon pairs.4 The operating physical mechanism in this source is nondegenerate fourphoton mixing, wherein two pump photons scatter through the Kerr nonlinearity of the fiber to create simultaneous signal and idler photons. Our experiment is conducted near the zero-dispersion wavelength of standard dispersion-shifted fiber, where such scattering is enhanced owing to phase matching of the photon wave functions. It must be pointed out here that in a conventional wavelength-divisionmultiplexed classical optical communication line, one strives to suppress the fourphoton or four-wave mixing process, which otherwise causes cross talk between the wavelength channels and sets limits on the total data capacity of the communication line. In our experiment, the four-photon mixing takes place in a nonlinear-fiber Sagnac interferometer (NFSI), which we previously used to generate quantum-correlated twin beams in the fiber.5 The pump is a mode-locked train of ~3-ps-long pulses. The pulsed operation serves two important purposes: the NFSI amplifier can be operated at low average powers and the production of the signal/ idler fluorescence photons is confined to well-defined temporal windows, allowing use of a gated detection scheme to increase the signal-to-noise ratio. To measure the nonclassical (i.e., quantum) correlations between the signal and the idler photons, one must effectively suppress the pump photons from reaching the detectors. Since a typical pump pulse contains ~108 photons and we are interested in detecting ~0.01 signal (idler) photons/pulse, a pump-to-signal (idler) rejection ratio in excess of 100 dB is required. We achieved this specification by sending the fluorescence photons through a free-space double-grating spectral filter that separates the signal and idler photons from each other and from the pump photons not rejected by the NFSI. To demonstrate the quantum nature of the four-photon scattering at the single photon level, we assembled a photonFigure 1.C oincidence rates as a function of the single-photon rates in two different cases: signalidler fluorescence produced by a pump pulse (diamonds) and signal-idler fluorescence produced by two consecutive pump pulses (triangles). T he line represents the calculated accidental counts. T he inset shows a plot of the detected idler photons as a function of the injected pump photons (hollow circles). A second-order polynomial is shown to fit the experimental data. T he contributions of the dark counts, linear scattering and quadratic scattering are plotted separately as well. counting apparatus for detecting the signal and idler photons in coincidence. This apparatus is based on commercial InGaAs avalanche photodiodes operating in the gated Geiger mode.4 In the inset in Fig. 1, we show the number of scattered photons, NS, versus the number of pump photons, NP, injected into the NFSI. We fit the experimental data with a second-order polynomial fit, including the number of dark counts during the gate interval, ND. The fit clearly shows that the quadratic scattering ( ∝NP) in the fiber can dominate over the residual linear scattering ( ∝NP) of the pump, owing to imperfect filtering. The main body of Fig. 1 shows the coincidence-counting results. The diamonds represent the rate of coincidence counts versus the rate of the signal (idler) photons generated during the same pump pulse. The triangles represent the measured coincidence rate versus the signalphoton count rate when the signal is delayed with respect to the idler by one pulse period. For two independent photon sources, each with a count rate RS <<1, the accidental coincidence rate RC is given by RC = RS 2, regardless of the photon statistics of the sources. This quadratic relation is plotted as the solid line in Fig. 1, which fits the delayed-coincidence data (triangles) very well. These measurements show that while the fluorescence photons produced by the adjacent pump pulses are independent, those coming from the same pump pulse show a strong correlation, which is a signature of their non-classical behavior. This work was supported by the Department of Defense Multidisciplinary University Research Initiative program administered by the Army Research Office under Grants DAAD19-00-1-0177 and DAAD19-00-1-0469, and by the U.S. Office of Naval Research under Grant N00014-91-J-1268.
A one-meter-long high nonlinear photonic crystal fiber is pumped by laser pulse train at room temperature, and the generated correlated idler and signal photons are centred at 830 nm and 1411 nm, respectively. The full widths at half maximum of the broad band filters of the two channel are 15 nm and 35 nm, respectively. The fitting results of single channel photon counts reveal that almost all the photons originate from spontaneous four wave mixing and the influence of Raman scattering is eliminated. When the production rate is 0.0085 photon per pulse, the ratio between coincidence rate and accidental coincidence rate is measured to be 102, which not only confirms the low noise property of the photon pair, but also shows that the photon pair are naturally narrow band, and the collecting efficiency in our experiment is high. Moreover, these high purity photon pairs connect different optical bands, and have potential applications in quantum information technologies.
L’analyse des corrélations temporelles entre des photons se trouve au cœur des protocoles de traitement de l’information quantique (communication, métrologie et calcul) présentés dans ce dossier. Ces mesures de corrélation sont issues de techniques d’optique quantique fondamentale formalisées par R. Glauber en 1963 [Phys. Rev. 130, 2529] qui permettent de mesurer les propriétés des champs électromagnétiques et d’en détecter des régularités, des signatures dans un signal bruité. D’une façon plus générale, elles sont le résultat d’interférences d’ordre supérieur et sont, dans certains cas, directement reliées à la cohérence « classique » des champs optiques.