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European Quantum Electronics Conference (EQEC)

Joint probability and conditional distribution of twin beams

Yun Zhang, Katsuyuki Kasai

Published Jan 1, 2003• 0 citations
Publisher

Abstract

Joint probability and conditional distribution of twin beams generated by an optical parametric oscillator is reported. We select the photon number fluctuation (intensity fluctuation) as our measured variable. In direct detection with a photodetector, given the high detection efficiency, the photocurrent fluctuation is corresponding to the photon number fluctuation.

DOI
10.1109/eqec.2003.1314237

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Joint probability and conditional distribution of twin beams generated by an optical parametric oscillator is reported. We select the photon number fluctuation (intensity fluctuation) as our measured variable. In direct detection with a photodetector, given the high detection efficiency, the photocurrent fluctuation is corresponding to the photon number fluctuation.
We give the intensity fluctuation joint probability of the twin-beam quantum state, which was generated with an optical parametric oscillator operating above threshold. Then we present what to our knowledge is the first measurement of the intensity fluctuation conditional probability distributions of twin beams. The measured inference variance of twin beams 0.62+/-0.02, which is less than the standard quantum limit of unity, indicates inference with a precision better than that of separable states. The measured photocurrent variance exhibits a quantum correlation of as much as -4.9+/-0.2 dB between the signal and the idler.
We present the results of an experiment in which we observed photon-number statistics of twin beams emerging from a nondegenerate optical parametric oscillator. We generated the photocurrent for recording by detecting the light and mixing it with a standard electrical oscillator. The measured photocurrent variances exhibited a quantum correlation of as much as -4.9 dB between signal and idler, whereas their photon number distributions were super-Poissonian. We also obtained the difference photon-number distribution.
Joint signal-idler photoelectron distributions of twin beams containing several tens of photons per mode have been measured recently. Exploiting a microscopic quantum theory for joint quasidistributions in parametric down-conversion developed earlier we characterize properties of twin beams in terms of quasidistributions using experimental data. Negative values as well as oscillating behavior in the quantum region are characteristic for the subsequently determined joint signal-idler quasidistributions of integrated intensities. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively.
The signal and idler beams from a non-degenerate, above threshold, optical parametric oscillator have a strong quantum correlation, which are called twin beams. This correlation arises from the simultaneous generation of the signal and idler photons in the form of twin pairs of photons through the parametric down conversion, and the generated twin beams have exactly the same photon statistics. As a result, the fluctuations on the difference between the intensities of the twin beams are reduced with respect to the shot noise limit, that is, intensity-difference squeezing. We give a comprehensive overview of the generation of twin beams using the optical parametric oscillator, and the applications exploiting the quantum correlation of twin beams are presented.
We investigated statistical fluctuations in the numbers of photons contained in the correlated twin photon beams generated by an optical parametric process. The coincidence between the signal- and idler-photoelectron pulses from a pair of avalanche photo-diodes was measured. The measured fluctuation in the number of signal-photons coinciding with idler-photons was equal to the standard deviation of a binomial distribution and was smaller than that of a Poisson distribution. We determined that even when the quantum efficiency of the photon detectors was much lower than unity, the uncertainty in the number of photons obtained with the twin photon beams was smaller, by a factor of 1/√2, than that with a classical light beam.
It has been recently shown theoretically1 and experimentally2 that nondegenerate optical parametric oscillators generate above threshold intense and highly correlated twin beams. More precisely, the noise on the difference between the intensities of the two beams is well below the shot noise for noise frequencies inside the cavity bandwidth. An application of this quantum correlation is to measure the intensity of one beam and use this information to correct the fluctuations of the other beam by optoelectronic means (photodiode, amplifier, and electrooptic modulator). The correction may be applied either on the pumping beam (feedback correction) or directly on the twin beam itself (feed-forward correction).