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Conference on Lasers and Electro-Optics

Nonclassical two-beam photon correlations in degenerate four-wave mixing

Roy S. Bondurant, Jeffrey H. Shapiro

Published Jan 1, 1985• 1 citation
Publisher

Abstract

The semiclassical theory of photodetection places well-established limits on the fluctuations seen in the outputs of photodetectors. Consider the semiclassical analysis of two identical quantum-efficiency η photodetectors Illuminated by two quast-monochromatic light beams of nominal frequency ν0 and randomly fluctuating powers P1(t) and P2(t).

DOI
10.1364/cleo.1985.thn5

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The semiclassical theory of photodetection places well-established limits on the fluctuations seen in the outputs of photodetectors. Consider the semiclassical analysis of two identical quantum-efficiency η photodetectors Illuminated by two quast-monochromatic light beams of nominal frequency ν0 and randomly fluctuating powers P1(t) and P2(t).
The usual formulations of the quantum and semiclassical theories of photodetection presume open-loop configurations, i.e., that there are no feedback paths leading from the output of the photodetector to the light beam impinging on that detector. In such configurations, the qualitative and quantitative distinctions between the quantum and semiclassical theories are well understood. In the quantum theory, photocurrent and photocount randomness arises from the quantum noise in the illumination beam, whereas in the semiclassical theory the fundamental source of randomness is associated with the excitations of the atoms forming the detector. Nevertheless, the quantum theory subsumes the semiclassical theory in a natural way.1
The usual open-loop quantum and semiclassical theories of light detection are extended to include closed-loop operation in which there is feedback from the detector to the source. It is shown that the unmistakable signatures of nonclassical light associated with open-loop detection, such as sub-shot-noise spectra and sub-Poisson photo-counts, do not carry over to closed-loopsystems. This behavior is illustrated through quantitatively indistinguishable quantum and semiclassical analyses of two recent closed-loop experiments in which sub-Poisson photocount statistics were produced. It turns out that if the open-loop illumination does not require the use of quantum photodetection theory, then neither does the closed-loop illumination. Conversely, if the open-loop illumination is nonclassical, then the closed-loop behavior must be analyzed quantum mechanically. The use of nonclassical field correlations to obtain light beams that give sub-Poisson open-loop photocounts from these closed-loop arrangements is discussed and generalized into a synthesis procedure for producing light beams with arbitrary open-loop photocount statistics.
A theoretical construct is presented for fourth-order interference between the signal and the idler beams of a parametric downconverter. Previous quantum treatments of fourth-order interference have employed correlated single-photon wave packets. The introduced approach, however, relies on Gaussian-state field correlations, which were previously used to characterize quadrature-noise squeezing produced by an optical parametric amplifier and nonclassical twin-beam generation in an optical parametric oscillator. Three principal benefits accrue from the correlation-function formalism. First, the quantum theory of fourth-order interference is unified with that for the other nonclassical effects of χ(2) interactions, i.e., squeezing and twin-beam production. Second, the semiclassical photodetection limit on Gaussian-state fourth-order interference is established; a purely quantum effect can be claimed at fringe visibilities substantially below the 50% level. Finally, both photon-coincidence counting (within the low-photon-flux regime) and intensity interferometry (in the high-photon-flux limit) are easily analyzed within a common framework.
An analysis is made of the process of measuring the parameters of a plane monochromatic light wave by mixing with a standard reference wave in a square-law photodetector. It is shown that the accuracy of measurements of the intensity, phase, frequency, and polarization of a plane light wave is consistent with the limitations derived from quantum field theory. In this case, fluctuations of the photocounts in the course of interaction between the photodetector and the reference wave are the physical cause of these limitations. It is established that, under threshold conditions, measurement of several parameters of a plane monochromatic light wave involves increasing its intensity in proportion to the number of parameters to be measured. An uncertainty relationship is found between the range of possible variation of the parameters to be measured and the dynamic range in which random errors predominate over systematic ones.
Although light quanta were known since the works by Planck and Einstein, for several decades after these works, there was no need to treat light quantum mechanically, and all experiments could be well explained using the quantum description of matter and classical description of light (the semiclassical approach). The situation changed with the development of sources of so-called nonclassical light, i.e., light whose properties cannot be understood in the framework of the semiclassical approach. Two simple examples can be given here. The first one is the suppression of shot noise in optical detectors. Shot noise, i.e., fluctuations of photocurrent scaling as the square root of the photocurrent mean value, can be, in principle, attributed to the discrete nature of the charge generated by the detector. At the same time, the effect of shot-noise suppression, which is observed with certain light sources (squeezed light) is clearly related to the statistics of light, and quantum mechanics is completely necessary for its description. Another example, which brings us closer to the subject of the present paper, is two-photon light. This type of light contains only pairs of photons (often called biphotons), and hence, a pair of properly aligned photon-counting detectors registering two-photon light, in an ideal case, will produce only simultaneous photocounts. This behavior, again, can only be explained in terms of a quantum-mechanical description for the light.