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Physical Review A

Two Descriptions for the Photocounting Detection of Radiation Passed through a Random Medium: A Comparison for the Turbulent Atmosphere

Jan Peřina, Vlasta Peřinová, Malvin Carl Teich, Paul Diament

Published May 1, 1973• 37 citations
Publisher

Abstract

Two descriptions of light passed through a random medium (the turbulent atmosphere), as recently proposed by Diament and Teich and by Tatarski, are derived from a unified approach based on the coherent-state technique. The photon counting distributions for both descriptions are numerically compared for special states of the field (chaotic and coherent radiation and their superposition); it is found that these distributions lie very close to each other for non-vacuum-states while they precisely coincide for the Fock states.

DOI
10.1103/physreva.7.1732

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Two descriptions of light passed through a random medium (the turbulent atmosphere), as recently proposed by Diament and Teich and by Tatarski, are derived from a unified approach based on the coherent-state technique. The photon counting distributions for both descriptions are numerically compared for special states of the field (chaotic and coherent radiation and their superposition); it is found that these distributions lie very close to each other for non-vacuum-states while they precisely coincide for the Fock states.
There has been considerable interest in recent years in the statistical properties of optical frequency electromagnetic fields. Of particular interest is the study of photon bunching and the probability density for waiting time between adjacent photocounts. In this paper we derive an expression for the probability density of the time interval distribution as well as some other quantities of interest in photon bunching for the case where the incident radiation is comprised of superposed coherent and chaotic radiation of arbitrary spectral shapes. Calculations show that the key parameters are the average number of chaotic counts per coherence time and the ratio of the strengths of coherent and chaotic parts (signal-to-noise ratio).
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This paper is concerned with the determination of the quantum statistics of the photoelectric detection, and the E-field detection of multiple-mode superposed chaotic and coherent radiation. The Glauber P-representation is utilized extensively, and results are obtained by a fully quantum-mechanical treatment. The generating function, the mean, and the variance of the photocount statistics are derived for illumination times of arbitrary duration and for modes of arbitrary statistical interdependence. For short illumination times, the complete photocount distribution is obtained. The distribution has the same form as that for a single mode of superposed chaotic and coherent radiation. The multiple-mode distribution, however, is nonstationary. The difference between experimental determinations of the mean and variance which utilize periodic sampling and those which utilize random sampling is derived. A method for determining the P-representation for modulated fields is described, and the detection statistics are derived. The statistics of the E field are found to be Gaussian, and it is found that for multiple-mode classical statistics and quantum statistics differ.
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.
Quantum light propagation through turbulent atmosphere has become a subject of intensive research, spanning both theoretical and experimental studies. This interest is driven by its important applications in free-space quantum communication, remote quantum sensing, and environmental monitoring. At the same time, this phenomenon itself poses an intriguing fundamental problem. A consistent theoretical description typically makes explicit assumptions about the measurement scheme at the receiver station and/or the method of quantum-information encoding. A common and straightforward approach encodes the information in quantum states of a quasi-monochromatic mode, representing a pulsed Gaussian beam. Atmospheric turbulence induces random distortions of the pulse shape and, consequently, random fluctuations of the transmittance through the receiver aperture. These fluctuations, characterized by the probability distribution of transmittance (PDT), directly affect the quantum state of the received light. In this paper we examine various analytical models of the PDT, validate them through numerical simulations, and assess their range of applicability. Furthermore, we extend the analysis beyond the standard ensemble-averaging approach, recognizing that realistic experiments typically involve time averaging. This requires a detailed examination of the underlying random process, including the study of temporal correlations and their impact on nonclassical properties of electromagnetic radiation.