Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Photon Counting Statistics of Harmonic Signal Mixed with Thermal Light. I. Single Photoelectron Counting

A. K. Jaiswal, C. L. Mehta

Published Jul 1, 1970• 42 citations
Publisher

Abstract

In this paper, we consider the photoelectron counting distribution when the wave field incident on the detector is a mixture of harmonic signal and thermal noise. An expression for the factorial moment-generating function of the number of counts is obtained in terms of the eigenvalues of an associated integral equation. This expression is then used to evaluate the factorial cumulants of the number of counts. The results are valid for an arbitrary counting interval. The extension to photoelectron counting with several detectors is considered in paper II of the present investigation.

DOI
10.1103/physreva.2.168

Related papers

Photon Counting Statistics of Harmonic Signal Mixed with Thermal Light. II. N -Fold Photocounting

C. L. Mehta, A. K. Jaiswal

The one-detector photoelectron counting statistics of a harmonic signal mixed with thermal light was considered in paper I. In the present paper, we consider the extension to the counting statistics with several detectors. An expression for the factorial moment generating function of the number of counts is obtained in terms of the eigenvalues of an associated matrix integral equation. This expression is used to evaluate the factorial cumulants of the number of counts.

Physical Review A•Dec 1, 1970•6 citations

Onefold photoelectron-counting statistics of mixtures of thermal and coherent radiation

Richard G. Barakat

We consider onefold photoelectron-counting statistics, for arbitrary counting times, when the wave field on the detector is a mixture of thermal light of a specified spectral profile (incoherent component) and a harmonic signal (coherent component). The probability density function of the time-integrated intensity W(Ω) is obtained from the inverse Laplace transform of the moment-generating function by the Dubner–Abate algorithm. The corresponding probability distribution of the detected photoelectrons, P(m), is then evaluated directly by numerical integration of W(Ω). Numerical results for W(Ω) and P(m) have been obtained when the thermal line shape is Lorentzian for both the homodyne situation (coherent line coincides with the mean frequency of the thermal spectral profile) and the heterodyne situation (coherent line is now off center with respect to the mean frequency of the thermal spectral profile).

Journal of the Optical Society of America A•Apr 1, 1985•3 citations

Counting statistics of partial coherent light with Lorentzian spectrum

Chia Chang Shih

Analytic aspects of the photon-counting distributions in quantum optics are investigated for the case where the underlying field includes a mixture of harmonic signal and thermal noise. A Lorentzian spectral profile for the thermal light is used to find simple iterative relations for the factorial cumulant moments. Explicit analytic expressions for the moments are then given to eighth order. Approximate interpolation formulas, which display proper limiting behavior at small and large correlation length, are also investigated.

Physical Review A•Aug 1, 1989•3 citations

STATISTICS OF PHOTOCOUNTS OF A FIELD FORMED BY SUPERPOSITION

Nick Laskin, Александр Сергеевич Мазманишвили

We consider the photocount statistics of a field formed by superposition of a coherent signal of an arbitrary form, and the Brownian noise (Ornstein--Uhlenbeck process). We obtain an analytical expression for the generating function of photocounts. In the case of a harmonic coherent signal, we analyze the count statistics of the superposed field as a function of the shift of the carrier frequency of the harmonic signal relative to the maximum of the Lorentz spectral contour, as a function of the partial intensity components of the superposed radiation, and also as a function of the product of the duration of photodetection and the spectral line width of the noise. I. The aim of the present work is to derive and study a formula for the probability of counts under the assumption that the photodetector registers an optical field formed by the superposition of a coherent signal and Brownian noise. This problem is of interest in the study of the count distribution in a detector which absorbs a mixture of coherent and incoherent radiation [i]. In the derivation of the formula for the probability density of the number of counts, one encounters specific mathematical difficulties associated with the fact that the photodetection process is extended in time. The probability P(m, T) that, during a time interval T, m photoelectrons are detected when the superposition of a coherent signal B(t) and noise ~(t) falls on the detector, is given by the Mandel formula [2]

•Jan 1, 1985•0 citations

Photon-counting statistics of the subthreshold transient degenerate parametric oscillator

Reeta Vyas, A. L. DeBrito

Transient photoelectron-counting statistics of a degenerate parametric oscillator (DPO) operating below threshold are studied. A generating-function technique has been used and analytical expressions for photon-counting distribution, factorial moments, and waiting-time distribution have been derived. These results are compared with the steady-state results for the DPO and thermal light.

Physical Review A•Jul 1, 1990•8 citations

Computation of photoelectron counting distributions by numerical contour integration II Light with rational spectral density

Carl W. Helstrom

For a mixture of an arbitrary number of sinusoidal coherent components and chaotic light with a rational spectral density having simple poles, the probability-generating function h(z) of the number of photoelectrons ejected by the light in an interval is expressed in terms of certain finite determinants. It figures in the integrands of contour integrals in the complex plane for the cumulative and complementary cumulative distributions of the number of photoelectron counts. When these are evaluated by numerical integration, h(z) can be computed at each point on the contour by standard computer routines for solving algebraic equations and evaluating determinants, permitting precise and efficient computation of the photocount distributions.

Journal of the Optical Society of America A•Jul 1, 1987•3 citations
In this paper, we consider the photoelectron counting distribution when the wave field incident on the detector is a mixture of harmonic signal and thermal noise. An expression for the factorial moment-generating function of the number of counts is obtained in terms of the eigenvalues of an associated integral equation. This expression is then used to evaluate the factorial cumulants of the number of counts. The results are valid for an arbitrary counting interval. The extension to photoelectron counting with several detectors is considered in paper II of the present investigation.
We consider onefold photoelectron-counting statistics, for arbitrary counting times, when the wave field on the detector is a mixture of thermal light of a specified spectral profile (incoherent component) and a harmonic signal (coherent component). The probability density function of the time-integrated intensity W(Ω) is obtained from the inverse Laplace transform of the moment-generating function by the Dubner–Abate algorithm. The corresponding probability distribution of the detected photoelectrons, P(m), is then evaluated directly by numerical integration of W(Ω). Numerical results for W(Ω) and P(m) have been obtained when the thermal line shape is Lorentzian for both the homodyne situation (coherent line coincides with the mean frequency of the thermal spectral profile) and the heterodyne situation (coherent line is now off center with respect to the mean frequency of the thermal spectral profile).
Analytic aspects of the photon-counting distributions in quantum optics are investigated for the case where the underlying field includes a mixture of harmonic signal and thermal noise. A Lorentzian spectral profile for the thermal light is used to find simple iterative relations for the factorial cumulant moments. Explicit analytic expressions for the moments are then given to eighth order. Approximate interpolation formulas, which display proper limiting behavior at small and large correlation length, are also investigated.
We consider the photocount statistics of a field formed by superposition of a coherent signal of an arbitrary form, and the Brownian noise (Ornstein--Uhlenbeck process). We obtain an analytical expression for the generating function of photocounts. In the case of a harmonic coherent signal, we analyze the count statistics of the superposed field as a function of the shift of the carrier frequency of the harmonic signal relative to the maximum of the Lorentz spectral contour, as a function of the partial intensity components of the superposed radiation, and also as a function of the product of the duration of photodetection and the spectral line width of the noise. I. The aim of the present work is to derive and study a formula for the probability of counts under the assumption that the photodetector registers an optical field formed by the superposition of a coherent signal and Brownian noise. This problem is of interest in the study of the count distribution in a detector which absorbs a mixture of coherent and incoherent radiation [i]. In the derivation of the formula for the probability density of the number of counts, one encounters specific mathematical difficulties associated with the fact that the photodetection process is extended in time. The probability P(m, T) that, during a time interval T, m photoelectrons are detected when the superposition of a coherent signal B(t) and noise ~(t) falls on the detector, is given by the Mandel formula [2]
For a mixture of an arbitrary number of sinusoidal coherent components and chaotic light with a rational spectral density having simple poles, the probability-generating function h(z) of the number of photoelectrons ejected by the light in an interval is expressed in terms of certain finite determinants. It figures in the integrands of contour integrals in the complex plane for the cumulative and complementary cumulative distributions of the number of photoelectron counts. When these are evaluated by numerical integration, h(z) can be computed at each point on the contour by standard computer routines for solving algebraic equations and evaluating determinants, permitting precise and efficient computation of the photocount distributions.