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

Proceedings of the Physical Society

Coherent intensity distributions from boson statistics

GORDON J. TROUP

Published Jul 1, 1965• 15 citations
Publisher

Abstract

The probability distributions of intensity for thermal and ideal laser beams are derived directly from the Bose-Einstein distribution for photons in phase space, using the correspondence principle. Thus the approach of Kastler is shown to yield the same result for the intensity distribution for an ideal laser as the work of Mandel.
DOI
10.1088/0370-1328/86/1/306

Related papers

Fluctuations in light beams: A simple student experiment

R. P. Wolf, Peter P. Crooker

Light emitted from a thermal source has a fluctuating intensity; these fluctuations are a direct illustration of the elementary principles of statistical and quantum physics. We describe here a student experiment demonstrating these ideas. First the probability density for the intensity of thermal light inhabiting s coherence volumes is derived, using the Bose–Einstein distribution for photons in phase space. Then a simple method is shown for measuring this probability density using a quasithermal light source and a multichannel analyzer. Data are presented and a scheme for fitting the data to the theory is outlined.

American Journal of Physics•May 1, 1982•1 citation

Photon-Counting Distributions of Modulated Laser Beams

Sebastian Fray, F. A. Johnson, Robin Jones +2 more

The first explicit experimental verification is given of Mandel's formula relating the photon-counting distribution of a radiation field to its intensity fluctuations. This was done by measuring the counting distributions obtained from a He-Ne gas-laser beam having superimposed square- and sine-wave modulations of various depths and frequencies.

Physical Review•Jan 10, 1967•34 citations

Fluctuations of Photon Beams: The Distribution of the Photo-Electrons

L. Mandeļ

The probability distribution p ( n , T ) of the number of counts n from a photoelectric detector illuminated by coherent light for a time T is studied, by associating photons stochastically with Gaussian random waves. The cumulants of the distribution are derived and it is shown to be of the expected form for a boson assembly in a limited volume of phase space. The distribution depends strongly on the degeneracy of the light beam. It approaches the Poisson form for classical particles at low degeneracies and the distribution characteristic of classical waves at high degeneracies. The analysis leads, incidentally, to an expression for the extent of the unit cell of phase space in the direction of the beam. It is argued that this should be adopted as the measure of coherence length.

Proceedings of the Physical Society•Sep 1, 1959•476 citations

Quantum statistics of a laser cooled ideal gas

J. I. Cirac, Maciej Lewenstein, P. Zoller

We study the dynamics of a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We show that the stationary state can be described by a Bose-Einstein or Fermi-Dirac distribution, respectively. Fluorescence from the system reflects quantum statistical properties.

Physical Review Letters•May 9, 1994•47 citations

Quantum Electrodynamics of Intense Photon Beams

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which $m$ photons are added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in $n$-photon states leading to the conclusion that for large $n$ such states are very much like classical statistical states with a given amplitude and evenly distributed phase.

Physical Review A•Dec 1, 1973•29 citations

Fluctuations of Photon Beams and their Correlations

L. Mandeļ

The distribution of counts from a photoelectric detector illuminated by light of bandwidth Δν 0 is analysed by associating the photons with Gaussian random waves. This is shown to lead to a full statistical description of the counts. It is shown that the number n T in a time interval T << 1/Δν 0 obeys pure Bose-Einstein statistics, and that the fluctuations in longer intervals T >> 1/Δν 0 are simply the density fluctuations of a boson assembly in a phase space of ~ Δν 0 T cells. The correlation coefficient ρ of the fluctuations of counts from two detectors illuminated by partially coherent beams is found to be proportional to the local time average of the square of the coherence function ⟨γ 12 2 ⟩. The correlation is shown to depend on the degeneracy of the beams in such a way that ρ → 2⟨γ 12 2 ⟩ for highly degenerate beams. The results are all consistent with those obtained by Hanbury Brown and Twiss in 1957.

Proceedings of the Physical Society•Dec 1, 1958•390 citations
Light emitted from a thermal source has a fluctuating intensity; these fluctuations are a direct illustration of the elementary principles of statistical and quantum physics. We describe here a student experiment demonstrating these ideas. First the probability density for the intensity of thermal light inhabiting s coherence volumes is derived, using the Bose–Einstein distribution for photons in phase space. Then a simple method is shown for measuring this probability density using a quasithermal light source and a multichannel analyzer. Data are presented and a scheme for fitting the data to the theory is outlined.
The probability distribution p ( n , T ) of the number of counts n from a photoelectric detector illuminated by coherent light for a time T is studied, by associating photons stochastically with Gaussian random waves. The cumulants of the distribution are derived and it is shown to be of the expected form for a boson assembly in a limited volume of phase space. The distribution depends strongly on the degeneracy of the light beam. It approaches the Poisson form for classical particles at low degeneracies and the distribution characteristic of classical waves at high degeneracies. The analysis leads, incidentally, to an expression for the extent of the unit cell of phase space in the direction of the beam. It is argued that this should be adopted as the measure of coherence length.
A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which mmm photons are added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in nnn-photon states leading to the conclusion that for large nnn such states are very much like classical statistical states with a given amplitude and evenly distributed phase.
The distribution of counts from a photoelectric detector illuminated by light of bandwidth Δν 0 is analysed by associating the photons with Gaussian random waves. This is shown to lead to a full statistical description of the counts. It is shown that the number n T in a time interval T << 1/Δν 0 obeys pure Bose-Einstein statistics, and that the fluctuations in longer intervals T >> 1/Δν 0 are simply the density fluctuations of a boson assembly in a phase space of ~ Δν 0 T cells. The correlation coefficient ρ of the fluctuations of counts from two detectors illuminated by partially coherent beams is found to be proportional to the local time average of the square of the coherence function ⟨γ 12 2 ⟩. The correlation is shown to depend on the degeneracy of the beams in such a way that ρ → 2⟨γ 12 2 ⟩ for highly degenerate beams. The results are all consistent with those obtained by Hanbury Brown and Twiss in 1957.