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

Optica Acta International Journal of Optics

Photon Statistics of Non-classical Fields

Vlasta Peřinová, J. Křepelka, Jan Peřina

Published Oct 1, 1986• 20 citations
Publisher

Abstract

The photon statistics of radiation of a damped harmonic oscillator with an initial squeezed state are investigated. It is shown that a generalized model of the superposition of coherent and chaotic fields involving possibly negative noise is appropriate in this case. The influence of quantum damping can easily be recognized in this process. A relationship between sub-Poissonian statistics and squeezing is thoroughly discussed. A degenerate parametric process is related to the investigated model.

DOI
10.1080/713821872

Related papers

Quantum Statistics of Single-mode Processes Preserving Generalized Superposition of Coherent and Chaotic Fields

Vlasta Peřinová, A. Lukš, Przemyslaw Szlachetka

A unified approach to the quantum statistics of single-mode linear processes described by the general Fokker-Planck equation and the generalized initial superposition of coherent and chaotic fields is developed to reveal the common traits in the mathematical models of several quantum optical systems. Processes such as the degenerate parametric amplification and the harmonic oscillator eventually coupled to the thermal or rigged reservoir are involved as special cases. A sufficient condition for the validity of the master equation is formulated as its being formally independent of possible reservoirs. The dependence of non-classical phenomena such as the sub-Poisson photon statistics and squeezing on the drift and diffusion coefficients is discussed.

Journal of Modern Optics•Nov 1, 1989•15 citations

Quantum Statistical Properties of Coupled Nonlinear Oscillators with Losses

Jan Peřina, R. Horák, Z. Hradil +2 more

The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.

Journal of Modern Optics•May 1, 1989•11 citations

Electromagnetic field fluctuations and uncertainty relation for general quantum superpositions of coherent states

A. V. Kozlovskiĭ

Quantum statistical properties of general superpositions of coherent states of the type Nα,βα+eiξβ have been studied. Formulas for fluctuations (variances) of the coordinate and momentum quadratures and fluctuations of the number of photons in these states are obtained. The amplitude Nα,βnαeiφ+eiξnβeiφ,φ=φα=φβ and phase Nα,βneiφα+eiξneiφβ,n=nα=nβ superpositions of coherent states are considered separately. In the case of amplitude superpositions, a field under certain conditions occurs in a quadrature-squeezed state. At the same time, the photon distribution in the case of amplitude superpositions is always super-Poissonian. In the case of phase superpositions, a field under certain conditions occurs in quadrature-squeezed states for small average numbers of photons. For certain parameters of coherent states, the photon statistics in phase superpositions is sub-Poissonian. Using amplitude superpositions, it is possible to generate a microscopic electromagnetic field with the average photon number below or on the order of unity, as well as mesoscopic and even macroscopic fields with arbitrary large average photon numbers, characterized by significant quadrature squeezing. Using phase superpositions, it is possible to create under certain conditions the electromagnetic field states with sub-Poissonian statistics (squeezed distribution of photon numbers) for an arbitrary large average photon number. Expressions for a ‘strict’ coordinate–momentum uncertainty relation (Cauchy inequality) are obtained and analysed in cases of general, amplitude and phase superpositions of coherent states.

Journal of Modern Optics•Jun 28, 2016•3 citations

Quantum statistics of nonclassical radiation in dissipative forward four-wave mixing. I. Method of generalized superposition of coherent and chaotic fields

Vlasta Peřinová, J. Křepelka

The Fokker-Planck equation approach to forward four-wave mixing developing from the initial coherent states is adopted to obtain a set of recursive relations for the expectation values of the normally ordered field operators. This set of equations is closed, in accordance with the model of the generalized superposition of coherent and chaotic fields, to provide differential equations for unknown quantities in this model. A numerical solution of these equations enables one to determine the photon number distribution, its factorial moments, squeezing variances, and entropy of radiation under discussion. Fully quantum-mechanical features of radiation such as its sub-Poisson behavior and squeezing of vacuum fluctuations are preserved in this approach. The validity of this approximation is discussed and numerical results are provided.

Physical Review A•Apr 1, 1989•2 citations

SQUEEZING AND OTHER NON-CLASSICAL FEATURES IN k-PHOTON ANHARMONIC OSCILLATOR IN BINOMIAL AND NEGATIVE BINOMIAL STATES OF THE FIELD

Amitabh Joshi, S. V. Lawande

A systematic study of squeezing obtained from k-photon anharmonic oscillator (with interaction hamiltonian of the form (a†)kak, k ≥ 2) interacting with light whose statistics can be varied from sub-Poissonian to poissonian via binomial state of field and super-Poissonian to poissonian via negative binomial state of field is presented. We predict that for all values of k there is a tendency increase in squeezing with increased sub-Poissonian character of the field while the reverse is true with super-Poissonian field. We also present non-classical behavior of the first order coherence function explicitly for k = 2 case (i.e., for two-photon anharmonic oscillator model used for a Kerr-like medium) with variation in the statistics of the input light.

Modern Physics Letters B•Jan 20, 1990•2 citations

Sub-Poissonian Photon Statistics and Squeezed Quantum States

L. Mandeļ

The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.

•Jun 18, 1984•1 citation
The photon statistics of radiation of a damped harmonic oscillator with an initial squeezed state are investigated. It is shown that a generalized model of the superposition of coherent and chaotic fields involving possibly negative noise is appropriate in this case. The influence of quantum damping can easily be recognized in this process. A relationship between sub-Poissonian statistics and squeezing is thoroughly discussed. A degenerate parametric process is related to the investigated model.
A unified approach to the quantum statistics of single-mode linear processes described by the general Fokker-Planck equation and the generalized initial superposition of coherent and chaotic fields is developed to reveal the common traits in the mathematical models of several quantum optical systems. Processes such as the degenerate parametric amplification and the harmonic oscillator eventually coupled to the thermal or rigged reservoir are involved as special cases. A sufficient condition for the validity of the master equation is formulated as its being formally independent of possible reservoirs. The dependence of non-classical phenomena such as the sub-Poisson photon statistics and squeezing on the drift and diffusion coefficients is discussed.
Quantum statistical properties of general superpositions of coherent states of the type Nα,βα+eiξβ have been studied. Formulas for fluctuations (variances) of the coordinate and momentum quadratures and fluctuations of the number of photons in these states are obtained. The amplitude Nα,βnαeiφ+eiξnβeiφ,φ=φα=φβ and phase Nα,βneiφα+eiξneiφβ,n=nα=nβ superpositions of coherent states are considered separately. In the case of amplitude superpositions, a field under certain conditions occurs in a quadrature-squeezed state. At the same time, the photon distribution in the case of amplitude superpositions is always super-Poissonian. In the case of phase superpositions, a field under certain conditions occurs in quadrature-squeezed states for small average numbers of photons. For certain parameters of coherent states, the photon statistics in phase superpositions is sub-Poissonian. Using amplitude superpositions, it is possible to generate a microscopic electromagnetic field with the average photon number below or on the order of unity, as well as mesoscopic and even macroscopic fields with arbitrary large average photon numbers, characterized by significant quadrature squeezing. Using phase superpositions, it is possible to create under certain conditions the electromagnetic field states with sub-Poissonian statistics (squeezed distribution of photon numbers) for an arbitrary large average photon number. Expressions for a ‘strict’ coordinate–momentum uncertainty relation (Cauchy inequality) are obtained and analysed in cases of general, amplitude and phase superpositions of coherent states.
The Fokker-Planck equation approach to forward four-wave mixing developing from the initial coherent states is adopted to obtain a set of recursive relations for the expectation values of the normally ordered field operators. This set of equations is closed, in accordance with the model of the generalized superposition of coherent and chaotic fields, to provide differential equations for unknown quantities in this model. A numerical solution of these equations enables one to determine the photon number distribution, its factorial moments, squeezing variances, and entropy of radiation under discussion. Fully quantum-mechanical features of radiation such as its sub-Poisson behavior and squeezing of vacuum fluctuations are preserved in this approach. The validity of this approximation is discussed and numerical results are provided.
A systematic study of squeezing obtained from k-photon anharmonic oscillator (with interaction hamiltonian of the form (a†)kak, k ≥ 2) interacting with light whose statistics can be varied from sub-Poissonian to poissonian via binomial state of field and super-Poissonian to poissonian via negative binomial state of field is presented. We predict that for all values of k there is a tendency increase in squeezing with increased sub-Poissonian character of the field while the reverse is true with super-Poissonian field. We also present non-classical behavior of the first order coherence function explicitly for k = 2 case (i.e., for two-photon anharmonic oscillator model used for a Kerr-like medium) with variation in the statistics of the input light.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.