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 SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Generalized distribution of negative binomial states

Richard D’Souza, Adya Prasad Mishra

Published Oct 28, 1992• 0 citations
Publisher

Abstract

We present analytical expression for the s-parametrized quasiprobability distribution W((alpha) , (epsilon) , s) for the negative binomial states. As special cases, for s equals -1, 0, and 1, W((alpha) , (epsilon) , s) reduces to the Q-distribution, the Wigner distribution, and the Glauber-Sudarshan P-function, respectively.
DOI
10.1117/12.130401

Related papers

Quasiprobability distributions of negative binomial states

Richard D’Souza, Adya Prasad Mishra

We present the s-parametrized quasiprobability distributions for the negative binomial states. Marked changes in the quasiprobability distributions W(\ensuremath{\alpha},\ensuremath{\epsilon},s) are exhibited by states that are close to the random-phase coherent state (\ensuremath{\epsilon}=0), as the parameter s is varied continuously from s=-1, corresponding to the Q function, to s=1, corresponding to the P function. However, states close to the thermal-noise state (\ensuremath{\epsilon}=1) exhibit the usual Gaussian-like distributions for all values of s.

Physical Review A•May 1, 1992•4 citations

Series representation of quantum-field quasiprobabilities

H. M. Moya-Cessa, P. L. Knight

The Wigner and Glauber-Sudarshan P functions for quantum fields are usually defined in terms of integrals over the phase space of characteristic functions. We show that they and, in general, any s-parametrized quasiprobability distribution may be represented as a series in terms of displaced number states facilitating a straightforward evaluation.

Physical Review A•Sep 1, 1993•188 citations

Glauber-SudarshanPrepresentation of negative binomial states

Kuniaki Matsuo

The Glauber-Sudarshan P representation of negative binomial states is presented and its properties are discussed. It is shown that for the limiting cases the states approach the random-phase coherent state and the thermal noise state. Thus these states may allow a unified description of coherent and thermal states of the field. The two-dimensional representation of the P function is plotted on the complex-\ensuremath{\alpha} plane. The probability density function of waiting-time intervals between the arrivals of successive photons on a photodetector irradiated by a beam of the negative binomial light is also investigated.

Physical Review A•Jan 1, 1990•36 citations

Inverse problem in the P representation of negative binomial states

C Gray, R Srinivasan, Ching Tsung Lee

The moment problem for the P function of negative binomial states is solved. The explicit expressions for the P function are presented as an ordinary function as well as a distribution.

Inverse Problems•Dec 1, 1994•4 citations

Properties of Squeezed Binomial States and Squeezed Negative Binomial States

Amitabh Joshi, S. V. Lawande

The effect of squeezing on binomial states and on negative binomial states is studied in terms of second-order correlation functions and quasi-probabilities of Wigner and Q-functions. The photon number distribution of these states is also discussed. The results presented for squeezed binomial (negative binomial) states may be useful for studying a transition from squeezed coherent states to squeezed number (quasi-thermal) states.

Journal of Modern Optics•Oct 1, 1991•32 citations

Quasiprobability distributions in dispersive optical bistability

Karl Vogel, H. Risken

For the model of Drummond and Walls [J. Phys. A 13, 725 (1980)] describing dispersive optical bistability, the s-parametrized quasidistributions W(\ensuremath{\alpha},s) introduced by Cahill and Glauber [Phys. Rev. A 117, 1882 (1969)] are investigated. The equation of motion for W(\ensuremath{\alpha},s) generally has derivative terms up to third order. For the Q function (s=-1) and the P function (s=1) the third-order terms vanish. The equation of motion is then a pseudo-Fokker-Planck equation, i.e., a Fokker-Planck equation where the diffusion matrix is not positive definite or semidefinite. It is shown that the equation of motion with the inclusion of third-order-derivative terms can be solved by the matrix continued-fraction method. In particular, results for the Wigner function (s=0) are presented and compared with the results of the Q function (s=-1). Furthermore, the results are compared also with those obtained from the equation of motion for the Wigner function where the third-order-derivative terms have been neglected.

Physical Review A•May 1, 1989•70 citations
We present the s-parametrized quasiprobability distributions for the negative binomial states. Marked changes in the quasiprobability distributions W(\ensuremath{\alpha},\ensuremath{\epsilon},s) are exhibited by states that are close to the random-phase coherent state (\ensuremath{\epsilon}=0), as the parameter s is varied continuously from s=-1, corresponding to the Q function, to s=1, corresponding to the P function. However, states close to the thermal-noise state (\ensuremath{\epsilon}=1) exhibit the usual Gaussian-like distributions for all values of s.
The Glauber-Sudarshan P representation of negative binomial states is presented and its properties are discussed. It is shown that for the limiting cases the states approach the random-phase coherent state and the thermal noise state. Thus these states may allow a unified description of coherent and thermal states of the field. The two-dimensional representation of the P function is plotted on the complex-\ensuremath{\alpha} plane. The probability density function of waiting-time intervals between the arrivals of successive photons on a photodetector irradiated by a beam of the negative binomial light is also investigated.
For the model of Drummond and Walls [J. Phys. A 13, 725 (1980)] describing dispersive optical bistability, the s-parametrized quasidistributions W(\ensuremath{\alpha},s) introduced by Cahill and Glauber [Phys. Rev. A 117, 1882 (1969)] are investigated. The equation of motion for W(\ensuremath{\alpha},s) generally has derivative terms up to third order. For the Q function (s=-1) and the P function (s=1) the third-order terms vanish. The equation of motion is then a pseudo-Fokker-Planck equation, i.e., a Fokker-Planck equation where the diffusion matrix is not positive definite or semidefinite. It is shown that the equation of motion with the inclusion of third-order-derivative terms can be solved by the matrix continued-fraction method. In particular, results for the Wigner function (s=0) are presented and compared with the results of the Q function (s=-1). Furthermore, the results are compared also with those obtained from the equation of motion for the Wigner function where the third-order-derivative terms have been neglected.