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

arXiv:1011.4402

A new quantum mechanical photon counting distribution formula

Hong-Yi Fan, Hong-Chun Yuan, Liyun Hu

Published Nov 19, 2010• 0 citations
arXivHTMLPDF

Abstract

By virtue of density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we find the photon counting distribution for the pure squeezed state relates to the Legendre function, which seems a new result.
DOI
10.48550/arxiv.1011.4402

Related papers

A new quantum mechanical photon counting distribution formula

Hong‐Chun Yuan, Hong-Yi Fan, Liyun Hu

By virtue of the density operator's P -representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we calculate photon counting distributions for some given light fields. It is found that the pure squeezed state's photon counting distribution is related to the Legendre function, which is a new result.

Chinese Physics B•Nov 1, 2011•4 citations

Coherent-State Representations for the Photon Density Operator

Kevin E. Cahill

The "diagonal" $P$ representation of the photon density operator in terms of the coherent states of the radiation field is studied. It is shown that the class of weight functions $P(\ensuremath{\alpha})$ required to represent all density operators by means of the $P$ representation is much larger than the class of all probability distributions and that therefore the analogy linking the use of the $P$ representation with certain classical stochastic techniques is useful only for a limited class of density operators. The class of density operators for which the $P$ representation is appropriate is shown to be limited in the sense that there are density operators that require weight functions so singular as to lie outside the class of all tempered distributions. Conditions on the weight function $P(\ensuremath{\alpha})$ under which the expectation values of the normal ordered operators ${({a}^{\ifmmode\dagger\else\textdagger\fi{}})}^{n}{a}^{m}$ assume a particularly simple integral form are presented. It is shown that if $P(\ensuremath{\alpha})$ is a tempered distribution, then these expectation values are given by a simple limiting process. A limited correspondence with classical optics is suggested by a formula for these expectation values. Conditions that a density operator must satisfy if its weight function is to be non-negative are presented and are shown to exclude all pure states except the coherent states themselves. The problem of representing an arbitrary operator in terms of the coherent states is studied. New measures of the completeness of the coherent states are established.

Physical Review•Jun 21, 1965•86 citations

New Form of Legendre Polynomials Obtained by Virtue of Excited Squeezed State and IWOP Technique in Quantum Optics

Fan Hong‐Yi, Meng Xiang-Guo, Ji‐Suo Wang

Using the technique of integration within an ordered product of operators and the intermediate coordinate-momentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.

Communications in Theoretical Physics•Nov 1, 2006•24 citations

Quantum mechanical photoncount formula derived by entangled state representation

胡利云, 王资生, Hong-Yi Fan

By introducing the thermo entangled state representation, we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas, which are convenient to calculate the photocount, can be expressed as integrations over a Laguerre—Gaussian function with a characteristic function, Wigner function, Q -function and P -function, respectively.

arXiv:1010.5555•Chinese Physics B•Aug 1, 2011•4 citations

Photon-counting distribution in squeezed states

Apostol Vourdas, Richard M. Weiner

We calculate the counting (multiplicity) distribution ${P}_{N}=〈N|\ensuremath{\rho}|N〉$ where $\ensuremath{\rho}$ is (i) the density matrix corresponding to a (pure) squeezed state and (ii) the density matrix of a superposition of squeezed states with thermal light. In the first case, we find that ${P}_{N}$ is an oscillating function of $N$. In the second case, this behavior, characteristic for squeezed states, disappears even for small amounts of noise.

Physical Review A•Dec 1, 1987•96 citations

Photoelectron Counting Probabilities for Non-classical Fields

Daniel F. Walls, Gerard J Milburn, H. J. Carmichael

The single-mode photoelectron counting formula derived using the Glauber-Sudarshan diagonal coherent state representation is generalised to fields for which no well behaved Glauber-Sudarshan P-distribution exists using the generalized P-representation. From this formula the photocount distributions for a number-state and a squeezed-state are calculated.

Optica Acta International Journal of Optics•Sep 1, 1982•7 citations
The "diagonal" PPP representation of the photon density operator in terms of the coherent states of the radiation field is studied. It is shown that the class of weight functions $P(\ensuremath{\alpha})$ required to represent all density operators by means of the PPP representation is much larger than the class of all probability distributions and that therefore the analogy linking the use of the PPP representation with certain classical stochastic techniques is useful only for a limited class of density operators. The class of density operators for which the PPP representation is appropriate is shown to be limited in the sense that there are density operators that require weight functions so singular as to lie outside the class of all tempered distributions. Conditions on the weight function $P(\ensuremath{\alpha})$ under which the expectation values of the normal ordered operators ${({a}^{\ifmmode\dagger\else\textdagger\fi{}})}^{n}{a}^{m}$ assume a particularly simple integral form are presented. It is shown that if $P(\ensuremath{\alpha})$ is a tempered distribution, then these expectation values are given by a simple limiting process. A limited correspondence with classical optics is suggested by a formula for these expectation values. Conditions that a density operator must satisfy if its weight function is to be non-negative are presented and are shown to exclude all pure states except the coherent states themselves. The problem of representing an arbitrary operator in terms of the coherent states is studied. New measures of the completeness of the coherent states are established.
We calculate the counting (multiplicity) distribution ${P}_{N}=〈N|\ensuremath{\rho}|N〉$ where $\ensuremath{\rho}$ is (i) the density matrix corresponding to a (pure) squeezed state and (ii) the density matrix of a superposition of squeezed states with thermal light. In the first case, we find that PN{P}_{N}PN​ is an oscillating function of NNN. In the second case, this behavior, characteristic for squeezed states, disappears even for small amounts of noise.