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arXiv:1010.5555 · Chinese Physics B

Quantum mechanical photoncount formula derived by entangled state representation

胡利云, 王资生, Hong-Yi Fan

Published Aug 1, 2011• 4 citations
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Abstract

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.

DOI
10.1088/1674-1056/20/8/084203

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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.
We show that the probability distribution pm,T of registering m photoelectrons can be explained in Thermo Field Dynamics theory as a matrix element of thermo entangling operator e1-ξa†a~† between ρ=∑mm,m~ρ and m,m~=mm~ where m~ is a fictitious Fock state. Based on this, the new integration formula for calculating pm,T, which involves both Laguerre polynomial and the characteristic function χη of ρ, is obtained. This provides us with convenience for evaluating photoelectric counting probability for various optical fields.
In this paper, we derive two new generating functions of Laguerre-polynomials, which look like the negative binomial theorem for the Laguerre function Lnx, by adopting the bi-partite entangled state representation and the operator-Hermite-polynomial HnX method, where X is the coordinate operator. Their application in investigating the density operator of photon loss of chaotic light is presented, and a new partition of Fock space in terms of the density operator of the negative binomial field is obtained. We also point out that the power-series definition of the Laguerre-polynomial originates from the Hermite polynomial. As a by-product, we derive a new Laguerre-polynomials-operator generating formula by virtue of the method of integration within an ordered product of operators.