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Journal of Guangdong University of Education

Statistical Properties of a New-style Excited Pair Coherent State

Jiang Jun-qin

Published Jan 1, 2012• 0 citations
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Abstract

A new-style excited pair coherent state(a-1)m(b-1)m|ζ,q〉 is constructed by acting repeatedly inverse boson operator on pair coherent state.The violation of Cauchy-Schwatz inequality and the sub-Poissonian character are numerically studied for q=0.

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In this paper, the excited odd q-coherent state a +m qα o q and excited even q-coherent state a +m qα e q are constructed. The q and m dependences of mean photon number and sub-Poissonian character and antibunching effect are numerically studied. It is shown that when the q is far from 1, the second-order q-correlation function exhibits oscillating phenomenon, whose amplitude and period are independent of m; but the mean photon number and the Mandel Q q parameter increase greatly as m increases; and the sub-Poissonian character is not equivalent to the antibunching effect unless q→1.
We construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation dε(q,x)/dx=ε(q,qx) with 0⩽q⩽1 and ε(q,0)=1. We use this function in place of the usual exponential to generate new coherent states |q,z〉 from the vacuum, which are normalized and continuous in their label z. These states allow the resolution of unity, and a corresponding weight function is furnished by the exact solution of the associated Stieltjes moment problem. They also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally-ordered function of boson operators. We exemplify this by showing that the photon number statistics for these states is sub-Poissonian. For any q<1 the states |q,z〉 are squeezed; we obtain and discuss their signal to quantum noise ratio. The function ε(q,x) allows a natural generation of multiboson coherent states of arbitrary multiplicity, which is impossible for the usual coherent states. For q=1 all the above results reduce to those for conventional coherent states. Finally, we establish a link with q-deformed bosons.
The superposition of excited double-mode SU(2) coherent state |ψ=Cm(|M,ξ;m+ei|M,ξ*;m) is constructed and its quantum statistical properties are investigated with numeric method.The results exhibit that when the photons are added to the mode b of the double mode SU(2) coherent state,the two field modes can preserve anti-relation character,and presents a special effect of light amplification;the sub-Poissonian photon statistics properties of mode b is obvious enhanced and that of mode a is slightly weakened;anti-bunching effect of two modes of field are all enhanced,but as the quantum number of excitation m is increased,the anti-relation character of the two modes of field is weakened.