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ACTA PHOTONICA SINICA

Peremolov SU（1,1）相干叠加态的二阶量子关联特性研究

王晓光, 于荣金

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

本文首先讨论了Ｂａｒｕｔ－Ｇｉｒａｒｄｅｌｌｏ ＳＵ（１，１）相干叠加态在Ｂａｒｇｍａｎｎ指数Ｋ≠１／２时的二阶量子关联特性。发现随着Ｂａｒｇｍａｎｎ指数的增大，Ｂａｒｕｔ－Ｇｉｒａｒｄｅｌｌｏ奇相干态呈现反关联的区域变大。然后提出并研究了Ｐｅｒｅｍｏｌｏｖ ＳＵ（１，１）相干叠加态，Ｐｅｒｅｍｏｌｏｖ奇相干态可呈现反关联，并且随着Ｂａｒｇｍａｎｎ指数的增加，反关联程度变弱，反关联区域变小。

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•Jan 1, 1997•0 citations
本文首先讨论了Ｂａｒｕｔ－Ｇｉｒａｒｄｅｌｌｏ ＳＵ（１，１）相干叠加态在Ｂａｒｇｍａｎｎ指数Ｋ≠１／２时的二阶量子关联特性。发现随着Ｂａｒｇｍａｎｎ指数的增大，Ｂａｒｕｔ－Ｇｉｒａｒｄｅｌｌｏ奇相干态呈现反关联的区域变大。然后提出并研究了Ｐｅｒｅｍｏｌｏｖ ＳＵ（１，１）相干叠加态，Ｐｅｒｅｍｏｌｏｖ奇相干态可呈现反关联，并且随着Ｂａｒｇｍａｎｎ指数的增加，反关联程度变弱，反关联区域变小。
We display the relationship of Perelomov and Barut–Girardello coherent states associated with the discrete series of SU(1,1) by establishing the interwining operators. Both Perelomov and Barut–Girardello coherent states are deformations of Glauber coherent states of Heisenberg–Weyl group, but they approximate the latter from different sides and exhibit a certain duality. We also develop a symbol calculus of SU(1,1) algebra in terms of Barut–Girardello coherent states (Perelomov coherent states are not suitable for this purpose) and rederive the disentanglement (Baker–Campbell–Hausdorff) formula for SU(1,1) generators by the symbol calculus and parameter differentiation technique.
We define Schrödinger cat states as superpositions of q-deformed Barut–Girardello su (1, 1) coherent states with an adjustable angle φ in a q-deformed Fock space. We study the statistical properties of the q-deformed Barut–Girardello su (1, 1) coherent states and Schrödinger cat states. The statistical properties of photons are always sub-Poissonian for q-deformed Barut–Girardello su (1, 1) coherent states. For Schrödinger cat states in the cases φ = 0, π /2, π , the statistical properties of photons are always sub-Poissonian if φ = π /2, and the other cases are hard to determine because they depend on the parameters q and k. Moreover, we find some interesting properties of Schrödinger cat states in the limit | z | → 0, where z is the parameter of those states. We also derive that the statistical properties of photons are sub-Poissonian in the undeformed case where π /2 ≤ φ ≤ 3 π /2.
This paper concerns the construction of su(r + 1) Barut–Girardello coherent states in terms of generalized Grassmann variables. We first introduce a generalized Weyl–Heisenberg algebra A(r) (r≥1) generated by r pairs of creation and annihilation operators. This algebra provides a useful framework to describe qubit and qukit (k-level) systems. It includes the usual Weyl–Heisenberg and su(2) algebras. We investigate the corresponding Fock representation space. The generalized Grassmann variables are introduced as variables spanning the Fock-Bargmann space associated with the algebra A(r). The Barut–Girardello coherent states for su(r + 1) algebras are explicitly derived and their over-completion properties are discussed.