Peremolov Su(1.1) coherent superposition states

Masashi Ban

Wang, X G

The ladder operator formalism of a general quantum state for su(1,1) Lie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Peremolov's coherent state is a su(1,1) nonlinear coherent state. The expansion and the exponential form of the nonlinear coherent state are given. We obtain the matrix elements of the su(1,1) displacement operator in terms of the hypergeometric functions and the expansions of the displaced number states and Laguerre polynomial states are followed. Finally some interesting su(1,1) optical systems are discussed.

Blagovest A. Nikolov, D. A. Trifonov

王晓光, 于荣金

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。

K. Berrada, M. El Baz, Y. Hassouni

Wang, X G, Pan, S H, Yang Guo Zhen

We study the non-classical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Peremolov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their non-classical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail.