Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra

Abstract

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 Perelomov'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.

16 pages, no figures, accepted by Int. J. Mod. Phy. B

References in corpus (1)

• Negative Binomial States of the Radiation Field and their Excitations are Nonlinear Coherent States

Cited by in corpus (1)

• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)