On SU(1,1) intelligent coherent states

Abstract

Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.

Q-Deformed SU(1,1) and SU(2) squeezed and intelligent states and quantum entanglement

“…and apply (6) to obtain the recurrence relation among the coefficients c n as fellow [14] α (n + 1)(n + 2k)c n+1 + β n(n + 2k − 1)c n−1 = 2ηc n .…”

Morse-like squeezed coherent states and some of their properties

“…For instance, intelligent states associated with the SU(1,1) dynamical group and some of their realizations are reviewed in Ref. [36], where the corresponding eigenvalue problem to be solved is established by using the raising and lowering generators K± for the said representation, namely,…”

su(3) intelligent states as coupledSU(3) coherent states

“…They were constructed for SU (2) using a nonunitary transformation by Rashid [2], and using polynomial states in [3]. For SU (1, 1) coherent states, the construction can involve solving recursion relations [4]. Properties of SU (2) and SU (1, 1) intelligent states have been used in the context of interferometry [5].…”

“…Although SU (3) Clebsch-Gordan (CG) technology can be quite formidable, the couplings we will require are of the simplest kind as we will restrict our discussion to states in representations of the type (λ, 0). The coupling method offers some distinct advantages over other possible constructions as it relies only on known special functions but not on recursion relations [4], and does not hinge on finding a suitable nonlinear transformation [2]. The coupling method is also immediately generalizable to higher groups once the appropriate coherent states have been found.…”