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Journal of Russian Laser Research

Improving and Controlling Quantum Entanglement from Excited Barut–Girardello Coherent States via Unitary Beam Splitters

K. Berrada, M. A. Al-Rajhi

Published Sep 1, 2013• 3 citations
Publisher
DOI
10.1007/s10946-013-9370-7

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Barut–Girardello coherent states corresponding to the (l−m)- and (l+m)-integer discrete irreducible representations of su(1,1) Lie algebra are calculated by the spherical harmonics Ylm(θ,ϕ). Their explicit compact forms and also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtained in terms of the known functions. It is also shown that coherent states of both positive and negative representations separately lead us to construct new representation bases for su(1,1) Lie algebra. Then, it is shown that the su(1,1)-Barut–Girardello coherent states corresponding to two particles containing the spatial parity symmetries of a bipartite quantum system can be entangled in ten different ways.
In this paper, we construct photon-added f -deformed coherent states (PA f -DCSs) for nonlinear bosonic fields by discussing Klauder's minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m . Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PA f -DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.