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arXiv:1404.3838 · The European Physical Journal D

Generalized su(2) coherent states for the Landau levels and their nonclassical properties

Alireza Dehghani, B. Mojaveri

Published Dec 1, 2013• 12 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2013-40550-2

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The Glauber minimum-uncertainty coherent states with two variables for Landau levels, based on the representation of Weyl-Heisenberg algebra by two different modes, have been studied about four decades ago. Here, we introduce new two-variable coherent states with minimum uncertainty relationship for Landau levels in three different methods: the infinite unitary representation of su(1, 1) is realized in two different methods, first, by consecutive levels with the same energy gaps and also with the same value for z-angular momentum quantum number, then, by shifting z-angular momentum mode number by two units while the energy level remaining the same. Besides, for su(2), whether by lowest Landau levels or Landau levels with lowest z-angular momentum, just one finite unitary representation is introduced. Having constructed the generalized Klauder-Perelomov coherent states, for any of the three representations, we obtain their Glauber coherency by displacement operator of Weyl-Heisenberg algebra.
In this paper, after a brief review on the entangled coherent state, a general form of the entangled nonlinear coherent state has been introduced based on the nonlinear coherent states approach. By choosing particular f-deformation functions, theoretical schemes for generation of two distinct classes of such states associated with SU(1,1) and SU(2) groups are presented. The entanglement characteristic of the corresponding entangled coherent states has been studied by evaluating the concurrence. In the continuation, other nonclassical behaviors of the produced states have been analyzed by investigating sub-Poissonian photon statistics, the oscillatory photon number distribution, one- and two-mode quadrature squeezing, and sum and difference squeezing. Accordingly, in addition to their entanglement property, other nonclassicality features of the introduced states are well established in detail.