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arXiv:1110.4995 · Journal of Physics A Mathematical and Theoretical

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

Benjamin R. Lavoie, Hubert de Guise

Published May 30, 2012• 0 citations
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Abstract

We extend previous work on intelligent states and show how to construct su(3) intelligent states by coupling Su(3) coherent states. We also discuss some properties of the resulting states.
DOI
10.1088/1751-8113/45/24/244013

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The construction of su (2) intelligent states is simplified using a polynomial representation of su (2). The cornerstone of the new construction is the diagonalization of a 2 × 2 matrix. The method is sufficiently simple to be easily extended to su (3), where one is required to diagonalize a single 3 × 3 matrix. For two perfectly general su (3) operators, this diagonalization is technically possible but the procedure loses much of its simplicity owing to the algebraic form of the roots of a cubic equation. Simplified expressions can be obtained by specializing the choice of su (3) operators. This simpler construction will be discussed in detail.
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.