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arXiv · 1708.05103

Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras

Kevin Zelaya·Oscar Rosas-Ortiz·Zurika Blanco-Garcia·Sara Cruz y Cruz
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Abstract

The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to clarify the likely contradiction between the nonclassical properties of such nonlinear coherent states and the possibility of finding a classical analog for them since they are P-represented by a delta function. In (1) we prove that a class of nonlinear coherent states can be constructed to satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. This property automatically defines the delta distribution as the P-representation of such states. Then, in principle, there must be a classical analog for them. Among other examples, we construct a family of nonlinear coherent states for a representation of the su(1,1) Lie algebra that is realized as a deformation of the oscillator algebra. In (2), we use a beam splitter to show that the nonlinear coherent states exhibit properties like anti-bunching that prohibit a classical description for them. We also show that these states lack second order coherence. That is, although the P-representation of the nonlinear coherent states is a delta function, they are not full coherent. Therefore, the systems associated with the generalized oscillator algebras cannot be considered `classical' in the context of the quantum theory of optical coherence.

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Kevin Zelaya, Oscar Rosas-Ortiz, Zurika Blanco-Garcia, Sara Cruz y Cruz. 2017-11-22. Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras. https://doi.org/10.1155/2017%2F7168592

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