Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras
Joint Authors
Zelaya, Kevin
Rosas-Ortiz, Oscar
Blanco-Garcia, Zurika
Cruz y Cruz, Sara
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-12-25
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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 antibunching 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.
American Psychological Association (APA)
Zelaya, Kevin& Rosas-Ortiz, Oscar& Blanco-Garcia, Zurika& Cruz y Cruz, Sara. 2017. Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1123284
Modern Language Association (MLA)
Zelaya, Kevin…[et al.]. Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras. Advances in Mathematical Physics No. 2017 (2017), pp.1-15.
https://search.emarefa.net/detail/BIM-1123284
American Medical Association (AMA)
Zelaya, Kevin& Rosas-Ortiz, Oscar& Blanco-Garcia, Zurika& Cruz y Cruz, Sara. Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1123284
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123284