|Title: ||Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras|
|Authors: ||Zelaya, K.|
Cruz y Cruz, S.
|Issue Date: ||2017|
|Citation: ||Adv. Math. Phys 2017 (2017) 7168592|
|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, theremust 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 beamsplitter to showthat 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.|
|Peer Review: ||SI|
|Appears in Collections:||FM - Artículos de revista|
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