The general q-oscillator algebra and its coherent states

Вадим Васильевич Борзов

Kevin Zelaya, Rosas-Ortiz, O., Blanco-Garcia, Z. +1 more

The purposes of this work are 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 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 -represented by a delta function. In 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 -function. This property automatically defines the delta distribution as the -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 Lie algebra that is realized as a deformation of the oscillator algebra. In , 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 -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.

Kevin Zelaya, Oscar Rosas-Ortiz, Zurika Blanco-Garcia +1 more

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.

Max A. Lohe, Lawrence C. Biedenharn

Phillial Oh, Chaiho P. Rim

Chi‐Fai Lo

In this paper we derive the coherent-state propagator of a generalized time-dependent parametric oscillator using the Lie algebraic approach. The method is simple and gives the same results as those obtained by the path integral approach. Furthermore, this Lie algebraic approach can be easily generalized to a time-dependent many-body system once the algebraic structure of its Hamiltonian is identified.