Deformed Gazeau-Klauder Schrödinger cat states with modified commutation relations

Abstract

Generalized coherent states under deformed quantum mechanics that exhibit intrinsic minimum length [Phys. Rev. D 86, 064038 (2012)PRVDAQ1550-799810.1103/PhysRevD.86.064038] and maximum momentum [Phys. Rev. D 88, 084009 (2013)PRVDAQ1550-799810.1103/PhysRevD.88.084009] have been well studied following the Gazeau-Klauder approach. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schrödinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schrödinger cat states (GKSCs) in [J. Phys. A 45, 244006 (2012)JPAMB51751-811310.1088/1751-8113/45/24/244006], we construct the deformed GKSCs for both phenomenological models that exhibit intrinsic minimum length and/or maximum momentum. All comparisons between minimum length and maximum momentum deformations are illustrated and plots are done in even and odd cat states since they are one of the most important classic statistical characteristics of SCs. Probability distribution and entropies are studied. In general, deformed cat states do not possess the original even and odd state statistical properties. Nonclassical properties of the deformed GKSCs are explored in terms of the Mandel Q parameter, quadrature squeezing (ΔXq)·(ΔYq), as well as Husimi quasiprobability distribution Q. Some of these distinguishing quantum-gravitational features may possibly be realized qualitatively and even be measured quantitatively in future experiments with the advanced development in quantum atomic and optics technology.