Curvature-induced nonclassicality in a generalized Jaynes–Cummings model

In this paper, we investigate the influence of spatial curvature on the Jaynes–Cummings model (JCM). We employ an analog model of general relativity, where the cavity field is represented by oscillators on a circle instead of a straight line, so that increasing curvature corresponds to decreasing the circle’s radius. We investigate the nonclassical features of this quantum system arising from the interaction between a two-level atom and a deformed harmonic oscillator on a circle, which serves as curved-space counterpart to the flat oscillator. We also propose an experimental scheme to realize this curvature-dependent JCM, based on the intensity-dependent Jaynes–Cummings interaction that appears in a laser-driven trapped ion inside a Kerr medium. By analyzing the time evolution of the atom-field system, we examine how spatial curvature influences the Mandel parameter, entropy, and the behavior of the Wigner distribution function. Our results demonstrate that the spatial curvature plays a crucial role in controlling these nonclassical properties.