Curvature-induced nonclassicality in a generalized Jaynes-Cummings model

In this paper, we investigate the influence of spatial curvature on the Jaynes-Cummings model. 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 curvedspace counterpart to the flat oscillator. We also propose an experimental scheme to realize this curvature-dependent Jaynes-Cummings model, 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.