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, representing the field inside a cavity using oscillators arranged in a circle instead of a straight line, where increasing curvature corresponds to a smaller circle 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 analyze the time evolution of atom-field states and, based on this dynamic, 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 critical roles in controlling these nonclassical properties.