Curvature effects on stimulated parametric down-conversion process: an analog model

In this paper, we utilize an analog model of the general relativity and investigate the influence of spatial curvature on quantum properties of stimulated parametric down-conversion process. For this purpose, we use two-mode sphere coherent state as the input beams of the aforementioned process. These states are realization of coherent states of two-dimensional harmonic oscillator, which lies on a two-dimension sphere. We calculate the entanglement of output states of stimulated parametric down conversion process, measured by linear entropy, and show that it depends on the spatial curvature. So, by preparing the suitable two-mode sphere coherent states, it is possible to control the entanglement between the output states in the laboratory. In addition, we consider mean number and Mandel parameter of the output states of the process and also, their cross-correlation function, as the convince measures of non-classical behaviors.