Higher-order nonclassical properties of nonlinear charge pair cat states

The concept of nonlinear charge pair cat states is introduced and their higher-order nonclassical properties are studied. By comparing the nonlinear cases of photon-added states f(2)(n) and a laser-driven trapped ion f(3)(n) with the linear case f(1)(n), it is shown that these states exhibit two-mode higher-order antibunching to all orders and the degree of antibunching depends on the suitable variables, especially on the nonlinear functions. We also show that in such states, the higher-order squeezing appears only in the even orders and the squeezing behaviours for the nonlinear cases f(2)(n) and f(3)(n) are quite opposite. These states are two-mode genuinely entangled regardless of the nonlinear functions and their entanglement properties are more obvious in the photon-added states f(2)(n) case.