Violation of Svetlichny inequality in Triple Jaynes-Cummings Models

We study the genuine tripartite nonlocality of some qubit states in a triple JCM. In this model, each atom state (A, B or C) was initially prepared with an independent cavity (a, b or c). By using two kinds of GHZ-like states as the atomic initial states, we investigate the genuine tripartite nonlocality as the time evolutions for the non-interaction three-qubit subsystems. We also study the genuine tripartite nonlocality of the subsystems by using the Svetlichny inequality. For the subsystems of three atoms ABC and three cavity modes abc, we show that they are genuinely nonlocal at certain period intervals of time. The states of all the other inequivalent subsystems satisfy the Svetlichny inequality for two types of GHZ-like states.