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We consider a single ion confined in a trap under radiation of two travelingwaves of lasers. In the strong-excitation regime and without the restriction ofLamb-Dicke limit, the Hamiltonian of the system is similar to a drivingJaynes-Cummings model without rotating wave approximation (RWA). The approachwe developed enables us to present a complete eigensolutions, which makes itavailable to compare with the solutions under the RWA. We find that, the groundstate in our non-RWA solution is energically lower than the counterpart underthe RWA. If we have the ion in the ground state, it is equivalent to a spindependent force on the trapped ion. Discussion is made for the differencebetween the solutions with and without the RWA, and for the relevantexperimental test, as well as for the possible application in quantuminformation processing.

Lower ground state due to counter-rotating wave interaction in trapped ion system