NOON state generation beyond the Lamb–Dicke limit in trapped-ion systems

In this paper, we show that multi-phonon NOON states can be generated in a two-dimensional anisotropic trapped-ion system. In the proposal, two laser pulses are applied to an ion along different directions in the ion trap plane to exchange the information between the external and internal states of the ion. Different from the previous frameworks, the proposal is outside the Lamb–Dicke regime. The distinct advantage of the proposed scheme is that the entanglement generation is deterministic and no measurement on the system is required. Numerical simulations show that the fidelity of the prepared entangled states is strongly affected by Lamb–Dicke parameters.