Higher dimensional quantum entanglement in a trapped three-level ion interacting with two laser beams in scheme is investigated beyond the Lamb-Dicke limit. It is shown that higher dimensional entanglement can be established in a single step, with a tunable dimensionality and duration via the Lamb-Dicke parameter.

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Our aim is to investigate the entanglement dynamics and quantum correlations of a full-trapped ion interacting with two time-independent laser beams in view of the Lamb-Dicke parameter. For this purpose, the three probability amplitudes in the trapped ion is taken as 1/3. Concurrence, negativity, and atomic Wehrl entropy of entanglement exhibit a long interacting time. We show that long survival is proved with these quantum measures.