We investigate ultrafast generation of spin-motion entanglement of a trapped and Gaussian-pulse-kicked two-level ion in the Lamb-Dicke limit and high field regime. A set of exact motional states and the probabilities occupying different pseudospin states are derived and the visible differences between the results with those of the delta-kick case are shown during a kick moment, which analytically evidence the ultrafast generation of an exact spin-motion entangled state regardless of initial state. Our results can be justified with the current experimental capability and provide an analytical method for further study of the ultrafast entanglement in atomic qubits.

We wish to point out and to correct a misprint in formula (3) of this paper where a factor 1 2 was missed. The correct expression for Eq. (3) should be, which governs the time evolution of the probability amplitudes. The factor 1/2 should also appear just before G(t) in Eq. (1) of this paper.This misprint does not affect the results and conclusions of the paper.