  For certain {\it specific} (or {\it"magic"}) Lamb-Dicke (LD) parameters,
Monroe {\it et al} showed [Phys. Rev. {\bf A 55}, R2489 (1997)] that a
two-qubit quantum operation, between the external and internal degrees of
freedom of a single trapped ion, could be implemented by applying a single
carrier laser pulse. Here, we further show that, such a two-qubit operation
(which is equivalent to the standard CNOT gate, only apart from certain phase
factors) could also be significantly-well realized for {\it arbitrarily}
selected LD parameters. Instead of the so-called "$\pi$-pulses" used in the
previous demonstrations, the durations of the pulses applied in the present
proposal are required to be accurately set within the decoherence times of the
ion. % We also propose a simple approach by using only one off-resonant (e.g.,
blue-sideband) laser pulse to eliminate the unwanted phase factors existed in
the above two-qubit operations for generating the standard CNOT gates.
