  In this paper, a scheme is put forward to design pulses which drive a
three-level system based on the reverse engineering with Lewis-Riesenfeld
invariant theory. The scheme can be applied to a three-level system even when
the rotating-wave approximation (RWA) can not be used. The amplitudes of pulses
and the maximal values of detunings in the system could be easily controlled by
adjusting control parameters. We analyze the dynamics of the system by an
invariant operator, so additional couplings are unnecessary. Moreover, the
approaches to avoid singularity of pulses are studied and several useful
results are obtained. We hope the scheme could contribute to fast quantum
information processing without RWA.
