  We analytically study the effects of periodically alternating magnetic fields
on the dynamics of a tight-binding ring. It is shown that an arbitrary quantum
state can be frozen coherently at will by the very frequent square-wave field
as well as the monochromatic-wave field when the corresponding optimal
amplitudes are taken. Numerical simulations show that the average fidelity
depends on not only the system parameters, but also the features of the quantum
state. Moreover, taking the initial zero-momentum Gaussian wave packets as
examples, we show the dependence of the threshold frequency on the width of the
packet for the given average fidelities. These observations provide a means to
perform the quantum state engineering.
