We consider the coherent control of a quantum bit by the use of short pulses
with finite duration \tau_p. By shaping the pulse, we perturbatively decouple
the dynamics of the bath from the dynamics of the quantum bit during the pulse.
Such shaped pulses provide single quantum bit gates robust against decoherence
which are useful for quantum information processing. We extend previous results
in two ways: (i) we treat frequency modulated pulses and (ii) we pass from
time-independent baths to analytically time-dependent baths. First and second
order solutions for \pi- and \pi/2-pulses are presented. They are useful in
experiments where amplitude modulation is difficult to realize.Comment: 10 pages, 6 figure
