  We propose a method for controlling the decoherence of a driven qubit that is
strongly coupled to a reservoir, when the qubit resonance frequency is close to
a continuum edge of the reservoir spectum. This strong-coupling regime is
outside the scope of existing methods of decoherence control. We demonstate
that an appropriate sequence of nearly abrupt changes of the resonance
frequency can protect the qubit state from decay and decoherence more
effectively than the intuitively obvious alternative, which is to fix the
resonance well within a forbidden bandgap of the reservoir spectrum, as far as
possible from the continuum edge. The "counterintuitive" nonadiabatic method
outlined here can outperform its adiabatic counterparts in maintaining a high
fidelity of quantum logic operations. The remarkable effectiveness of the
proposed method, which requires much lower rates of frequency changes than
previously proposed control methods, is due to the ability of appropriately
alternating detunings from the continuum edge to augment the interference of
the emitted and back-scattered quanta, thereby helping to stabilize the qubit
state against decay. Applications to the control of decoherence near the edge
of radiative, vibrational an photoionization continua are discussed.
