  Quantum systems are affected by interactions with their environments, causing
decoherence through two processes: pure dephasing and energy relaxation. For
quantum information processing it is important to increase the coherence time
of Josephson qubits and other artificial two-level atoms. We show theoretically
that if the coupling between these qubits and a cavity field is longitudinal
and in the ultrastrong-coupling regime, the system is strongly protected
against relaxation. Vice versa, if the coupling is transverse and in the
ultrastrong-coupling regime, the system is protected against pure dephasing.
Taking advantage of the relaxation suppression, we show that it is possible to
enhance their coherence time and use these qubits as quantum memories. Indeed,
to preserve the coherence from pure dephasing, we prove that it is possible to
apply dynamical decoupling. We also use an auxiliary atomic level to store and
retrieve quantum information.
