  We propose a scheme of stabilizing the persistent-current Rabi oscillation
based on the flux qubit-resonator-atom hybrid structure. The LC resonator
weakly interacts with the flux qubit and maps the persistent-current Rabi
oscillation onto the intraresonator electric field. This field is further
coupled to a Rydberg-Rydberg transition of the $^{87}$Rb atom. The
Rabi-frequency fluctuation of the flux qubit is deduced from measuring the
atomic population and stabilized via feedback controlling the external flux
bias. Our numerical simulation indicates that the feedback-control method can
efficiently suppress the background fluctuations in the flux qubit, especially
in the low-frequency limit. This technique may be extensively applicable to
different types of superconducting circuits, paving a new way to
long-term-coherence superconducting quantum information processing.
