  Increasing and stabilizing the coherence of superconducting quantum circuits
and resonators is of utmost importance for various technologies ranging from
quantum information processors to highly sensitive detectors of low-temperature
radiation in astrophysics. A major source of noise in such devices is a bath of
quantum two-level systems (TLSs) with broad distribution of energies, existing
in disordered dielectrics and on surfaces. Here we study the dielectric loss of
superconducting resonators in the presence of a periodic electric bias field,
which sweeps near-resonant TLSs in and out of resonance with the resonator,
resulting in a periodic pattern of Landau-Zener transitions. We show that at
high sweep rates compared to the TLS relaxation rate, the coherent evolution of
the TLS over multiple transitions yields a significant reduction in the
dielectric loss relative to the intrinsic value. This behavior is observed both
in the classical high-power regime and in the quantum single-photon regime,
possibly suggesting a viable technique to dynamically decouple TLSs from a
qubit.
