Resonant enhancement of macroscopic quantum tunneling in Josephson junctions: Influence of coherent two-level systems

We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature T-cr the thermal fluctuations of the Josephson phase induce such a switching, and as T < T-cr the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of T-cr(Phi), where Phi is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of T-cr(Phi) occurring in the intermediate range of Phi, i.e., 0 < Phi < phi(0) (phi(0) is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.