Spin and current variations in Josephson junctions

We study the dynamics of a single spin embedded in the tunneling barrier between two superconductors. As a consequence of pair correlations in the superconducting state, the spin displays rich and unusual dynamics. To properly describe the time evolution of the spin we derive the effective Keldysh action for the spin. The superconducting correlations lead to an effective spin action, which is nonlocal in time, leading to unconventional precession. We further illustrate how the current is modulated by this novel spin dynamics.