Spin dynamics in tunneling decay of a metastable state

We analyze spin dynamics in the tunneling decay of a metastable localized state in the presence of spin-orbit coupling. We find that the spin polarization at short-time scale is affected by the initial state, while at long-time scale both the probability and the spin density exhibit diffraction-in-time phenomenon. We find that in addition to the tunneling time the tunneling in general can be characterized by a new parameter, the tunneling length. Although the tunneling length is independent of the spin-orbit coupling, it can be accessed by the spin rotation measurement.