Tunneling dynamics between superconducting bound states at the atomic limit

A Yu-Shiba-Rusinov (YSR) state is a pair of protected in-gap levels generated by magnetic atoms on a superconductor. We are able to introduce YSR state of desired properties to the apex of a superconducting vanadium tip of a scanning tunneling microscope (STM) with a base temperature of 10mK, and then use this novel tip to tunnel into intrinsic YSR states on superconducting vanadium sample, thus studying the transport between YSR states, the Shiba-Shiba tunneling. As a realization of the fundamental tunneling process between two single levels, Shiba-Shiba tunneling features unusual sharp current peaks in the I(V) spectrum. By varying the conductance and tracing the evolution of the intensity of such peaks, we demonstrate a transition from sequential tunneling to emergent coherent tunneling from which we can extract the lifetime of YSR states directly. This paves the road for characterizing and manipulating coupled superconducting bound states, such as Andreev levels and Majorana bound states using STM.