Tunnelling dynamics between superconducting bound states at the atomic limit

A magnetic impurity is placed on the tip of a scanning tunnelling microscope, allowing direct tunnelling between two Yu-Shiba-Rusinov bound states. This technique can probe and enhance the impurity state lifetime. There is a limit to the miniaturization of every process, and for charge transport this is realized by the coupling of two single discrete energy levels at the atomic scale. In superconductors, Yu-Shiba-Rusinov (YSR) states are such levels. Here, we place a magnetic impurity on the tip of a scanning tunnelling microscope (YSR-STM) and use it to demonstrate sequential tunnelling of electrons between parity-protected YSR states on the tip and in the sample. Using this Shiba-Shiba tunnelling technique we probe the YSR lifetime, which we can enhance by reducing the relaxation of the excited YSR state to the intrinsic channel. Our work offers a way to characterize and manipulate coupled superconducting bound states, such as Andreev levels, YSR states or Majorana bound states at the atomic limit.