  The pair breaking potential of individual magnetic impurities in s-wave
superconductors generates localized states inside the superconducting gap
commonly referred to as Yu- Shiba-Rusinov (YSR) states whose isolated nature
makes them ideal building blocks for artificial structures that may host
Majorana fermions. One of the challenges in this endeavor is to understand
their intrinsic lifetime, $\hbar/\Lambda$, which is expected to be limited by
the inelastic coupling with the continuum thus leading to decoherence. Here we
use shot-noise scanning tunneling microscopy to reveal that electron tunnelling
into superconducting 2H-NbSe$_2$ mediated by YSR states is ordered as function
of time, as evidenced by a reduction of the noise. Moreover, our data show the
concomitant transfer of charges e and 2e, indicating that incoherent single
particle and coherent Andreev processes operate simultaneously. From the
quantitative agreement between experiment and theory we obtain $\Lambda$ = 1
$\mu$eV $\ll$ $k_BT$ demonstrating that shot-noise can probe energy- and time
scales inaccessible by conventional spectroscopy whose resolution is thermally
limited.
