The exchange coupling between magnetic adsorbates and a superconducting
substrate leads to Shiba states inside the superconducting energy gap and a
Kondo resonance outside the gap. The exchange coupling strength determines
whether the quantum many-body ground state is a Kondo singlet or a singlet of
the paired superconducting quasiparticles. Here we use scanning tunnelling
spectroscopy to identify the different quantum ground states of manganese
phthalocyanine on Pb(111). We observe Shiba states, which are split into
triplets by magnetocrystalline anisotropy. Their characteristic spectral
weight yields an unambiguous proof of the nature of the quantum ground state.
Our results provide experimental insights into the phase diagram of a magnetic
impurity on a superconducting host and shine light on the effects induced by
magnetic anisotropy on many-body interactions