  The impact of superconducting correlations on localized electronic states is
important for a wide range of experiments in fundamental and applied
superconductivity (SC). This includes scanning tunneling microscopy of atomic
impurities at the surface of superconductors, as well as
superconducting-ion-chip spectroscopy of neutral ions and Rydberg states.
Moreover, atom-like centers close to the surface are currently believed to be
the main source of noise and decoherence in qubits based on superconducting
devices. The proximity effect is known to dress atomic orbitals in
Cooper-pair-like states known as Yu-Shiba-Rusinov states (YSR), but the impact
of SC on the measured orbital splittings and optical/noise transitions is not
known. Here we study the interplay between orbital degenerescence and particle
number admixture in atomic states, beyond the usual classical spin
approximation. We model the atom as a generalized Anderson model interacting
with a conventional $s$-wave superconductor. In the limit of zero on-site
Coulomb repulsion ($U=0$), we obtain YSR subgap energy levels that are
identical to the ones obtained from the classical spin model. When $\Delta$ is
large and $U>0$, the YSR spectra is no longer quasiparticle-like, and the
highly degenerate orbital subspaces are split according to their spin, orbital,
and number-parity symmetry. We show that $U>0$ activates additional poles in
the atomic Green's function, suggesting an alternative explanation for the peak
splittings recently observed in scanning tunneling microscopy of
orbitally-degenerate impurities in superconductors. We describe optical
excitation and absorption of photons by YSR states, showing that many
additional optical channels open up in comparison to the non-superconducting
case. Conversely, the additional dissipation channels imply increased
electromagnetic noise due to impurities in superconducting devices.
