Quantum theory of an atom in proximity to a superconductor

TL;DR

This paper develops a quantum model of an atom near a superconductor, revealing how superconducting correlations influence atomic states, optical transitions, and noise, with implications for quantum devices and microscopy.

Contribution

It introduces a generalized Anderson model to analyze the interplay between atomic degeneracy and superconductivity, extending understanding beyond classical spin approximations.

Findings

YSR energy levels match classical models at U=0

Orbital degeneracy is split by interactions for U>0

Additional optical and noise channels are identified in superconducting environments

Abstract

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.