Finite-frequency noise in a quantum dot with normal and superconducting leads

We consider a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. We employ a diagrammatic real-time approach to calculate the finite-frequency current noise for subgap transport. The noise spectrum gives direct access to the internal dynamics of the dot. In particular the noise spectrum shows sharp dips at the frequency of the coherent oscillations of Cooper pairs between dot and superconductor. This feature is most pronounced when the superconducting correlation is maximal. Furthermore, in the quantum-noise regime, $\omega >k_{\text{B}}T,{\mu }_{\text{N}}$, the noise spectrum exhibits steps at frequencies equal to the Andreev addition energies. The height of these steps is related to the effective coupling strength of the excitations. The finite-frequency noise spectrum hence provides a full spectroscopy of the system.