Single-photon pump by Cooper-pair splitting

Hybrid quantum dot-oscillator systems have become attractive platforms to inspect quantum coherence effects at the nanoscale. Here, we investigate a Cooper-pair splitter setup consisting of two quantum dots, each linearly coupled to a local resonator. The latter can be realized either by a microwave cavity or a nanomechanical resonator. Focusing on the subgap regime, we demonstrate that cross-Andreev reflection, through which Cooper pairs are split into both dots, can induce nonlocal correlations between the two resonators. Harnessing these correlations allows to establish and control a nonlocal photon transfer between them. The proposed scheme can act as a photonic valve with single-photon accuracy, with potential applications for quantum heat engines and refrigerators involving mesoscopic resonators.