Strong nonlocal tuning of the current-phase relation of a quantum dot based Andreev molecule

Recent realization of minimal Kitaev chains brought a breakthrough in Majorana research, which made arrays of quantum dots coupled by superconductor spacers the most promising synthetic quantum material for topological quantum architectures. In this paper, we investigate the basic building block of this platform—two dots coupled via a superconductor (referred to as an Andreev molecule)—in a configuration where two superconducting (SC) loops are created to tune the SC phase difference across the dots. This enables us to consider Coulomb interactions which was not possible in previously studied systems. We demonstrate that the Andreev molecule shows a strong nonlocal Josephson effect: As the dot in one junction is tuned, the current-phase relation (CPR) of the other dot is modified. This architecture hosts $0\text{−}\pi$ transitions and shows a tunable anomalous ${\phi }_0$ phase shift, nonlocally controlled in both cases, without relying on spin-orbit interaction or Zeeman fields used in previous studies. In addition, a significant SC diode effect and $\pi$-periodic CPRs can be observed. The presented nonlocal CPR can be used as a signature of the formation of an Andreev molecular state and in general to introduce ways to tune quantum architectures.