An Alternate Scheme to Mode-Lock Quantum Phase Slip Junctions

It has been proposed that locking the voltage oscillations of a Quantum Phase Slip Junction (QPSJ) to a microwave source could achieve the transfer of an integer number of elementary charges per microwave cycle. Such a synchronized transfer of charge would correspond to current steps in the current-voltage characteristic of the QPSJ, which could be used to realize a current standard. These proposals focus on realizing a circuit dual to the Josephson voltage standard and therefore require placing a QPSJ close to a resistor whose value is larger than the superconducting quantum of resistance. The observation of current steps for such a circuit is however extremely challenging experimentally, mostly due to the large Joule heating occurring in the resistor. To address this problem, we consider alternative designs that relax the constraint on the resistance and instead rely on the feedback provided by a high-impedance resonator. Through numerical simulations, we demonstrate that mode-locking indeed occurs in such systems and that synchronized charge transfer can be achieved in a resonant environment, without the need for a large resistor. Such a circuit may offer an alternative path toward the realization of a current standard.