Flux transfer circuits breaking conventional limit in transfer coefficient based on a negative inductance of a -junction

We have demonstrated transfer coefficients breaking the conventional limit in flux transfer circuits (FTCs) by introducing a pi-phase-shifted Josephson junction (pi-junction), where the FTCs include an input/output inductor. According to the current-phase relationship of a pi-junction, the pi-junction behaves as an inductor with intrinsically negative kinetic inductance. When a single-pi-junction superconducting quantum interference device (pi-SQUID) in which a geometric inductor is placed in parallel with the pi-junction is formed, a current flowing on the inductor, that is, the internal flux is increased against an input current or an input flux supplied externally to the pi-SQUID in case that the pi-SQUID shows no hysteresis in characteristics of internal-external flux. The FTC under investigation (pi-FTC) is composed of two identical pi-SQUIDs sharing a pi-junction. The magnitude of the internal flux exceeds that of the external flux in the pi-SQUID near zero external flux. Using this effect, the transfer coefficients are expected to be increased in the pi-FTCs. Numerical analysis for pi-FTCs reveals that the transfer coefficients exceed the conventional limit in a wide range of input currents corresponding to the input flux, although the negative kinetic inductance depends on the magnitude of the input. We made several pi-FTCs for critical currents of the pi-junctions of 50 pi A and 60 pi A. The output flux was measured by constructing a flux-locked loop. The experimentally obtained ratios of the transfer coefficients of the pi-FTCs to the coefficient of the conventional FTC made on the same chip agree with the numerical results, which supports the negative kinetic inductances cause the increased coefficients breaking the conventional limit. Because the transfer coefficient is almost independent of input currents, we believe that the pi-FTCs are applicable for strengthening not only couplings used in quantum annealers or SQUID sensors but also couplings used in superconductor digital circuits.