On-chip microwave circulators - Breaking time-reversal symmetry with quantum phase slips

Quantum phase slip (QPS) junctions are dual circuit-elements that are equivalent to Josephson junctions under the exchange of voltage and current\footnote{Mooij et al, Nat.Phys. 2, 169 (2006)} and they have recently been employed to observe coherent quantum phase slips\footnote{Astafiev et al, Nature 484, 355 (2012)}. We propose a QPS-junction based circulator, where the three ports of the circulator are inductively connected to superconducting loops hosting trapped flux quanta. The role of a symmetry-breaking magnetic field is played by an external gate charge on a central island. The design is similar to one previously proposed using Josephson junctions\footnote{Koch et al, PRA 82, 043811 (2010)}, but exchanges the charge and flux degrees of freedom. The QPS circulator therefore is much less sensitive to environmental perturbations, since fluctuations in background magnetic flux are many orders of magnitude suppressed as compared to charge fluctuations. We find that our design offers high isolation even when taking into account realistic fabrication imperfections and experimental conditions and find a circulator bandwidth in excess of 400MHz for standard device parameters.