Directional photon transport in a superconducting circuit lattice

One of the current bottlenecks in quantum computing devices based on circuit quantum electrodynamics (cQED) is in the circulators used for routing microwave photons. The circulators currently used in novel devices are bulky and require large, localized magnetic fields in order to achieve directional transport of the electromagnetic waves, making them incompatible for on-chip implementation with superconducting circuits. We address these limitations by studying a simple superconducting circuit design that achieves directional photon transport using components currently present in standard cQED devices. In a lattice of coupled microwave resonators, with an effective complex hopping term between lattice sites, we achieve directionality by engineering an effective magnetic field for photons that results in a Peierls phase. Implementations that make use of such a phase have already been proposed, using frequency mixers or magnetic fields in Josephson junction rings, but such devices are currently not considered due to their complexity. We instead investigate the possibility of using voltage-driven planar transmission lines to generate the effective Peierls phase. This will result in a simpler implementation of a superconducting circuit that can also be used for on-chip signal routing.