Topological photonics on superconducting quantum circuits with parametric couplings.

Topological phases of matter is an exotic phenomena in modern condense matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials has been exploited in many other fields of physics. Motivated by designing and controlling the behavior of electromagnetic waves, in optical, microwave, and sound frequencies, topological photonics emerges as a rapid growing field of research. Due to the flexibility and diversity of superconducting quantum circuits system, it is an promising platform to realize exotic topological models and to probe and explore topologically-protected effects in new ways. Here, we review theoretical and experimental advances of topological photonics on superconducting quantum circuits via the experimentally demonstrated parametric tunable coupling techniques, including using of the superconducting transmission line resonator, superconducting qubits, and the coupled system of them. On superconducting circuits, the flexible interactions and intrinsic nonlinearity making topological photonics in this system not only a simple photonic analog of topological effects for novel devices, but also a realm of exotic but less-explored fundamental physics.