Simulation of topological nodal-loop bands on a superconducting circuits chain

Nodal-loop semimetal is one of the exotic gapless topological states of matter that are discovered recently. Here we propose an experimentally feasible scheme to simulate the three-dimensional topological nodal-loop semimetal bands in a one-dimensional circuit quantum electrodynamics lattice, by introducing two additional parameter dimensions. A unit-cell of the lattice consists of a transmissionline resonator coupled by a superconducting transmon qubit, and two of the dressed states in a unit-cell are used to simulate the spin-1/2 states of an electron. The neighboring transmission-line resonators are connected by a superconducting quantum interference device, and the effective hopping among them is induced by parametric coupling. Meanwhile, the two artificial dimensions are simulated by tunable Zeeman terms of the spins. The detection of the mimic nodal-loop bands is also discussed and is shown to be well within current technology. Therefore, our scheme provides a feasible way to explore nodal-loop semimetal bands and other topological bands of different spin-orbit coupling forms in this controllable artificial system.