Synthetic spin–orbit coupling and topological polaritons in Janeys–Cummings lattices

The interaction between a photon and a qubit in the Janeys–Cummings (JC) model generates a kind of quasiparticle called polariton. While they are widely used in quantum optics, difficulties in engineering-controllable coupling of them severely limit their applications to simulate spinful quantum systems. Here we show that, in the superconducting quantum circuit context, polariton states in the single-excitation manifold of a JC lattice can be used to simulate a spin-1/2 system, based on which tunable synthetic spin–orbit coupling and novel topological polaritons can be generated and explored. The lattice is formed by a sequence of coupled transmission line resonators, each of which is connected to a transmon qubit. Synthetic spin–orbit coupling and the effective Zeeman field of the polariton can both be tuned by modulating the coupling strength between neighboring resonators, allowing for the realization of a large variety of polaritonic topological semimetal bands. Methods for detecting the polaritonic topological edge states and topological invariants are also proposed. Therefore, our work suggests that the JC lattice is a versatile platform for exploring spinful topological states of matter, which may inspire developments of topologically protected quantum optical and information-processing devices