Witness of topological phase transition and Weyl points in an open topological system

Recently, the tunable Weyl-semimetal bands and the associate topological phase transition have been successfully simulated in superconducting quantum circuits \[X. Tan, et al. Phys. Rev. Lett. {\bf 122}, 010501 (2019)\]. Since the superconducting quantum circuits inevitably couple to the environment, we here focus on the steady state and decoherence process by taking the reservoir into consideration via quantum master equation. Our results show that the purity of the steady state can be used to indicate the topological phase transition and Weyl points. Furthermore, the coherence will exponentially decay to zero at the Weyl points, and decay to a nonzero value with oscillation at other points in the momentum space. Our work may have significant impact on the study of quantum open topological system.