Unconventional steady states and topological phases in an open two-level non-Hermitian system

Decoherence and non-Hermiticity are two different effects of the open quantum systems. Both of them have triggered many interesting phenomena. In this paper, we theoretically study an open two-level non-Hermitian system coupling to a dissipative environment by solving the vectorized Lindblad equation. This scheme provides us a powerful framework to address widespread open systems with gain, loss and dissipation. Our results show that there exist a new class of exceptional points (EPs) and steady states due to the interplay between non-Hermiticity and decoherence. Furthermore, we also demonstrate new-type topological properties of eigenstates with zero real-part of eigenvalues ($Re[\lambda ]=0$) which are corresponding to Fermi arcs. It is revealed that the phases of eigenstates located in Fermi arcs regime have a topological phase $\mathrm{\mid }\pi \mathrm{/}2\mathrm{\mid }$ which is totally unaffected by the dissipative environment. Our results provide a promising approach for further uncovering and understanding the intriguing properties of non-Hermitian open systems.