  Time-periodic driving in the form of coherent radiation provides powerful
tool for the manipulation of topological materials or synthetic quantum matter.
In this paper we propose a scheme to realize non-Hermitian semimetals
exhibiting exceptional rings in the spectra through Floquet engineering. A
transition from a concentric pair of the rings to a dipolar pair is observed.
The concentric pair carries only a quantized Berry phase while the dipolar pair
possesses opposite Chern numbers in addition, signaling a topological Lifshitz
transition of the Fermi surface. The transport properties of the system are
addressed, and we find that this transition process is accompanied by the
emergency of a nontrivial Hall conductivity. Furthermore, we explore the
quantum simulation of non-Hermitian semimetals with a quantum spin system and
the characterization of the topology via the long-time dynamics.
