An attractor dynamics in a non-Hermitian two-level system

Exceptional points in non-Hermitian systems possess fascinating properties. We present an exactly solvable attractor dynamics for the first time from the two-level time-dependent non-Hermitian Hamiltonian. This allows the evolution from a pure or mixed initial state to the coalescence state by varying the imaginary parameter along a specific diabatic passage. In contrast to a chaotic attractor that is ultrasensitive to initial conditions, the designed attractor is insensitive to initial conditions. The attractor-like behavior is applicable to several adiabatic processes.