Generation of unstable states via encircling exceptional nexus

An exceptional nexus (EX), a higher-order exceptional point where multiple exceptional arcs converge, has garnered significant attention in various physical domains, such as hybrid topological invariants and asymmetric state transfer. Previous studies on the dynamics encircling EX have primarily concentrated on transitions between stable states. To explore the transition from stable to unstable state in a nonlinear system, we construct an EX by coupling a saturated gain and a linear lossy optical microcavity and modulate the evolution rate of this EX. When dynamically encircling this EX, the stable state transfers to an unstable state at an optimal evolution rate range, exhibiting an asymmetric state transfer dependent on the starting point. Increasing the system's gain parameter or reducing the loss parameter broadens the optimal evolution rate range for the transition from the stable to the unstable. By altering the starting point and shape of the evolution trajectory, the optimal range for the evolution rate will adjust correspondingly. Our work elucidates the fundamental physics of encircling EX and provides an alternative approach for manipulating optical modes in nonlinear non-Hermitian systems, particularly regarding transitions to the unstable state.