Transition from exceptional points to observable nonlinear bifurcation points in anti-PT symmetric coupled cavity systems

Exceptional points (EPs) in anti-parity-time (APT)-symmetric systems have attracted significant interest. While linear APT-symmetric systems exhibit structural similarities with nonlinear dissipative systems, such as mutually injection-locked lasers, the correspondence between exceptional points in linear non-Hermitian Hamiltonians and bifurcation phenomena in nonlinear lasing dynamics has remained unclear. We demonstrated that, in a two-cavity system with APT symmetry and gain saturation nonlinearity, an EP coincides with a bifurcation point of nonlinear equilibrium states, which appears exactly at the lasing threshold. Although the EP and the bifurcation point originate from fundamentally different physical concepts, the bifurcation point is observable and retains key EP characteristics even above the lasing threshold. Notably, the bifurcation point that originates from the linear EP also bridges linear and nonlinear dynamics of the system: It serves as an accessible transition point in the nonlinear dynamics between the limit cycle and synchronization regimes. Furthermore, we clarified that beat oscillation that conserves the energy difference, which is a unique dynamic in the weak-coupling regime of a linear APT system, evolves into a nonlinear limit cycle with equal amplitudes in the two cavities in the presence of gain saturation. Our findings establish a direct link between EP-induced bifurcation points and nonlinear dynamics, providing fundamental insights into non-Hermitian and nonlinear optical systems.