Title: Transition from exceptional points to observable nonlinear bifurcation points in anti-PT symmetric coupled cavity systems Show Chinese title

Title: 反PT对称耦合腔系统中从特殊点到可观察的非线性分岔点的转变

Abstract: 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. Show Chinese abstract

Abstract: 反宇称时间（APT）对称系统中的异常点（EPs）引起了广泛关注。 虽然线性APT对称系统与非线性耗散系统（如相互注入锁定的激光器）表现出结构相似性，但线性非厄米哈密顿量中的异常点与非线性激光动力学中的分岔现象之间的对应关系仍然不明确。 我们证明，在具有APT对称性和增益饱和非线性的双腔系统中，异常点与非线性平衡态的分岔点重合，并且恰好出现在激光阈值处。 尽管异常点和分岔点源于根本不同的物理概念，但分岔点在激光阈值以上仍可观测，并保留了关键的异常点特征。 值得注意的是，源自线性异常点的分岔点还连接了系统的线性和非线性动力学：它在非线性动力学中作为极限环和同步区域之间的可访问过渡点。 此外，我们澄清了在存在增益饱和的情况下，一种保持能量差的拍频振荡——这是线性APT系统弱耦合区域的独特动态——会演变为两个腔中振幅相等的非线性极限环。 我们的发现建立了由异常点引起的分岔点与非线性动力学之间的直接联系，为非厄米和非线性光学系统提供了基本的见解。