We introduce an optical system (a coupler) obeying parity-time ($\mathcal{P}\mathcal{T}$) symmetry with odd-time reversal, ${\mathcal{T}}^2=-1$. It is implemented with two birefringent waveguides embedded in an anti-$\mathcal{P}\mathcal{T}$-symmetric medium. The system possesses properties that are untypical for most physical systems with the conventional even-time reversal. Having a symmetry-protected degeneracy of the linear modes, the coupler allows for the realization of a coherent switch operating with a superposition of binary states that are distinguished by their polarizations. When a Kerr nonlinearity is taken into account, each linear state, being doubly degenerated, bifurcates into several distinct nonlinear modes, some of which are dynamically stable. The nonlinear modes are characterized by amplitude and by polarization and come in $\mathcal{P}\mathcal{T}$-conjugate pairs.

中文翻译：

---

反PT对称介质引起的奇数时间逆PTS对称

我们引入遵循奇偶性时间的光学系统（耦合器）（$\mathcal{P}\mathcal{Ť}$）具有奇数时间反转的对称性， ${\mathcal{Ť}}^{\mathrm{2个}}=-\mathrm{1个}$。它是通过将两个双折射波导嵌入到抗反射层中来实现的$\mathcal{P}\mathcal{Ť}$对称介质。对于具有常规偶数时间反转功能的大多数物理系统，该系统具有非典型的属性。线性模式具有对称保护的简并性，耦合器允许实现以二进制状态的叠加操作的相干开关，该二进制状态通过其极化来区分。当考虑Kerr非线性时，每个双重退化的线性状态会分叉成几个不同的非线性模式，其中一些是动态稳定的。非线性模式以振幅和极化为特征，并进入$\mathcal{P}\mathcal{Ť}$-共轭对。