双曲极化激元凝聚体中不定 Bogoliubov 度量产生的奇异锥
Exceptional Cones from an Indefinite Bogoliubov Metric in Hyperbolic Polariton Condensates
浏览论文内容
中文总结 AI 辅助
研究双曲极化激元凝聚体中 Bogoliubov 度量，其能带曲率相反符号形成不定度量，转换光锥为稳定性楔。驱动耗散下零判别表面成奇异锥，分支合并、相刚度崩溃、光谱变化，揭示其为非厄米奇异简并的可控环境。
中文摘要 AI 辅助
普通凝聚体中的长波 Bogoliubov 声子实现了标准声学洛伦兹度量。我们表明，在双曲极化激元带中形成的凝聚体实现了一种不同的集体几何结构，具有不定 Bogoliubov 度量，其空间特征继承自能带曲率的相反符号。该度量将声光锥转换为双曲稳定性楔，将传播的准粒子与动态不稳定的准粒子分开。在驱动耗散凝聚体中，增益饱和将这种度量关系转变为非厄米 Bogoliubov 色散。零判别表面在参数空间$(q_x,q_y,\Delta_{\rm NH})$中成为一个奇异锥，在固定增益饱和时表现为奇异双曲线。在这个表面上，Bogoliubov 分支合并,双正交相刚度崩溃，光谱从传播变为放大或过阻尼动力学。我们的结果表明，双曲极化激元凝聚体是一个可控的环境，其中非厄米奇异简并由有效的 Bogoliubov 度量组织。
英文摘要
Long-wavelength Bogoliubov phonons in an ordinary condensate realize the standard acoustic Lorentz metric. We show that a condensate formed in a hyperbolic polariton band realizes a different collective geometry with an indefinite Bogoliubov metric whose spatial signature is inherited from the opposite signs of the band curvatures. This metric converts the acoustic light cone into a hyperbolic stability wedge, separating propagating quasiparticles from dynamically unstable ones. In a driven-dissipative condensate, gain saturation turns this metric relation into a non-Hermitian Bogoliubov dispersion. The zero-discriminant surface becomes an exceptional cone in the parametric space $(q_x,q_y,Δ_{\rm NH})$, appearing as an exceptional hyperbola at fixed gain saturation. Across this surface the Bogoliubov branches coalesce, the biorthogonal phase rigidity collapses, and the spectrum changes from propagation to amplified or overdamped dynamics. Our results identify hyperbolic polariton condensates as a controllable setting where non-Hermitian exceptional degeneracies are organized by an effective Bogoliubov metric.
