腔内耦合$χ^{(2)}$波导的非经典统计：量子光学二聚体
Nonclassical statistics of intracavity coupled $χ^{(2)}$ waveguides: the quantum optical dimer
摘要：
提出了一个模型，其中两个$χ^{(2)}$非线性波导包含在一个腔适合于二次谐波产生。波导之间的倏逝波耦合被认为是弱的，并且这种耦合与波导内的非线性相互作用之间的相互作用引起经典极限的量子违反。当两个不稳定性竞争时，这些违规行为特别强烈，其中发现双光束行为几乎完全抑制基本强度差异中的噪声。此外，接近双跃迁完美的双光束的相关性被认为是在基本强度的总和，也自脉冲不稳定性以及从对称到非对称状态的过渡显示非经典的双光束的相关性的基本和二次谐波强度。结果基于从哈密顿量导出的包含腔阻尼效应的全量子朗之万方程。输出场的强度相关性的计算使用的线性化版本的朗之万方程通过正P表示。通过对截断Wigner表示的非线性Langevin方程的数值模拟，证实了分析结果。
英文摘要：
A model is proposed where two $χ^{(2)}$ nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives rise to quantum violations of the classical limit. These violations are particularly strong when two instabilities are competing, where twin-beam behavior is found as almost complete noise suppression in the difference of the fundamental intensities. Moreover, close to bistable transitions perfect twin-beam correlations are seen in the sum of the fundamental intensities, and also the self-pulsing instability as well as the transition from symmetric to asymmetric states display nonclassical twin-beam correlations of both fundamental and second-harmonic intensities. The results are based on the full quantum Langevin equations derived from the Hamiltonian and including cavity damping effects. The intensity correlations of the output fields are calculated semi-analytically using a linearized version of the Langevin equations derived through the positive-P representation. Confirmation of the analytical results are obtained by numerical simulations of the nonlinear Langevin equations derived using the truncated Wigner representation.
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