二次谐波产生中横向斑图形成的量子特性
Quantum properties of transverse pattern formation in second-harmonic generation
摘要：
研究了腔内二次谐波产生中一维横向斑图形成不稳定性的空间量子噪声特性。准概率分布的Q表示是用非线性随机朗之万方程实现的。我们研究这些方程，通过广泛的数值模拟和分析在线性化的限制。我们的研究，低于和高于斑图形成的阈值，是指导下的光子相互作用的微观计划的斑图形成在二次谐波产生。在接近斑图形成的阈值时，具有离轴临界波数相反方向的光束显示出高度相关。这是观察到的基本字段，为第二谐波字段，也为两个字段之间的互相关。还描述了涉及均匀横波数的非线性相关性，这些非线性相关性在线性化分析中未被识别。的远场的相对点之间的强度差异示出展示亚泊松统计，揭示了量子性质的相关性。我们观察到的基本和二次谐波领域的孪生光束的相关性，也非经典之间的相关性。
英文摘要：
We investigate the spatial quantum noise properties of the one dimensional transverse pattern formation instability in intra-cavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second harmonic field and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.
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