AI 中文总结
研究光子对产生过程中的二阶关联，引入对二阶关联函数\(g_{\textrm{pairs}}^{\left(2\right)}\)，通过它可表征对聚束和反聚束情况，利用不等式表明对反聚束是量子非经典标志，评估了多种量子态的该函数，还指出其可实验获取且有相关优势。
AI 中文摘要
我们引入对二阶关联函数\(g_{\textrm{pairs}}^{\left(2\right)}=\left\langle \left(P^{\dagger}\right)^{2}P^{2}\right\rangle /\left\langle P^{\dagger}P\right\rangle ^{2}\)（通过对算符\(P^{\dagger}=a^{\dagger}b^{\dagger}\)定义）来表征光子对产生过程中的二阶关联以及对聚束和反聚束。该量直接探测单双模量子态内对产生事件之间的关联。\(g_{\textrm{pairs}}^{\left(2\right)}\)大于、等于或小于1分别对应对聚束、泊松对统计和对反聚束。利用柯西 - 施瓦茨不等式表明经典双模场满足\(g_{\textrm{pairs}}^{\left(2\right)}\geq1\)，对反聚束是量子非经典性的明确标志。评估了几种代表性量子态的\(g_{\textrm{pairs}}^{\left(2\right)}\)，指出即使是任意弱的双模压缩真空态也表现出对聚束。与预告二阶关联的比较突出了这些可观测量提供的互补信息。所提出的关联函数可通过标准符合测量实验获取，无需相位参考或态重构，且在均匀损耗下不变。
英文摘要
We introduce the pair second-order correlation function $g_{\textrm{pairs}}^{\left(2\right)}=\left\langle \left(P^{\dagger}\right)^{2}P^{2}\right\rangle /\left\langle P^{\dagger}P\right\rangle ^{2}$, defined through the pair operator $P^{\dagger}=a^{\dagger}b^{\dagger}$, to characterize second-order correlations and pair bunching and antibunching in photon-pair creation processes. This quantity directly probes correlations between pair-generation events within a single two-mode quantum state, providing access to the intrinsic pair-generation process beyond conventional single-mode or heralded second-order correlations, which do not directly capture correlations between pair events. Values of $g_{\textrm{pairs}}^{\left(2\right)}$ greater than, equal to, or less than unity correspond respectively to pair bunching, Poissonian pair statistics, and pair antibunching. Using the Cauchy--Schwarz inequality, we further show that all classical two-mode fields described by a positive Glauber--Sudarshan \ensuremath{P}-function satisfy $g_{\textrm{pairs}}^{\left(2\right)}\geq1$, so that pair antibunching is classically forbidden and constitutes an unambiguous signature of nonclassicality. We evaluate $g_{\textrm{pairs}}^{\left(2\right)}$ for several representative quantum states and show, in particular, that even arbitrarily weak two-mode squeezed vacuum states exhibit pair bunching. Comparison with heralded second-order correlations highlights the complementary information provided by these observables. The proposed correlation function is experimentally accessible via standard coincidence measurements, requires no phase reference or state reconstruction, and remains invariant under uniform loss.
Comments6 pages, 2 figures
