Abstract Multimode quantum correlation has important applications in the field of quantum information. In this paper, we propose a compact scheme to generate multiple quantum correlated beams based on energy-level cascaded four-wave mixing (EC-FWM) process in a single atomic medium of rubidium. Injecting two strong pump beams with different frequencies and one weak probe beam into one rubidium vapor, four possible parametrically amplified FWM (PA FWM) processes can coexist under different phase matching conditions. Within the scheme, the weak probe beam is amplified and three coherent beams are generated, which can also be seen as an eight-wave mixing (EWM) process when certain phase matching condition is satisfied. Based on the energy level system of the scheme, three different cascaded structure models are employed to study the quantum correlation between the four generated beams. Amplitude and phase quadratures squeezing and intensity squeezing of the three- and four-mode are calculated via the input–output relations of the system. We found versatile multimode squeezing can be generated in all the structures, but the degree of squeezing and its distribution among the modes are different, depending on the specific structure. Furthermore, the relation of the quantum correlation, as well as the eigenmodes and eigenvalues of the four-mode quantum states are studied.

中文翻译：

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用能级级联四波混频过程产生多模量子相关性

摘要 多模量子关联在量子信息领域有着重要的应用。在本文中，我们提出了一种基于能级级联四波混合（EC-FWM）过程在铷单原子介质中产生多个量子相关光束的紧凑方案。将两个不同频率的强泵浦光束和一个弱探测光束注入一个铷蒸气中，四种可能的参数放大 FWM (PA FWM) 过程可以在不同的相位匹配条件下共存。在该方案中，弱探测光束被放大并产生三个相干光束，这也可以看作是满足一定相位匹配条件时的八波混合（EWM）过程。基于方案的能级体系，采用三种不同的级联结构模型来研究四个产生的光束之间的量子相关性。三模和四模的幅度和相位正交压缩和强度压缩是通过系统的输入-输出关系计算的。我们发现在所有结构中都可以产生通用的多模挤压，但挤压的程度及其在模式之间的分布是不同的，这取决于具体的结构。此外，还研究了量子相关性的关系，以及四模量子态的本征模和本征值。我们发现在所有结构中都可以产生通用的多模挤压，但挤压的程度及其在模式之间的分布是不同的，这取决于具体的结构。此外，还研究了量子相关性的关系，以及四模量子态的本征模和本征值。我们发现在所有结构中都可以产生通用的多模挤压，但挤压的程度及其在模式之间的分布是不同的，这取决于具体的结构。此外，还研究了量子相关性的关系，以及四模量子态的本征模和本征值。