在迅速发展的量子信息领域，产生介观量子纠缠和EPR导引关联具有重要意义，并引起研究者的一些关注。现有方案主要基于腔光力系统及Bose-Hubbard模型。而目前利用Bose-Hubbard模型产生量子关联主要集中在一维链状结构的势阱中。基于目前实验上可以制备各种几何形状势阱，本项目提出一种利用多个势阱呈非链状结构的Bose-Hubbard模型产生空间分离的原子模式间量子纠缠和EPR导引关联的方案。利用全量子化正定的P表示方法，我们将揭示这些系统中产生量子关联的物理机制，阐明不同结构下原子布居、量子态及碰撞相互作用、遂穿耦合速率等参数与量子关联间内在联系。另外考虑了在这些非链状结构中独立地加入耗散和泵浦到每个势阱中，从而可以调控原子模式间量子关联，这展现了一种区别于光腔耦合系统的灵活性。该方案将为实验上在原子装置中实现介观的量子关联提供一种可供选择的方式。

In the rapidly developing field of quantum information, generation of mesoscopic quantum entanglement and EPR steering has important significance and has been attracting some research attention. The present schemes are based on cavity optomechanical systems and Bose-Hubbard models. The existing schemes by using Bose-Hubbard models are mainly concentrated in a few wells forming a linear configuration. Based on the realization of fabrication of lattice potentials for ultracold atoms in a variety of geometric configurations, in this project we will suggest a plan that quantum entanglement and EPR steering between the spatially separated atomic modes can be achieved based on multi-well Bose-Hubbard models. Through the fully quantum positive-P representation, we will reveal the physical mechanism of the quantum entanglement and EPR steering of these systems, and show the internal relationships between the quantum correlations and initial atomic population, initial quantum states, collisional interaction, tunneling coupling rates, respectively. Besides, pumping and dissipation are able to added to each well, then it can control the quantum correlations between the atomic modes, which offers a flexibility, not found in optical coupled cavity system. This project would supply a selective way for the experimentally realization of the mesoscopic quantum correlations in the atomtronic device.