基于新型耦合机制的超导传输线腔阵列量子模拟

超导传输线腔阵列被认为是最有希望对若干强关联多体物理模型实现有效量子模拟的物理体系之一。当前最常被使用的电容耦合机制只能诱导出强度固定且为实数的紧束缚型腔间光子跳跃，这种不可调性大大制约了超导传输线腔阵列在量子模拟中的潜力。我们在本项目中提出使用超导量子干涉仪（SQUID）来连接超导传输线腔阵列以实现量子模拟。相较于传统的电容耦合方法，我们使用的新型SQUID耦合机制可以给出可调性更为强大的腔间光子跳跃，这一优势可以被用来简化已有的理论方案乃至模拟固有耦合机制下难以达成的一些模型。我们将先完善这种新型耦合机制，讨论如何在本征频率相近的超导传输线腔间实现复数光子跳跃因子，再分别发扬这种新型耦合机制的强度可调性和相位可调性，探讨在超导传输线腔阵列中模拟自旋阻挫现象和实现人工阿贝尔规范势。我们的研究将为探索自旋阻挫和人工规范势现象提供新的方法与思路，为未来的相关实验进行提供理论基础。

The superconducting transmissionline resonator (TLR) array has been regarded as one of the most promising candidates for quantum simulation of strong correlation physics. Currently most of the reported experimental and theoretical results relied on the capacitance inter-TLR coupling mechanism which provides untunable-and-real inter-TLR photon hopping rates. Such untunability is a major obstacle to implementing efficient quantum simulation in the TLR array system. In this project, we propose to use the superconducting quantum interference device (SQUID) as inter-TLR coupler to build the TLR array quantum simulators. Compared with the conventional capacitance coupling, this novel SQUID coupling can offer unprecedented flexibility in designing the inter-TLR photon tunneling. This advantage can be exploited to simplify many already-proposed schemes and simulate a variety of many-body models which are intractable in the situation of untunable inter-TLR photon hopping. We first consummate the SQUID coupling mechanism by developing methods for realizing complex tunable photon hopping rates between two TLRs with similar eigenfrequencies, and then apply the consummated SQUID coupling mechanism to construct the TLR array quantum simulators for frustrated spin systems and Abelian artificial gauge. Our research will offer new ways to study these many-body phenomena and provide theoretical support for the related experimental realizations in the future.