基于超冷Rydberg原子耦合微腔阵列量子模拟多体问题和光子输运的研究

The area of quantum simulation many-body physics based on the system of the coupled cavity array assisted with ultracooled atoms has triggered an immense interest in recent years. Despite the plentiful and substantial achievements, unfortunately, most of these studies only focused on the short-range interaction cases. However, the cases of considering the long-range interaction between atoms are absent. It will be interesting to further investigate how the unique advantages of the long-range interaction can be harnessed for the purpose of quantum simulations and studying photon transport and photon router. Then the quantum simulation of many-body phenomena and its robustness, the photon transport/router in an array of driven dissipative nonlinear cavities embedded with long-range interaction Rydberg atoms are focused in this project. As the coupling between the large system and the environment gives rise to great hurdles to fully describe the properties, our research will based on the quasi-bosons approach to eliminate the coordinates of the bath and redescribe the system via an effective Hamiltonian. The requirements to realize different strong-correlated models with Rydberg atoms coupled to the coupled cavity array with dissipation are conducted systematically. Then the dynamics of this system based on these models is solved analytically and numerically using the method of quantum Monte Carlo simulations to investigate the effects of the controlling parameters, dissipation, decoherence, detunings, long-range interaction coupling strength, pump strength and finite temperatures on the strong-correlated effects and the photon transport and photon router. Our research may open up a wealth of possibilities for pronounced understanding the mechanism of the strong correlated effects and its robustness in the driven dissipative array of coupled cavity systems with long-range interaction conveniently. We expect that our approach could be beyond the scope of previous work and provide a starting point for discussing more complicated situations, such as quantum information and quantum control.

基于超冷原子耦合微腔阵列体系量子模拟多体问题是近年备受关注的热点之一，但是考虑原子间长程相互作用的研究工作甚少，物理机制尚待探究。本项目拟基于光场驱动和环境作用下超冷Rydberg原子耦合微腔阵列体系开展量子模拟多体问题、光子输运和光子路由器实现的理论研究，系统地探讨新奇量子相的发生条件及其roubustness、反射谱和透射谱与失谐、Rydberg原子之间长程相互作用强度、Rydberg原子-光场耦合强度、耗散等控制参数的关系。本项目的研究对于认识环境作用下长程作用Rydberg原子耦合腔阵列体系量子模拟强关联多体系统的物理机制及其robustness具有重要意义，同时可为量子信息科学、超冷原子体系的量子调控提供理论依据。

量子模拟是量子信息科学的热点研究领域之一，但基于腔阵列耦合超冷原子体系开展的大部分研究工作都不计及原子间的长程相互作用，其规律和机制缺乏深入探究。项目依托超冷Rydberg原子耦合微腔阵列体系构建了不同的理论模型，采用解析求解和蒙特卡洛数值求解相结合的方法开展了量子多体问题的光学模拟及其光子输运的理论研究，系统地探究了长程相互作用强度、原子-光场耦合强度、失谐、有限温度和耗散等控制参数调控量子相变和光子输运的物理规律和相应的机制。研究结果表明：. (1) 原子间长程相互作用对EJCH模型的量子相变有重要影响，可导致体系产生新奇量子相。对于确定温度下的一维情况，大尺寸体系可出现稳定的莫特绝缘相和超流相，而强的偶极-偶极相互作用可导致小尺寸的体系出现不稳定的密度波相。 对于确定温度下的二维正方晶格，弱偶极-偶极相互作用可导致系统出现棋盘相和超流相；但在强偶极-偶极相互作用下，体系可存在涨落和尺寸依赖性小的稳定超固相；. (2) 显著的光力学耦合强度使得有效的格点排斥势发生改变，导致高激发数的莫特绝缘相消失；腔光子-磁子耦合强度的增大可使 Mott 叶的稳定区域受到压缩，有利于体系相干；质心运动的JCH模型可出现莫特绝缘相，非相干振动相，超流相和相干振动相四种量子相；. (3) 调控长程相互作用可使体系发生拓扑相变，产生缠绕数为2的拓扑相；改变长程相互作用可使末态等概率的占据在多个格点，形成拓扑路由器；. (4) 偶极-偶极相互作用会导致弱隧穿极限下低密度 EJCH模型的中间态更接近可积点；费米近似后的JCH模型是近可积的并且不能热化；当光子的隧穿强度与光子-原子的耦合强度在同一量级时，JCH 系统在共振情况下出现量子混沌现象并且满足本征态热化假设；. (5) 调控里德堡相互作用可实现三种不同频率光子量子路由；耗散会降低转移谱的峰值和全透射谱的峰值，对全反射谱的峰产生非对称影响；. (6) 里德堡相互作用会使系统出现由能级非线性导致的常规光子阻塞效应和由不同路径之间的量子干涉导致的非常规光子阻塞效应。. 本项目的理论研究成果对于认识超冷Rydberg耦合腔阵列体系量子模拟强关联多体系统的物理机制具有重要意义，并可为量子信息科学、超冷原子体系的量子调控提供理论依据。

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