Exact k -body representation of the Jaynes-Cummings interaction in the dressed basis: Insight into many-body phenomena with light
Exact k -body representation of the Jaynes-Cummings interaction in the dressed basis: Insight into many-body phenomena with light
复制标题
DOI：
10.1103/physreva.104.013707
复制
发表时间：
2021-03
影响因子：
2.9
通讯作者：
Kevin C. Smith;A. Bhattacharya;D. Masiello
中科院分区：
文献类型：
--
作者：
Kevin C. Smith;A. Bhattacharya;D. Masiello
模拟量子模拟-使用一个实验控制良好的物理系统来模拟另一个物理系统的行为的技术-已迅速成为研究强关联量子多体系统的最有前途的近期策略之一。特别是，系统的相互作用的光子，可实现在固态腔和电路QED框架，例如，持有巨大的承诺，为非平衡多体现象的研究，部分原因是由于本地创建和销毁光子的能力。这些系统通常使用Jaynes-Cummings-Hubbard（JCH）哈密顿量建模，由于与Bose-Hubbard哈密顿量相似而命名。虽然两者之间的比较经常在文献中进行，但JCH哈密顿量包括玻色子和赝自旋算符，导致特定参数区域的玻色-哈伯德模型的物理偏差。在这里，我们提出了一个非微扰的程序转换成一个穿着运营商表示，在其最一般的形式，承认一个无限的玻色子k-体项的总和，其中k是唯一的约束系统中的激发数的Jaynes-Cummings哈密顿。我们仔细研究了色散和共振耦合机制中的这一结果，发现前者快速收敛，而后者中k 1的贡献。通过扩展到两个站点的JCH系统的简单情况下，我们表明，这种方法有利于密切检查之间的类比JCH和玻色-哈伯德模型和它的故障共振光物质耦合。最后，我们使用这个框架来调查一般系统参数的两个站点JCH的多体特征，确定四个独特的量子相位和它们被实现的参数制度，从而突出了超越玻色-哈伯德模型的基于有限JCH的量子模拟器可实现的现象。更广泛地说，这项工作的目的是作为一个明确的数学阐述玻色子多体相互作用的基础Jaynes-Cummings型系统，通常假设通过类比克尔类非线性极化率或匹配系数，以获得适当的本征值谱。
Analog quantum simulation – the technique of using one experimentally well-controlled physical system to mimic the behavior of another – has quickly emerged as one of the most promising near term strategies for studying strongly correlated quantum many-body systems. In particular, systems of interacting photons, realizable in solid-state cavity and circuit QED frameworks, for example, hold tremendous promise for the study of nonequilibrium many-body phenomena in part due to the capability to locally create and destroy photons. These systems are typically modeled using a Jaynes-Cummings-Hubbard (JCH) Hamiltonian, named due to similarities with the Bose-Hubbard Hamiltonian. While comparisons between the two are often made in the literature, the JCH Hamiltonian comprises both bosonic and psuedo-spin operators, leading to physical deviations from the Bose-Hubbard model for particular parameter regimes. Here, we present a non-perturbative procedure for transforming the Jaynes-Cummings Hamiltonian into a dressed operator representation that, in its most general form, admits an infinite sum of bosonic k-body terms where k is bound only by the number of excitations in the system. We closely examine this result in both the dispersive and resonant coupling regimes, finding rapid convergence in the former and contributions from k 1 in the latter. Through extension to the simple case of a two-site JCH system, we demonstrate that this approach facilitates close inspection of the analogy between the JCH and Bose-Hubbard models and its breakdown for resonant light-matter coupling. Finally, we use this framework to survey the many-body character of a two-site JCH for general system parameters, identifying four unique quantum phases and the parameter regimes in which they are realized, thus highlighting phenomena realizable with finite JCH-based quantum simulators beyond the Bose-Hubbard model. More broadly, this work is intended to serve as a clear mathematical exposition of bosonic many-body interactions underlying Jaynes-Cummings-type systems, often postulated either through analogy to Kerr-like nonlinear susceptibilities or by matching coefficients to obtain the appropriate eigenvalue spectrum.