Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also can play the role of actual degrees of freedom, and hence allow for a viable implementation of cold-atom based devices and qubit systems. In this work, we exhaustively investigate the ground state properties and the low-lying energy spectrum of two linearly coupled Bose–Hubbard rings. We show that the competition among interactions, intra- and inter-ring hopping processes gives place to a rather rich physical scenario, where Mott-like states and (different kinds of) superfluid-like states emerge. The latter ones depend also on the (in)commensurate filling of the atoms. Our analysis, carried out within a simple analytical framework and by means of the exact numerical diagonalization of the system Hamiltonian, provides one with a rather complete characterization of the static properties of the two-ring ladder, including, but not limited to, coherence, fragmentation, correlations, and entanglement. We complement our investigation by studying how these indicators depend on the commensurability of the total number of bosons with respect to the total number of sites and show that the two stacked rings are always entangled for an odd number of atoms.

玻色子双环梯构成了一类重要的原子电子电路，其中相干电流不仅可以提供对多体物理学的新见解，而且可以发挥实际自由度的作用，因此允许可行的实现基于冷原子的设备和量子位系统。在这项工作中，我们详尽地研究了两个线性耦合 Bose-Hubbard 环的基态特性和低能谱。我们表明，相互作用、环内和环间跳跃过程之间的竞争让位于相当丰富的物理场景，其中出现了类莫特状态和（不同类型的）类超流体状态。后者还取决于原子的（不）相称填充。我们的分析，在一个简单的分析框架内并通过系统哈密顿量的精确数值对角化进行，提供了一个相当完整的二环阶梯静态特性的表征，包括但不限于相干性、碎片化、相关性，和纠缠。我们通过研究这些指标如何取决于玻色子总数相对于位点总数的可公度性来补充我们的研究，并表明两个堆叠的环总是纠缠为奇数个原子。