Static properties of two linearly coupled discrete circuits

TL;DR

This paper investigates the static properties of two linearly coupled Bose-Hubbard rings, revealing a rich interplay of Mott-like and superfluid-like states influenced by interactions, filling, and entanglement, using analytical and numerical methods.

Contribution

It provides a comprehensive analysis of ground state and low-energy spectrum properties of coupled Bose-Hubbard rings, highlighting the emergence of various quantum states and entanglement features.

Findings

Identification of Mott-like and superfluid-like states

Dependence of properties on atom filling and interactions

Entanglement persists for odd atom numbers

Abstract

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.