Excitation spectrum and supersolidity of a two-leg bosonic ring ladder

We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases: the Meissner phase, where the flow of particles is carried at the edges of the system without transverse current; a vortex phase, characterized by nonzero transverse current; and a biased-ladder phase, characterized by an imbalance of the population of the two rings. We use the Bogoliubov approximation to determine the excitation spectrum in the three phases, the dynamic structure factor, and the quantum fluctuation corrections to the first-order correlation function. Our analysis reveals supersolid features as well as Josephson modes, corresponding to out-of-phase modes of the finite ring.