Coupled-cluster theory for bosons in rings and optical lattices

Abstract

Bosons in optical lattices and rings are attractive and active fields of research in cold-atom physics. Here, we apply our recently developed coupled-cluster approach for bosons in external traps to these systems, and extend it to the lowest-in-energy excited states with total quasi- or angular-momentum k. In the coupled-cluster approach the exact many-boson ground state is obtained by applying an exponential operator exp{ T}, T = ∑ n = 1 N T n to the ground configuration, which is (usually) the state where the bosons occupy a single orbital. For excited states, a second exponential operator exp{ T ( k) }, T ( k ) = ∑ n = 1 N T n ( k ) is employed to accommodate the remaining excitations from the unperturbed excited configuration. Due to the conservation of momentum, T 1 and T 1 ( k ) can vanish. Working equations for coupled-cluster (singles) doubles (CCD) are provided and their implications are briefly discussed.