Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer

Abstract

We investigate the structure of resonance widths of a Bose-Hubbard Dimer with intersite hopping amplitude $k$, which is coupled to continuum at one of the sites with strength $γ$. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term $χ$ the resonances undergo consequent bifurcations. For $Λ=k/γ\geq 0.5$, the bifurcation points follow a scaling law ${\tilde χ}_n \equiv χ_n N/k = f_Λ(n-0.5/Λ)$, where $N$ is the number of bosons. For the function $f_Λ$ two different $Λ$ dependences are found around the minimum and the maximum bifurcation point.