Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer

TL;DR

This paper studies how resonance widths in an open Bose-Hubbard Dimer change and bifurcate as the on-site interaction varies, revealing a scaling law and different behaviors depending on the coupling ratio.

Contribution

It introduces a non-Hermitian Hamiltonian approach to analyze bifurcations in resonance widths of an open Bose-Hubbard Dimer, identifying a scaling law and $ extLambda$-dependent behaviors.

Findings

Resonance widths undergo bifurcations as on-site interaction varies.

A scaling law relates bifurcation points to system parameters.

Different $ extLambda$ dependences are observed near bifurcation points.

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 $\gamma$. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term $\chi$ the resonances undergo consequent bifurcations. For $\Lambda=k/\gamma\geq 0.5$, the bifurcation points follow a scaling law ${\tilde \chi}_n \equiv \chi_n N/k = f_{\Lambda}(n-0.5/\Lambda)$, where $N$ is the number of bosons. For the function $f_{\Lambda}$ two different $\Lambda$ dependences are found around the minimum and the maximum bifurcation point.