Bound States in Boson Impurity Models

The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work, we show the existence of an infinite number of such states for some boson impurity models. They describe free bosons coupled to an impurity and include some of the most representative models in quantum optics. We also propose a family of wave functions to describe the bound states and verify that it accurately characterizes all parameter regimes by comparing its predictions with exact numerical calculations for a one-dimensional tight-binding Hamiltonian. For that model, we also analyze the nature of the bound states by studying the scaling relations of physical quantities, such as the ground-state energy and localization length, and find a nonanalytical behavior as a function of the coupling strength. Finally, we discuss how to test our theoretical predictions in experimental platforms, such as photonic crystal structures and cold atoms in optical lattices.