Bound states in boson impurity models

TL;DR

This paper demonstrates the existence of infinitely many bound states in boson impurity models, introduces a wavefunction family to describe them, and verifies predictions through numerical analysis and potential experimental tests.

Contribution

It reveals the presence of infinite bound states in boson impurity models and proposes a wavefunction approach validated by numerical calculations.

Findings

Infinite bound states exist in certain boson impurity models

A family of wavefunctions accurately describes these bound states

Non-analytical behavior observed in physical quantities as a function of coupling

Abstract

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 wavefunctions 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 non-analytical 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.