Exploring bosonic bound states with parallel reaction coordinates

TL;DR

This paper investigates the emergence and stability of bosonic bound states in quantum systems strongly coupled to reservoirs with band gaps, using an exactly solvable model and a perturbative approach.

Contribution

It introduces a weak-coupling supersystem method to analyze bound state existence and stability, extending understanding of their behavior in complex reservoir structures.

Findings

Bound states occur when their energy lies within the reservoir band gap.

Weak interactions give bound states a finite lifetime, which can be increased by stronger coupling.

The supersystem approach reproduces exact results and handles multiple band gaps.

Abstract

Bound states are dissipation-resilient states that may emerge when quantum systems are strongly coupled to reservoirs with band gaps. We analyze an exactly solvable bosonic model for bound state existence and reproduce these results by a weak-coupling treatment of a supersystem composed of the original system and multiple reaction coordinates, which are individually representing small energy intervals of the reservoir spectral function. Within the perturbative supersystem treatment, the bound state stability results from its energy being inside the band gap. We discuss cases of multiple band gaps and also show that already in presence of weak interactions the bound state's lifetime is finite -- but can be increased by raising the system-reservoir coupling strength.