Effective many-body Hamiltonians of qubit-photon bound states

TL;DR

This paper investigates the formation of effective many-body Hamiltonians in qubit-photon bound states beyond the weak coupling regime, revealing complex excitations and phase transitions in strongly coupled, non-Markovian systems.

Contribution

It introduces analytical and numerical models for non-Markovian regimes with multiple excitations, highlighting the emergence of doublons, triplons, and tunable polariton interactions.

Findings

Existence of doublon and triplon states in non-Markovian regimes.

Emergence of polariton models with tunable interactions.

Observation of superfluid-Mott insulator transition in ground state.

Abstract

Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.