Phonon dressing of a facilitated one-dimensional Rydberg lattice gas

TL;DR

This paper investigates how phonon interactions influence the dynamics of a one-dimensional Rydberg lattice gas under facilitation conditions, revealing bound states that slow down relaxation processes.

Contribution

It introduces an analytical framework for understanding phonon dressing effects on Rydberg facilitation dynamics using perturbation theory and Fano resonance analysis.

Findings

Phonon dressing creates slowly decaying bound states.

These bound states inhibit fast relaxation of initial states.

Analytical effective Hamiltonian describes cluster evolution with phonon effects.

Abstract

We study the dynamics of a one-dimensional Rydberg lattice gas under facilitation (anti-blockade) conditions which implements a so-called kinetically constrained spin system. Here an atom can only be excited to a Rydberg state when one of its neighbors is already excited. Once two or more atoms are simultaneously excited mechanical forces emerge, which couple the internal electronic dynamics of this many-body system to external vibrational degrees of freedom in the lattice. This electron-phonon coupling results in a so-called phonon dressing of many-body states which in turn impacts on the facilitation dynamics. In our theoretical study we focus on a scenario in which all energy scales are sufficiently separated such that a perturbative treatment of the coupling between electronic and vibrational states is possible. This allows to analytically derive an effective Hamiltonian for the evolution of consecutive clusters of Rydberg excitations in the presence of phonon dressing. We analyze the spectrum of this Hamiltonian and show -- by employing Fano resonance theory -- that the interaction between Rydberg excitations and lattice vibrations leads to the emergence of slowly decaying bound states that inhibit fast relaxation of certain initial states.