Quantum simulation of electron–phonon interactions in strongly deformable materials

J P Hague,C Maccormick

doi:10.1088/1367-2630/14/3/033019

Abstract

We propose an approach for quantum simulation of electron–phonon interactions using Rydberg states of cold atoms and ions. We show how systems of cold atoms and ions can be mapped onto electron–phonon systems of the Su–Schrieffer–Heeger type. We discuss how properties of the simulated Hamiltonian can be tuned and how to read physically relevant properties from the simulator. In particular, use of painted spot potentials offers a high level of tunability, enabling all physically relevant regimes of the electron–phonon Hamiltonian to be accessed.

Highlights

Electron-phonon interactions lead to some dramatic effects in condensed matter systems, with lattice vibrations leading to phenomena such as superconductivity [1] and colossal magnetoresistance [2]
We will show how a system of Rydberg atoms can be directly mapped to a Su–Schrieffer–Heeger electron-phonon Hamiltonian, which is of direct interest in the modelling of polymers and other condensed matter phenomena relating to highly deformable materials, and to our knowledge has not been investigated before in the context of cold atoms
We begin by discussing how electron-phonon interactions can be simulated in a system of cold Rydberg atoms such as rubidium in a deep optical lattice where there is a single atom per lattice site

Summary

Introduction

Electron-phonon interactions lead to some dramatic effects in condensed matter systems, with lattice vibrations leading to phenomena such as superconductivity [1] and colossal magnetoresistance [2]. Which are very easy to deform, the hopping of electrons along the chain can be strongly modified by the presence of lattice vibrations This leads to the Su–Schrieffer–Heeger (SSH) model, which describes a chain of CH groups in polyacetylene [4], which for a chain of N groups of mass M has the Hamiltonian, HSSH = −. Ising model by making a Lang–Firsov transformation [20] Their proposed system has the form of phonons coupled to a single Rydberg state via an interaction of the Holstein type, and the interaction is generated using a laser. We will show how a system of Rydberg atoms can be directly mapped to a Su–Schrieffer–Heeger electron-phonon Hamiltonian, which is of direct interest in the modelling of polymers and other condensed matter phenomena relating to highly deformable materials, and to our knowledge has not been investigated before in the context of cold atoms. We discuss how to read properties of electron-phonon interactions from the simulator, and describe a simple experiment to investigate the self-trapping problem

Mapping between cold Rydberg atoms and a Su–Schrieffer–Heeger model

Cold Rydberg Ions

Experimental considerations

Summary and outlook