Simulation of Jahn-Teller-Dicke Magnetic Structural Phase Transition with Trapped Ions

TL;DR

This paper presents a theoretical study of a collective Jahn-Teller-Dicke transition in trapped ions, demonstrating their suitability for exploring spontaneous symmetry breaking and phase transitions in mesoscopic quantum systems.

Contribution

It introduces an exactly solvable model of spin-vibrational mode interactions in trapped ions, highlighting their potential for studying magnetic structural phase transitions.

Findings

Trapped ions can simulate Jahn-Teller-Dicke distortions.

The model is exactly solvable in the thermodynamic limit.

Spontaneous symmetry breaking can be observed in mesoscopic ion systems.

Abstract

We study theoretically the collective E$\otimes$e Jahn-Teller-Dicke distortion in a system of trapped ions. We focus in the limit of infinite range interactions in which an ensemble of effective spins interacts with two collective vibrational modes with U(1) symmetric couplings. Our model is exactly solvable in the thermodynamical limit and it is amenable to be solved by exact numerical diagonalization for a moderate number of ions. We show that trapped ions are ideally suited to study the emergence of spontaneous symmetry breaking of a continuous symmetry and magnetic structural phase transition in a mesoscopic system.