Double wells, scalar fields and quantum phase transitions in ions traps

TL;DR

This paper demonstrates how trapped ion chains can simulate Klein-Gordon fields, enabling the study of quantum phase transitions and tunneling phenomena through controllable double well potentials.

Contribution

It introduces a method to simulate scalar quantum fields and phase transitions in ion traps by controlling radial degrees of freedom, including non-linearity and mass.

Findings

Simulation of Klein-Gordon fields on a lattice

Control over phase transition dynamics in ion chains

Observation of tunneling in double well potentials

Abstract

Since Hund's work on the ammonia molecule, the double well potential has formed a key paradigm in physics. Its importance is further underlined by the central role it plays in the Landau theory of phase transitions. Recently, the study of entanglement properties of many-body systems has added a new angle to the study of quantum phase transitions of discrete and continuous degrees of freedom, i.e., spin and harmonic chains. Here we show that control of the radial degree of freedom of trapped ion chains allows for the simulation of linear and non-linear Klein-Gordon fields on a lattice, in which the parameters of the lattice, the non-linearity and mass can be controlled at will. The system may be driven through a phase transition creating a double well potential between different configurations of the ion crystal. The dynamics of the system are controllable, local properties are measurable and tunnelling in the double well potential would be observable.