Quantum zigzag transition in ion chains

TL;DR

This paper investigates the quantum phase transition in trapped ion chains from a linear to a zigzag structure, highlighting the quantum effects near the critical point and proposing experimental measurement methods.

Contribution

It introduces a quantum description of the zigzag transition in ion chains, mapping it to the Ising model and estimating the quantum critical point.

Findings

Identification of the quantum critical point in ion chains.

Finite deviation from classical critical point predictions.

Proposed measurement procedure for quantum fluctuations.

Abstract

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one dimensional optical lattice.