Quantum quenches of ion Coulomb crystals across structural instabilities

TL;DR

This paper investigates how quantum quenches induce entangled motional states in ion Coulomb crystals near structural transitions, analyzing the dynamics and revivals of quantum coherence through Ramsey interferometry.

Contribution

It provides an analytical expression for interferometric visibility in ion chains of arbitrary size, revealing entanglement creation and coherence revivals near the linear-zigzag transition.

Findings

Visibility decays rapidly near the instability

Revivals occur at the mode oscillation period

Revivals are size-independent signals of entanglement

Abstract

Quenches in an ion chain can create coherent superpositions of motional states across the linear-zigzag structural transition. The procedure has been described in [Phys. Rev. A 84, 063821 (2011)] and makes use of spin-dependent forces, so that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. The properties of the crystalline state so generated are theoretically studied by means of Ramsey interferometry on one ion of the chain. An analytical expression for the visibility of the interferometric measurement is obtained for a chain of arbitrary number of ions and as a function of the time elapsed after the quench. Sufficiently close to the linear-zigzag instability the visibility decays very fast, but exhibits revivals at the period of oscillation of the mode that drives the structural instability. These revivals have a periodicity that is independent of the crystal size, and they signal the creation of entanglement by the quantum quench.