  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.
