Eur. Phys. J. D 41, 325-330 (2007)
https://doi.org/10.1140/epjd/e2006-00220-2

Frenkel-Kontorova model with cold trapped ions

¹ Laboratoire de Physique Théorique, UMR 5152 du CNRS, Univ. P. Sabatier, 31062 Toulouse, France
² Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia

Received: 26 June 2006
Revised: 24 August 2006
Published online: 27 September 2006

Abstract

We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. We show that at zero temperature the quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. After melting the ion chain can slide in an optical lattice. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.