Frenkel-Kontorova model with cold trapped ions

TL;DR

This paper investigates the phase transition behaviors of a one-dimensional chain of cold trapped ions in a periodic optical potential, revealing classical and quantum phase transitions relevant to Wigner crystals.

Contribution

It provides analytical and numerical analysis of ion chains in optical lattices, highlighting quantum effects and phase transitions in a Frenkel-Kontorova-like system.

Findings

Transition from sliding to pinned phase with increasing lattice potential

Quantum fluctuations induce a quantum phase transition and melting of the pinned phase

Results applicable to Wigner crystals in periodic potentials

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. Quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.