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Frenkel-Kontorova model with cold trapped ions

I. Garcia-Mata·O. V. Zhirov·D. L. Shepelyansky
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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.

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I. Garcia-Mata, O. V. Zhirov, D. L. Shepelyansky. 2006-06-06. Frenkel-Kontorova model with cold trapped ions. https://doi.org/10.1140/epjd%2Fe2006-00220-2

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