A 1D ion chain on a laser field: a Wigner solid with vacancies

Abstract Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. We study a model for a 1D chain of such ions, as well as an approximation by a Frenkel–Kontorova model. The FK model, however, has other long-range properties. We discuss the meaning of structures like kink or anti-kink in the frame of the soliton theory, and that ion chains with large distances against the laser frame can have difficulties to move solitons. We study the case with 3 particles only for which all important properties can be demonstrated.