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A: Fachverband Atomphysik
A 11: Poster – Cold Atoms and Molecules, Matter Waves (joint session Q/A/MO)
A 11.29: Poster
Dienstag, 11. März 2025, 14:00–16:00, Tent
Fractal ground state of mesoscopic ion chains in periodic potentials — Raphael Menu1, Jorge Yago Malo2, •Joshua Weißenfels1, Vladan Vuletic3, Maria Luisa Chiofalo2, and Giovanna Morigi1 — 1Universität des Saarlandes, Saarbrücken, Germany — 2Università di Pisa, Pisa, Italy — 3Massachusetts Institute of Technology, Cambridge, USA
Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. The dynamics is captured by a long-range Frenkel-Kontorova model. We show that the classical ground state can be mapped to the one of a long-range Ising spin chain in a magnetic field, whose strength is determined by the mismatch between chain’s and substrate lattice’s periodicity. The mapping is exact when the substrate potential is a piecewise harmonic potential and holds for any two-body interaction decaying as 1/rα with the distance r. The ground state is a devil’s staircase of regular, periodic structures as a function of the mismatch and of the interaction exponent α. While the staircase is well defined in the thermodynamic limit for α>1, for Coulomb interactions, α=1, we argue that it disappears and the sliding-to-pinned transition becomes a crossover, with a convergence to the thermodynamic limit scaling logarithmically with the chain’s size. Due to this slow convergence, fractal properties can be observed even in chains of hundreds of ions at laser cooling temperatures.