Mainz 2026 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 37: Ultra-cold Atoms, Ions and BEC II (joint session A/Q)
Q 37.7: Talk
Wednesday, March 4, 2026, 16:15–16:30, N 1
Fractal ground state of mesoscopic ion chains in periodic potentials — Raphaël Menu1, Jorge Yago Malo2, •Joshua Weißenfels1, Vladan Vuletić3, Maria Luisa Chiofalo2, and Giovanna Morigi1 — 1Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany — 2Dipartimento di Fisica Enrico Fermi, Universita di Pisa and INFN, Largo B. Pontecorvo 3, I-56127 Pisa, Italy — 3Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. The dynamics are 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 the 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. We show that the ground state is a devil’s staircase of regular, periodic structures as a function of the mismatch and of the interaction exponent α. The predictions of the piecewise parabolic potentials are compared with the case when the substrate is a sinusoidal potential.
Keywords: Frenkel-Kontorova; Wigner crystal; Devil's staircase; commensurate-incommensurate; Aubry