H. Weimer

Trapped-ion arrays offer interesting possibilities for quantum simulation. We show that a proper arrangement of elliptical micro-traps combined with the external driving of the micro-trap frequencies allows, without the need of any precise fine-tuning, for the robust realization of non-Abelian vibron dynamics. We show that this non-Abelian nature may be readily probed experimentally in a simple plaquette arrangement. This study opens interesting perspectives for the study of non-Abelian spin-orbit coupling with motional excitations in two- and three-dimensional ion arrays.

The thermodynamics of low-dimensional systems departs significantly from phenomenologically deducted macroscopic laws. Particular examples, not yet fully understood, are provided by the breakdown of Fourier's law and the ballistic transport of heat. Low-dimensional trapped ion systems provide an experimentally accessible and well-controlled platform for the study of these problems. In our work, we study the transport of thermal energy in low-dimensional trapped ion crystals, focusing in particular on the influence of the Aubry-like transition that occurs when a topological defect is present in the crystal. We show that the transition significantly hinders efficient heat transport, being responsible for the rise of a marked temperature gradient in the non-equilibrium steady state. Further analysis reveals the importance of the motional eigenfrequencies of the crystal.

Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.