We present a detailed study of quantum simulations of coupled spin systems in surface-electrode ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics 321,2 (2006)]. The e effective (pseudo)spin interactions making up such quantum simulators are found to be proportional to the dipole-dipole interaction between the trapped ions, and are mediated by motion driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of a surface electrode and a cover electrode. These results are the starting point to derive an optimized surface-electrode geometry for trapping ions in the desired honeycomb lattice of Kitaev's model, where we design the dipole-dipole interactions in a way that allows for coupling all three bond types of the model simultaneously, without the need for time discretization. Finally we propose a simple wire structure that can be incorporated in a microfabricated chip to drive the couplings prescribed by this particular model and should be adaptable to many other situations.
Citation: New Journal of Physics
Pub Type: Journals
dipole-dipole interaction, ion trap, quantum simulation, surface electrode trap