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Quantum simulation of the hexagonal Kitaev model with trapped ions

Published

Author(s)

Dietrich G. Leibfried, Roman Schmied , Janus H. Wesenberg

Abstract

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
Volume
13

Keywords

dipole-dipole interaction, ion trap, quantum simulation, surface electrode trap

Citation

Leibfried, D. , Schmied, R. and Wesenberg, J. (2011), Quantum simulation of the hexagonal Kitaev model with trapped ions, New Journal of Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=909138 (Accessed October 28, 2021)
Created November 25, 2011, Updated February 19, 2017