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Published July 1, 2013 | Published + Submitted
Journal Article Open

Kitaev honeycomb and other exotic spin models with polar molecules

Abstract

We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole–dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_2, q (θ, φ), where (θ, φ) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S.R. Manmana et al., Phys. Rev. B. 87, 081106 (2013)], we focus on the realisation of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry.

Additional Information

© 2013 Taylor & Francis. Received 17 April 2013; final version received 19 April 2013. The authors thank S. Manmana, E.M. Stoudenmire, J. Preskill, J. Ye, D. Jin, M. Lukin, N. Yao, J. Taylor, S. Stellmer, W. Campbell, P. Julienne, E. Tiemann, M. Foss-Feig, M. Hermele, and V. Gurarie for discussions. This work was supported by NSF, IQIM, NRC, AFOSR, ARO, KITP, the ARO-DARPA-OLE program, and theLee A. DuBridge andGordon andBetty Moore foundations. All authors thank KITP for hospitality. This manuscript is the contribution of NIST and is not subject to US copyright.

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Published - Gorshkov_2013p1908.pdf

Submitted - 1301.5636v1.pdf

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