Kitaev honeycomb and other exotic spin models with polar molecules

TL;DR

This paper proposes using ultracold polar molecules in optical lattices to simulate exotic spin models, including the Kitaev honeycomb model, by controlling dipole interactions with electric and microwave fields.

Contribution

It introduces a method to realize and control complex spin Hamiltonians, such as the Kitaev model, using polar molecules with tunable interactions via microwave fields.

Findings

Demonstrates how to encode spins in molecular rotational states.

Shows the interaction can be decomposed into five controllable Hamiltonian terms.

Discusses potential for realizing non-Abelian anyons and higher-spin models.

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}(theta,phi), where (theta,phi) 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., arXiv:1210.5518v2], we focus on the realization 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.