Realizing Hopf Insulators in Dipolar Spin Systems

There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

Abstract

The Hopf insulator represents a topological state of matter that exists outside the conventional ten-fold way classification of topological insulators. Its topology is protected by a linking number invariant, which arises from the unique topology of knots in three dimensions. We predict that three-dimensional arrays of driven, dipolar-interacting spins are a natural platform to experimentally realize the Hopf insulator. In particular, we demonstrate that certain terms within the dipolar interaction elegantly generate the requisite non-trivial topology, and that Floquet engineering can be used to optimize dipolar Hopf insulators with large gaps. Moreover, we show that the Hopf insulator's unconventional topology gives rise to a rich spectrum of edge mode behaviors, which can be directly probed in experiments. Finally, we present a detailed blueprint for realizing the Hopf insulator in lattice-trapped ultracold dipolar molecules; focusing on the example of \({}^{40}\)K\(^{87}\)Rb, we provide quantitative evidence for near-term experimental feasibility.

Related collections

Most cited references 5

Record: found
Abstract: found
Article: found

Is Open Access

Realizing a lattice spin model with polar molecules

Deborah S. Jin, Kaden R A Hazzard, Jacob P. Covey … (2013)

With the recent production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models for exploring quantum magnetism. In atomic systems, where interactions require wave function overlap, effective spin interactions on a lattice can be realized via superexchange; however, the coupling is weak and limited to nearest-neighbor interactions. In contrast, dipolar interactions exist in the absence of tunneling and extend beyond nearest neighbors. This allows coherent spin dynamics to persist even at high entropy and low lattice filling. Effects of dipolar interactions in ultracold molecular gases have so far been limited to the modification of chemical reactions. We now report the observation of dipolar interactions of polar molecules pinned in a 3D optical lattice. We realize a lattice spin model with spin encoded in rotational states, prepared and probed by microwaves. This spin-exchange interaction arises from the resonant exchange of rotational angular momentum between two molecules. We observe clear oscillations in the evolution of the spin coherence in addition to an overall decay. The frequency of these oscillations, the strong dependence of the spin coherence time on the lattice filling, and the effect of a multi-pulse sequence designed to reverse dynamics due to two-body exchange interactions all provide evidence of dipolar interactions. We also demonstrate suppression of loss in weak lattices due to a quantum Zeno mechanism. Measurements of these tunneling-induced losses allow us to independently determine the lattice filling factor. These results comprise an initial exploration of the behavior of many-body spin models with direct, long-range spin interactions and lay the groundwork for future studies of many-body dynamics in spin lattices.