Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices

Abstract

These authors contributed equally to this work.Quantum mechanical superexchange interactions form the basis of quantum magnetism in strongly correlated electronic media. We report on the direct measurement of superexchange interactions with ultracold atoms in optical lattices. After preparing a spin-mixture of ultracold atoms in an antiferromagnetically ordered state, we measure a coherent superexchange-mediated spin dynamics with coupling energies from 5 Hz up to 1 kHz. By dynamically modifying the potential bias between neighboring lattice sites, the magnitude and sign of the superexchange interaction can be controlled, thus allowing the system to be switched between antiferromagnetic or ferromagnetic spin interactions. We compare our findings to predictions of a two-site Bose-Hubbard Quantum spin systems on a lattice have served for decades as paradigms for condensed matter and statistical physics, elucidating fundamental properties of phase transitions and acting as models for the emergence of quantum magnetism in strongly correlated electronic media.In all these cases, the underlying systems rely on a spin-spin interaction between particles on neighboring lattice sites, such as in the Ising or Heisenberg model (1,2,3). As initially proposed for electrons by Dirac (4, 5) and Heisenberg (2, 6), effective spin-spin interactions can arise due to the interplay between the spin-independent Coulomb repulsion and exchange symmetry and do not require any direct coupling between the spins of the particles. The nature of such spin-exchange interactions is typically short-ranged, as it is governed by the wave function overlap of the underlying electronic orbitals. In several topical insulators, such as ionic solids like e.g. CuO and MnO, however, antiferromagnetic order arises even though the wave function overlap between the magnetic ions is practically zero. In this case a "superexchange" interaction mediated by higher order virtual hopping processes can be effective over large distance (7,8) which leads to an (anti)-ferromagnetic coupling between bosons (fermions) on neighboring lattice sites (3). Such superexchange interactions are believed to play an important role in the context of high-T c superconductivity (9). Furthermore, they can form the basis for the generation of robust quantum gates similar to recent work in electronic double quantum dot systems (10, 11), and can be used for the efficient generation of multi-particle entangled states (12, 13), as well as for the production of many-body quantum phases with topological order (14,15,16).We report on the direct observation of superexchange interactions with ultracold atoms in optical lattices (17,18). Previous experiments have shown that spin-spin interactions between neighboring atoms can be implemented in discrete time steps (19,20) by bringing the atoms together on a single site and carrying out controlled collisions (21,20,22) or onsite exchange interactions (23). The superexchange interactions demonstrated here, however, directly implement nearest-neigh...

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