Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices

We describe a general technique that allows one to induce and control strong interaction between spin states of neighboring atoms in an optical lattice. We show that the properties of spin exchange interactions, such as magnitude, sign, and anisotropy, can be designed by adjusting the optical potentials. We illustrate how this technique can be used to efficiently “engineer” quantum spin systems with desired properties, for specific examples ranging from scalable quantum computation to probing a model with complex topological order that supports exotic anyonic excitations.

Figure 1

Phase diagrams of the Hamiltonians (2) for bosonic and fermionic atoms: (a) at zero magnetic field, (b) with a longitudinal field $h_z$, and (c) (for bosons only) with a transverse field $h_x$. Each phase is characterized by the following order parameter: I, $z$-Néel order; II, $z$-ferromagnetic order; III, $xy$-Néel order for fermionic atoms and $xy$-ferromagnetic order for bosonic atoms; IV and V, spin polarization in the direction of applied field, $z$ and $x$, respectively.

Figure 2

(a) The contours with the three potentials in the form of Eq. (5). The minima are at the centers of the triangles when ${\phi }_0=\pi /2$. (b) The illustration of the model Hamiltonian (4). (c) The schematic atomic level structure and the laser configuration to induce spin-dependent tunneling.