Spin transport and transverse spin dynamics in a tunable Heisenberg model realized with ultracold atoms*

Simple models of interacting spins play an important role in physics. The field of quantum simulation aims at implementing such systems in a controlled and tunable way. So far, spin transport has only been studied in systems with isotropic spin–spin interactions. Here we realize the spin-1/2 anisotropic Heisenberg model, with fully adjustable anisotropy of the nearest-neighbour spin–spin couplings (called the XXZ model). In this model we study spin transport far from equilibrium after quantum quenches from imprinted spin-helix patterns. When spins are coupled only along two of three possible orientations (the XX model), we find ballistic behaviour of spin dynamics, whereas for isotropic interactions (the XXX model), we find diffusive behaviour. More generally, for positive anisotropies, the dynamics ranges from anomalous superdiffusion to subdiffusion. Furthermore, with anisotropic spin couplings, transverse spin components are no longer conserved and can decay not only by transport, but also by dephasing. We observe fast, local spin decay controlled by the anisotropy. Additionally, we directly observe an effective magnetic field created by superexchange which causes an inhomogeneous decay mechanism due to variations of lattice depth between chains, as well as a homogeneous dephasing mechanism due to the twofold reduction of the effective magnetic field at the edges of the chains and due to fluctuations of the effective magnetic field in the presence of mobile holes.