| Summary: | Spin is the elementary unit of magnetism. The interactions between many spins give a material its magnetic properties. This thesis focusses on one of the simplest magnetic materials: A one-dimensional chain of spins with tunable nearest-neighbor interactions. This system is described by the Heisenberg model, a paradigmatic model, which has been studied for almost a century now. But so far, experiments on spin dynamics have been mostly limited to isotropic spin-spin interactions.
In this work we use ultracold atoms to implement the first quantum simulator for the anisotropic Heisenberg model, with fully adjustable anisotropy of nearest-neighbor spin-spin interactions (also called the XXZ model). We study spin dynamics in previously unexplored regimes far away from equilibrium, as well as stable spin patterns far away from the ground state, which are even exact many-body eigenstates. For this we utilize quantum quenches from initial far-from-equilibrium spin-helix patterns:
Spin transport: By using a longitudinal spin-helix pattern, which involves a modulation in the population of spin up and spin down atoms, we see a drastic impact on the transport properties, when the anisotropy is varied. When spins are coupled only along two of three possible orientations (the XX model), we find ballistic behavior of spin dynamics, whereas for isotropic interactions (the XXX model), we find diffusive behavior. More generally, for positive anisotropies, the dynamics ranges from anomalous superdiffusion to subdiffusion, whereas for negative anisotropies, we observe a crossover in the time domain from ballistic to diffusive transport.
Spin dephasing: A transverse spin-helix pattern is sensitive to additional decay mechanisms: Anisotropic spin couplings break spin-rotational symmetry. Transverse spin components are no longer conserved and can decay not only by transport, but also by fast, local dephasing. However, even for isotropic interactions, we observe dephasing due to a new effect: an effective magnetic field created by superexchange, which has its origin in the mapping from the Hubbard model and which has not been observed before.
Bethe phantom states — excited many-body eigenstates of the Heisenberg model: For a given anisotropy, there exists one special winding angle, such that the transverse spin helix is an exact many-body eigenstate of the Hamiltonian. We find this eigenstate experimentally, by varying the winding angle and measuring the decay rate, which reveals a pronounced minimum. In a next step, we then use the sensitivity of the Bethe phantom states as a tool, to actually measure the anisotropy directly. We then find that the anisotropy can be strongly affected by nearest-neighbor off-site interactions, which have never been observed before for particles, which only interact with contact interactions.
Our new quantum simulator platform with tunable interactions opens up possibilities for many new studies which are likely to provide new insight into the rich dynamics of Heisenberg spin models and beyond.
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