Thermal activation, long-range ordering, and topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, are ubiquitous in nature and display many rich phenomena and novel physics. Artificial spin ices (ASIs), arrays of lithographically patterned Ising-like single-domain magnetic nanostructures, are highly tunable systems that have proven to be a novel method for studying the effects of frustration and associated properties. The strength and nature of the frustrated interactions between individual magnets are readily tuned by design and the exact microstate of the system can be determined by a variety of characterization techniques. Recently, thermal activation of ASI systems has been demonstrated, introducing the spontaneous reversal of individual magnets and allowing for new explorations of novel phase transitions and phenomena using these systems. In this work, we introduce a new, robust material with favorable magnetic properties for studying thermally active ASI and use it to investigate a variety of ASI geometries. We reproduce previously reported perfect ground-state ordering in the square geometry and present studies of the kagome lattice showing the highest yet degree of ordering observed in this fully frustrated system. We consider theoretical predictions of long-range order in ASI and use both our experimental studies and kinetic Monte Carlo simulations to evaluate these predictions. Next, we introduce controlled topological defects into our square ASI samples and observe a new, extended frustration effect of the system. When we introduce a dislocation into the lattice, we still see large domains of ground-state order, but, in every sample, a domain wall containing higher energy spin arrangements originates from the dislocation, resolving a discontinuity in the ground-state order parameter. Locally, the magnets are unfrustrated, but frustration of the lattice persists due to its topology. We demonstrate the first direct imaging of spin configurations resulting from topological frustration in any system and make predictions on how dislocations could affect properties in numerous materials systems.

Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.