Quantum simulations with 8̳8̳Sr+̳ ions on planar lattice traps

Abstract

Quantum simulations are the use of well controlled many-body quantum systems to simulate and solve other many-body quantum systems that are not understood. This thesis describes theoretical proposals and experimental progress towards simulating quantum spin Hamiltonians with trapped SSSr+ ions on microfabricated planar lattice traps. These types of quantum simulations help solve exponentially complex quantum systems, which are challenging to current classical computers. Porras and Cirac's work has shown that off-resonance laser light couples the internal states of the trapped ions with their external motional states; the external states of the ions are coupled through their Coulomb repulsion. Therefore the internal states of ions can be mapped to effective spin states and spin coupling is mediated by phonons. I propose two simulation schemes for quantum spin Hamiltonians in two dimensions: the time evolution of a spin state in a system of three ions with ferromagnetic interaction and spin frustration in a triangle. To realize these proposals, I design and microfabricate a hexagonal lattice trap and install it into an ultrahigh vacuum chamber. This thesis also presents the construction of the experimental test apparatus for the trapped ion quantum simulator, including the electronics, optics, and vacuum systems.