Quantum Computing Operations via Hamiltonian Engineering in Ultracold Neutral Atoms

Neutral atoms are a versatile platform for quantum simulation, where a desired Hamiltonian is engineered by tuning interactions between states. In this work, we explore possible quantum computing operations in ultracold ⁸⁷Rb, including those with non-trivial topological character. Our apparatus couples atomic states via optical, microwave, and modulated magnetic fields. We create Raman coupling between states with Δm_F of 1 or 2 by sending two beams with appropriate polarizations and a tuned frequency difference. In some cases, we can dynamically change the manifold dimensionality of the interacting system, as Raman coupling to specific states is suppressed via destructive interference between interaction paths. We also use microwave sources to directly couple between hyperfine levels, and we adjust the splitting between Zeeman sublevels by changing the strength of an external magnetic field. We combine these schemes to achieve useful Hamiltonians for quantum computing applications. Once computing operations are complete, we measure the output by Stern-Gerlach imaging. Typically, fully characterizing a qubit state requires several measurements to determine x-, y-, and z-populations. Here, we explore full state characterization by coupling to a higher dimensional manifold before imaging.