All-microwave control of hyperfine states in ultracold spin-1 rubidium
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The manipulation of quantum spin states in a spinor Bose-Einstein condensate is critical for nearly all types of studies in these systems. State control methods are used to initialize the state of the system, apply Hamiltonian terms to modify the dynamics, and to measure properties of the quantum states. This thesis details the implementation of circularly polarized microwaves to selectively drive hyperfine transitions in the context of a spin-1 Bose-Einstein condensate of rubidium. This provides a new powerful tool for addressing specific transitions in the presence of frequency-degenerate transitions, allowing for new possibilities in state control. With this tool, we demonstrate a factor of 1/45.3 reduction in the coupling strength between polarization selected and blocked transitions by the application of a circularly polarized microwave field. This newly-developed tool is used to explore a couple of important applications. First, this polarized field is used to couple only three levels, out of all eight levels in the F=1, 2 hyperfine structure of ground-state rubidium-87, to drive an otherwise degenerate lambda system with 99.5% fidelity in state transfer from one base state of the lambda to the other. This is comparable to two-level transition fidelities measured in our system. This lambda transition has applications such as in implementing a non-adiabatic holonomic gate within the spin-1 states and could be extended to give full SU(2) control over two of the spin-1 states. Second, the circularly polarized field is applied to selectively drive hyperfine transitions in low bias fields, where the Zeeman splitting between the spin-1 states is small and comparable to the spectral linewidth of the driving field. In such low fields, microwave transitions without polarization selection scramble the state, as there are couplings between multiple levels within the hyperfine structure. This thesis demonstrates the selection of transitions using polarization control of the microwave field to solve this problem. These measurements imply the utility of circular polarization selected transitions for more rapid manipulations than otherwise possible.
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