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Quantum State Mapping in the Cs 133 Full Hyperfine Ground Manifold

Aaron Smith, University of Arizona

(Session 6 : Saturday from 10:45-11:15)

Abstract. Aaron Smith, Brian E. Anderson, Poul Jessen: Center for Quantum Information and Control, College of Optical Sciences, University of Arizona Quantum systems with Hilbert space dimension greater than two (qudits) are often thought of as carriers of quantum information, usually by isolating a convenient pair of states (qubit) and working entirely within this two dimensional embedded subspace. Quantum control of the entire qudit system could prove to be very useful for information processing tasks allowing for the implementation of novel protocols for robust qubit manipulation and error correction. Quantum control of systems with large Hilbert space dimension, especially collective spins, also has near-term applications in quantum metrology. We will describe a method in which to achieve universal quantum control of the entire 16 dimensional hyperfine ground manifold of Cesium using a nearly decoherence free protocol involving the application of static, RF, and microwave magnetic fields. A simple numerical optimization routine can be used to design time dependent control fields that map any initial state onto any target state. We have implemented this control protocol in our experiment and have successfully mapped our initial state, |F=4, m=4>, onto all 16 magnetic eigenstates. We measure the fidelity of the state mapping using Stern-Gerlach analysis and we have achieved fidelities in the range ~ 94% - 98% which is limited almost entirely by errors in the control fields. Our next step is to implement a weak measurement in combination with dynamical control, and to perform quantum state reconstruction based on the resulting measurement record.