Quantum control in the Cs 6S_1/2 ground manifold using radio-frequency and microwave magnetic fields

We implement arbitrary maps between pure states in the 16-dimensional Hilbert space associated with the ground electronic manifold of Cs133. This is accomplished by driving atoms with phase modulated radio-frequency and microwave fields, using modulation waveforms found via numerical optimization and designed to work robustly in the presence of imperfections. We evaluate the performance of a sample of randomly chosen state maps by randomized benchmarking, obtaining an average fidelity >99%. Our protocol advances state-of-the-art quantum control and has immediate applications in quantum metrology and tomography.