Quantum Control in the Cs6S1/2Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields

Abstract

We implement arbitrary maps between pure states in the 16-dimensional Hilbert space associated with the ground electronic manifold of ^{133}Cs. 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.

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

“…On average, for large samples of randomly chosen transformations, we achieve fidelities from 0.982(2) for unitary maps to 0.995(1) for state maps (errors are one standard deviation). These results represent a significant advance in control complexity and fidelity compared to our prior work on state-to-state maps [13], and to stateof-the art for other systems with similar-sized Hilbert spaces [11,14]. Furthermore, given that the optimal control paradigm applies to any physical platform regardless of specifics, our work provides a useful template for similar advances elsewhere.…”

“…A similar approach might suffice for robust control of many other well behaved physical systems. In more challenging scenarios, our experiments on state maps [13] and our numerical exploration of waveform design for more complex tasks show that robust control can be extended to additional inhomogeneous parameters. One can also compensate for larger inhomogeneous bandwidths than done here.…”

“…We study the efficacy of numerical design and the performance of the resulting Hamiltonians, using as our test bed the electron and nuclear spins of individual 133 Cs atoms driven by radio frequency (rf) and microwave (µw) magnetic fields [12,13]. Our experiments show that the optimal control strategy is adaptable to a wide range of tasks, and that it can generate control Hamiltonians with excellent performance in the presence of static and dynamic perturbations.…”

“…Technical aspects of our laboratory setup were described in [13]. The basic experimental sequence is performed in parallel on ∼ 10 6 laser cooled Cs atoms, and consists of initial state preparation, implementation of a quantum map, and a measurement of the output populations in the magnetic sublevels |F, m .…”

“…In principle one can reconstruct a quantum map through process tomography, but in practice this procedure is too error prone for our needs here. We rely instead on randomized benchmarking, a protocol originally developed for qubits [28], applied to state-to-state maps in [13], and here extended to general maps H i → H f . The idea is to start with a random input state, apply a random sequence of l maps, and estimate its overall fidelity by measuring the population of the expected output state.…”