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New Tools for Unitary Control of Cold Atom Qudits

Hector Sosa Martinez, University of Arizona

(Session 9c : Friday from 4:00pm - 4:30pm)

Accurate and robust quantum control of single or coupled qubit systems is a key element of quantum information science. In practice, the actual physical building blocks (atoms, ions, superconducting devices) are often qudits with state space dimension d>2, and the available auxiliary levels have proven useful for information processing tasks such as implementing Toffoli gates with two-body interactions. More generally, large internal state spaces may prove a useful resource if good laboratory tools for qudit manipulation can be developed. As a laboratory test bed for such development, we have implemented a protocol to perform arbitrary unitary transformations in the 16 dimensional ground hyperfine manifold of individual 133Cs atoms, by driving this system with phase modulated rf and microwave magnetic fields and using the tools of optimal control to find appropriate control waveforms. Similar to what can be achieved for qubits, we show that accurate unitary control can be achieved in the presence of simultaneous static and dynamical perturbations and imperfections in the control fields, simply by optimizing with respect to the appropriate cost function when designing control waveforms. We anticipate this approach to prove helpful for control in less than ideal environments, such as atoms moving around in the light shift potential of a dipole trap. We are currently exploring the prospects for inhomogeneous quantum control, with the goal of performing different unitary transformations on qudits that see different light shifts from an optical addressing field. Ultimately this may lead to addressable unitary control similar to what has been demonstrated for atomic qubits in optical lattices.