Robust control of an ensemble of springs: Application to Ion Cyclotron Resonance and two-level Quantum Systems

Abstract

We study the simultaneous control of an ensemble of springs with different frequencies by means of adiabatic, shortcut to adiabaticity and optimal processes. The linearity of the system allows us to derive analytical expressions for the control fields and the time evolution of the dynamics. We discuss the relative advantages of the different solutions. These results are applied in two different examples. For Ion Cyclotron Resonance, we show how to optimally control ions by means of electric field. Using a mapping between spins and springs, we derive analytical shortcut protocols to realize robust and selective excitations of two-level quantum systems.

arXiv comment25 pages, 7 figures

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• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Robust transitionless quantum driving: Concatenated approach
• Open loop linear control of quadratic Hamiltonians with applications
• On the optimality of optical pumping for a closed $\Lambda$-system with large decay rates of the intermediate excited state