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We study the simultaneous control of an ensemble of springs with differentfrequencies by means of adiabatic, shortcut to adiabaticity and optimalprocesses. The linearity of the system allows us to derive analyticalexpressions for the control fields and the time evolution of the dynamics. Wediscuss the relative advantages of the different solutions. These results areapplied in two different examples. For Ion Cyclotron Resonance, we show how tooptimally control ions by means of electric field. Using a mapping betweenspins and springs, we derive analytical shortcut protocols to realize robustand selective excitations of two-level quantum systems.

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