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

TL;DR

This paper develops control strategies for an ensemble of springs with applications to ion resonance and quantum systems, deriving analytical solutions for robust and selective excitation protocols.

Contribution

It introduces analytical control methods for ensembles of springs, applying them to ion resonance and quantum systems with a focus on robustness and selectivity.

Findings

Analytical expressions for control fields and dynamics derived.

Optimal control protocols for ion resonance demonstrated.

Robust and selective excitation protocols for quantum systems developed.

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.