Optimal ion shuttling for a noisy trap

Abstract We find continuous optimal trap trajectories to shuttle one ion with minimal excitation, when the trap spring constant is affected by white noise. The Euler-Lagrange method gives a lower bound for the dynamical (trajectory-dependent) energy sensitivity to the noise. Using a trigonometric ansatz for the state trajectories, the optimal trap trajectories are found for a given shuttling time and a fixed number of terms in the ansatz. The corresponding dynamical sensitivity tends to the lower bound as the number of terms increases. While the dynamical sensitivity increases by shortening the shuttling times, the static (trajectory-independent) one decreases, so we also find optimal shuttling times that minimize the global (static plus dynamical) sensitivity.