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arXiv:1502.01430 · Physica Scripta

Optimal transport of two ions under slow spring-constant drifts

Xiao-Jing Lu, Mikel Palmero, A. Ruschhaupt, Xi Chen, Juan Gonzalo Muga

Published Jun 1, 2015• 13 citations
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Abstract

We investigate the effect of slow spring-constant drifts of the trap used to shuttle two ions of different mass. We design transport protocols to suppress or mitigate the final excitation energy by applying invariant-based inverse engineering, perturbation theory, and a harmonic dynamical normal-mode approximation. A simple, explicit trigonometric protocol for the trap trajectory is found to be robust with respect to the spring-constant drifts.

DOI
10.1088/0031-8949/90/7/074038

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We investigate the effect of slow spring-constant drifts of the trap used to shuttle two ions of different mass. We design transport protocols to suppress or mitigate the final excitation energy by applying invariant-based inverse engineering, perturbation theory, and a harmonic dynamical normal-mode approximation. A simple, explicit trigonometric protocol for the trap trajectory is found to be robust with respect to the spring-constant drifts.
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We study the fast transport of a particle or a Bose-Einstein condensate in a harmonic potential. An exact expression for the final excitation energy in terms of the Fourier transform of the trap acceleration is used to engineer optimal transport protocols (with no final excitation) that are robust with respect to spring-constant errors. The same technique provides a way to design the simultaneous and robust transport of a few noninteracting species that experience different harmonic trap frequencies in the same trap.
We design fast trajectories of a trap to transport two ions using a shortcut-to-adiabaticity technique based on invariants. The effects of anharmonicity are analyzed first perturbatively, with an approximate, single relative-motion mode, description. Then, we use classical calculations and full quantum calculations. This allows us to identify discrete transport times that minimize excitation in the presence of anharmonicity. An even better strategy to suppress the effects of anharmonicity in a continuous range of transport times is to modify the trajectory using an effective trap frequency shifted with respect to the actual frequency by the coupling between relative and center-of-mass motions.
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