Shortcuts to adiabatic rotation of a two-ion chain

TL;DR

This paper develops and compares methods for fast, excitation-free rotation of a two-ion chain in a trap, including analytical and numerical approaches for different ion species and trap configurations.

Contribution

It introduces inverse engineering techniques for rapid ion chain rotation, analyzing separable and non-separable cases with new protocols and optimization methods.

Findings

Separable cases allow simpler protocol calculations.

Non-separable cases require numerical optimization.

Protocols successfully avoid final excitation during rotation.

Abstract

We inverse engineer fast rotations of a linear trap with two ions for a predetermined rotation angle and time, avoiding final excitation. Different approaches are analyzed and compared when the ions are of the same species or of different species. The separability into dynamical normal modes for equal ions in a common harmonic trap, or for different ions in non-harmonic traps with up to quartic terms allows for simpler computations of the rotation protocols. For non-separable scenarios, in particular for different ions in a harmonic trap, rotation protocols are also found using more costly numerical optimisations.