Optimal trajectories for efficient atomic transport without final excitation

TL;DR

This paper develops optimal control-based trajectories for transporting cold atoms in harmonic traps efficiently, avoiding excitation and considering real trap constraints, with solutions including bang-bang and bang-off-bang protocols.

Contribution

It introduces a combined inverse engineering and optimal control approach to design realistic, efficient atom transport protocols with bounded trap displacements.

Findings

Minimum time transport follows a bang-bang protocol.

Minimum displacement transport follows a bang-off-bang protocol.

Optimal trajectories minimize transient energy under physical constraints.

Abstract

We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering techniqe based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really harmonic, we keep the relative displacement between the center of mass and the trap center bounded. Under this constraint, optimal protocols are found according to different physical criteria. The minimum time solution has a "bang-bang" form, and the minimum displacement solution is of "bang-off-bang" form. The optimal trajectories for minimizing the transient energy are also discussed.