Robust Control of Unstable Non-linear Quantum Systems

TL;DR

This paper demonstrates that adiabatic passage is highly non-robust in unstable driven nonlinear quantum systems and introduces inverse-engineered trajectories that achieve high-fidelity, robust transfer.

Contribution

It reveals the non-robustness of adiabatic passage in unstable nonlinear quantum systems and proposes a novel inverse engineering method for robust state transfer.

Findings

Adiabatic passage fails in unstable nonlinear quantum systems.

Inverse-engineered trajectories improve robustness and fidelity.

Applicable to Bose-Einstein condensates and nonlinear optics.

Abstract

Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that, in the context of driven nonlinear Hamiltonian systems, adiabatic passage becomes highly non-robust when the target is unstable. We show this result for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point in the classical phase space featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially non-adiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the target in a robust way. These results can be applicable to atom-molecule Bose-Einstein condensate conversion and to nonlinear optics.