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arXiv · 2005.12321

Robust Control of Unstable Non-linear Quantum Systems

Jing-Jun Zhu·Xi Chen·Hans-Rudolf Jauslin·Stéphane Guérin
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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.

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Jing-Jun Zhu, Xi Chen, Hans-Rudolf Jauslin, Stéphane Guérin. 2020-05-25. Robust Control of Unstable Non-linear Quantum Systems. https://doi.org/10.1103/physreva.102.052203

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