Robust Control of Unstable Non-linear Quantum Systems
arXiv:2005.12321 · doi:10.1103/PhysRevA.102.052203
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.
arXiv comment5 pages, 4 figures
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- Optimal control of a Bose-Eintein Condensate in an optical lattice: The non-linear and two-dimensional cases
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