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Physical Review A

Efficient adiabatic tracking of driven quantum nonlinear systems

S. Guérin, Mariam Gevorgyan, Claude Leroy, Hans Rudolf Jauslin, Artur Mikhailovich Ishkhanyan

Published Dec 11, 2013• 16 citations
Publisher

Abstract

We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically for an infinite pulse area.

DOI
10.1103/physreva.88.063622

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We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically for an infinite pulse area.
Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that in driven nonlinear quantum systems adiabatic passage becomes highly nonrobust when the target is unstable. This occurs for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially nonadiabatic 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.
Robust stimulated Raman exact passages are requisite for controlling nonlinear quantum systems, with wide applications, ranging from ultracold molecules to nonlinear optics to superchemistry. Inspired by shortcuts to adiabaticity, we propose the fast-forward scaling of stimulated Raman adiabatic processes with nonlinearity involved, describing the transfer from an atomic Bose-Einstein condensate to a molecular one by controllable external fields. The fidelity and robustness of atom-molecule conversion are shown to surpass those of conventional adiabatic passages, assisted by the fast-forward driving field. Finally, our results are extended to fractional stimulated Raman adiabatic processes for the coherent superposition of atomic and molecular states.
A new scheme of controlling molecular processes by a sequence of linearly chirped pulses is proposed and is applied to selective excitation of an energy level among closely lying ones and to complete electronic excitation of a diatomic molecule. The basic idea is quite different from the conventional ones utilizing chirped pulses in the sense that the present one does not rely on the idea of adiabatic rapid passage at all, but tries to control basic nonadiabatic transitions explicitly. Control of molecular processes can be achieved by controlling nonadiabatic transitions among Floquet (or dressed) states with use of the interference effects. The scheme can be formulated with use of the analytical theories of nonadiabatic transitions, and the proper control parameters can be estimated theoretically. Numerical demonstrations are provided to confirm the robustness of the method in comparison with the other conventional ones. Namely, the present scheme is shown to be stable against the variation of pulse area, complete and selective in population transfer, and fast to accomplish the transition. It is expected that the method can be applied to general multilevel systems and various types of wave packet dynamics. Its experimental realizability can also be expected, since linear chirping can now be relatively easily realized and manipulated.
We explore the efficiency and robustness of population transfer in two-state systems by adiabatic passage (i) when the driving pulse is optimally designed in order to lead to parallel adiabatic passage or (ii) with a linear chirping. We show how one could practically implement the corresponding designs of the pulses in the spectral domain. We analyze the robustness of the two shapings taking into account fluctuations of the phase, amplitude, and the area of the pulse. We show the overall superiority of the parallel adiabatic passage especially when one faces the issue of a pulse area that is not well known. We show that the robustness of parallel adiabatic passage is not improved when it is complemented by a correcting field that cancels out the nonadiabatic losses.