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arXiv:0806.4217 · Journal of Modern Optics

Resonant analytic fields applied to generic multi-state systems

Toshiya Takami, Hiroshi Fujisaki

Published Nov 3, 2008• 1 citation
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Abstract

The rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approaches. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the Schrödinger equation. First, we introduce an extension of the rotating-wave approximation for multi-state systems. Under an assumption that a smooth transition is induced by the optimal field, we obtain three types of analytic control fields to demonstrate their validity and deficiency for generic systems represented by random matrices. Through the comparison, we conclude that the analytic field based on our coarse-grained approach outperforms the other ones for generic quantum systems with a large number of states. Finally, the further extension of the analytic field is introduced for realistic chaotic systems and its validity is shown in banded random matrix systems.

DOI
10.1080/09500340802296331

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We study the interplay between rotating-wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time independent under the rotating-wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multivariable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an NNN-level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic NNN-level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulse atoms in an experimentally relevant range of parameters.