Coherent pulsed excitation of degenerate multistate systems: Exact analytic solutions

Abstract

We show that the solution of a multistate system composed of N degenerate lower (ground) states and one upper (excited) state can be reduced by using the Morris-Shore transformation to the solution of a two-state system involving only the excited state and a (bright) superposition of ground states. In addition, there are N-1 dark states composed of ground states. We use this decomposition to derive analytical solutions for degenerate extensions of the most popular exactly soluble models: the resonance solution, the Rabi, Landau-Zener, Rosen-Zener, Allen-Eberly and Demkov-Kunike models. We suggest various applications of the multistate solutions, for example, as tools for creating multistate coherent superpositions by generalized resonant pi-pulses. We show that such generalized pi-pulses can occur even when the upper state is far off resonance, at special detunings, which makes it possible to operate in the degenerate ground-state manifold without populating the (possibly lossy) upper state, even transiently.

arXiv comment11 pages, 6 figures

References in corpus (2)

• Quantum Computing
• Counterintuitive transitions between crossing energy levels

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