Coherent pulsed excitation of degenerate multistate systems: Exact analytic solutions

TL;DR

This paper derives exact analytical solutions for multistate quantum systems with degenerate ground states and one excited state, enabling efficient creation of superpositions and control without populating the upper state.

Contribution

It provides a reduction method using Morris-Shore transformation and extends popular models to degenerate multistate systems with analytical solutions.

Findings

Analytical solutions for degenerate multistate models derived

Generalized pi-pulses can operate off-resonance within ground states

Methods enable creating superpositions without populating the excited state

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.