A criterion for population inversion by arbitrary pulses

TL;DR

This paper develops a theoretical criterion for achieving population inversion in N-level quantum systems using arbitrary shaped pulses, extending previous pi-pulse criteria beyond simple approximations.

Contribution

It generalizes the pi-pulse resonance condition to arbitrary pulse shapes using Floquet theory and constructs an effective 2-level system for describing the dynamics.

Findings

Resonance criteria based on Floquet quasienergies.

Eigenvector analysis provides a sufficient condition for resonance.

Effective 2-level system simplifies the N-level dynamics.

Abstract

We investigate theoretically population dynamics in an N-level system for pulses of arbitrary shape. In order to use Floquet theory the pulse only has to have finite support in time, which is well fulfilled in experiments. Furthermore the dynamics must be approximately time-local, which restricts to negligible memory effects. Despite the few requirements we are able to derive criteria for resonances, which means that all population rests in a preselected state after the pulse has been applied. We show that the necessary criterion on the Floquet quasienergies is a generalization of the pi-pulse criterion, derived within the Rotating Wave Approximation and adiabatic aproximation for the envelope by Holthaus et. al., to pulses of arbitrary shape. Furthermore we find that only the eigenvectors contain enough information to give a sufficient criterion for a resonance. We constuct the resonant N-level propagator and show that it is block diagonal, leading to a description by an effective 2-level-system composed of the initial and final state.