Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance

TL;DR

This paper derives exact transition probabilities for a localized electron spin system undergoing a linear frequency sweep through a Kramers-Kronig resonance, accounting for both spin state changes and electron escape into a continuum.

Contribution

It provides an exact analytical solution for transition probabilities during a linear sweep through a resonance, extending previous models to include continuum states.

Findings

Exact transition probabilities are derived for the linear sweep case.

The results are applicable regardless of the resonance shape.

Extensions to multistate systems are discussed.

Abstract

We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the Inverse Faraday Effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can also escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly regardless the shape of the resonance. We also discuss extension of our results to multistate systems.