State-Population Narrowing Effect in Two-Photon Absorption for Intense Hard X-ray Pulses

Krzysztof Tyrała,Marek Pajek,Christopher Milne,Jacinto Sá,Jakub Szlachetko,Klaudia Wojtaszek,Yves Kayser

doi:10.3390/app7070653

Abstract

We report on studies of state-populations during the two-photon absorption process using intense X-ray pulses. The calculations were performed in a time-dependent manner using a simple three-level model expressed by coupled rate equations. We show that the proposed approach describes well the measured rates of X-rays excited in the one-photon and two-photon absorption processes, and allows detailed investigation of the state population dynamics during the course of the incident X-ray pulse. Finally, we demonstrate that the nonlinear interaction of X-ray pulses with atoms leads to a time-narrowing of state populations. This narrowing-effect is attributed to a quadratic incidence X-ray intensity dependence characteristic for nonlinear interactions of photons with matter.

Highlights

In X-ray spectroscopy, the photon absorption and emission processes are usually treated within a weak photon-matter interaction limit, which implies that photon-in and photon-out processes are linearly correlated
At femtosecond-durations, the intense pulses made available by X-ray Free Electron Lasers (XFELs) presently allow us to access a -far-uninvestigated area of physics, and to probe the physical mechanisms that drive the nonlinear interaction of X-rays with matter [11,12,13]
X-rays resulting from the two-photon absorption process

Summary

Introduction

In X-ray spectroscopy, the photon absorption and emission processes are usually treated within a weak photon-matter interaction limit, which implies that photon-in and photon-out processes are linearly correlated. For strong enough X-ray fields, the nonlinear regime may be accessed and multi-photon processes are possible, leading to a nonlinear dependence of the X-ray photons in/out signals. Such a nonlinear regime, available for many years at optical frequencies in laser spectroscopy [1,2,3,4], remained an unexplored area at X-ray wavelengths due to the lack of strong enough X-ray sources. At femtosecond-durations, the intense pulses made available by XFELs presently allow us to access a -far-uninvestigated area of physics, and to probe the physical mechanisms that drive the nonlinear interaction of X-rays with matter [11,12,13]

Methods

Results

Conclusion