Instantaneous ionization rate as a functional derivative

I A Ivanov,Chang Hee Nam,C Hofmann,A S Landsman,Kyung Taec Kim,L Ortmann

doi:10.1038/s42005-018-0085-5

Abstract

The notion of the instantaneous ionization rate (IIR) is often employed in the literature for understanding the process of strong field ionization of atoms and molecules. This notion is based on the idea of the ionization event occurring at a given moment of time, which is difficult to reconcile with the conventional quantum mechanics. We describe an approach defining instantaneous ionization rate as a functional derivative of the total ionization probability. The definition is based on physical quantities, such as the total ionization probability and the waveform of an ionizing pulse, which are directly measurable. The definition is, therefore, unambiguous and does not suffer from gauge non-invariance. We compute IIR by numerically solving the time-dependent Schrödinger equation for the hydrogen atom in a strong laser field. In agreement with some previous results using attoclock methodology, the IIR we define does not show measurable delay in strong field tunnel ionization.

Highlights

The notion of the instantaneous ionization rate (IIR) is often employed in the literature for understanding the process of strong field ionization of atoms and molecules
The notion of IIR underlies many successful simulations of tunneling ionization phenomena, relying on Classical Trajectory Monte Carlo method[7] or quantum trajectories[8,9] Monte-Carlo simulations. These methods become practically indispensable if the system in question is too complicated to allow an ab initio treatment based on the numerical solution of the time-dependent Schrödinger equation (TDSE)
In the present work we describe a different approach to IIR, which is based on the notion of a functional derivative

Summary

Introduction

The notion of the instantaneous ionization rate (IIR) is often employed in the literature for understanding the process of strong field ionization of atoms and molecules. The notion of IIR underlies many successful simulations of tunneling ionization phenomena, relying on Classical Trajectory Monte Carlo method[7] or quantum trajectories[8,9] Monte-Carlo simulations These methods become practically indispensable if the system in question is too complicated to allow an ab initio treatment based on the numerical solution of the time-dependent Schrödinger equation (TDSE). The projection of the solution of the TDSE onto the subspace of the bound states performed during the interval of the pulse duration generally depends on the gauge used to describe atom-field interaction Another approach which allows us to define IIR from the solution of the TDSE is based on the notion of the electron flux and was given in ref. Another approach which allows us to define IIR from the solution of the TDSE is based on the notion of the electron flux and was given in ref. 24

Methods

Results

Conclusion