Treating Branch Cuts in Quantum Trajectory Models for Photoelectron Holography

TL;DR

This paper introduces an efficient method for handling branch cuts in quantum trajectory models, improving the accuracy of photoelectron holography simulations by removing artifacts caused by these cuts.

Contribution

The authors develop a novel, computationally light approach to treat branch cuts in complex Coulomb trajectories, enhancing the modeling of photoelectron holography.

Findings

Branch cuts cause artifacts in holographic fringes.

The method effectively removes discontinuities and caustics.

Comparison shows improved agreement with Schrödinger equation solutions.

Abstract

Most implementations of Coulomb-distorted strong-field approaches that contain features such as tunneling and quantum interference use real trajectories in continuum propagation, while a fully consistent approach must use complex trajectories throughout. A key difficulty in the latter case are branch cuts that appear due to the specific form of the Coulomb potential. We present a method for treating branch cuts in quantum-trajectory models, which is subsequently applied to photoelectron holography. Our method is not numerically intensive, as it does not require finding the location of all branching points and branch cuts prior to its implementation, and is applicable to Coulomb-free and Coulomb-distorted trajectories. We show that the presence of branch cuts leads to discontinuities and caustics in the holographic fringes in above-threshold ionization (ATI) photoelectron angular distributions (PAD). These artefacts are removed applying our method, provided they appear far enough from the polarization axis. A comparison with the full solution of the time-dependent Schr\"odinger equation is also performed, and a discussion of the applicability range of the present approach is provided.