Treating branch cuts in quantum trajectory models for photoelectron holography

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 Schrödinger equation is also performed, and a discussion of the applicability range of the present approach is provided.

Spiral-like holographic structures: Unwinding interference carpets of Coulomb-distorted orbits in strong-field ionization

“…The integral in Eq. 3diverges at the lower bound; this is fixed using a regularization procedure [37][38][39]. The variables t s , p s , and r s are determined by the saddle-point equations…”

“…In contrast to previous calculations [18,[33][34][35]37,46], 1 here we employ the single-electron effective potential [47,48]…”

Holographic detection of parity in atomic and molecular orbitals

“…The main features of the fan-shaped, spiderlike, and carpetlike structures for Ar and N 2 are faithfully reproduced. The CQSFA underestimates the signal near the polarization axis due to approximations in the continuum propagation [42]. Figure 3(b) displays the calculated differential hologram highlighting the difference of the carpet structures.…”

“…For simplicity, we used −1/r as the form of Coulomb potential for both Ar and N 2 in the simulations. Close to the origin, a regularization procedure was implemented to treat the Coulomb singularities in the complex time plane (See [42] and references therein). The GAMESS code [43] was adopted to calculate the exact wave functions of the 3p, m = 0 state for Ar, neglecting spin orbit interaction and the HOMO of N 2 .…”

Semiclassical two-step model for ionization by a strong laser pulse: further developments and applications

“…However, a significant progress along these lines has been made in the last decade. The trajectory-based Coulomb SFA (TCSFA) [37,53], the quantum trajectory Monte Carlo model (QTMC) [54], the semiclassical two-step model (SCTS) [55], and the Coulomb quantum orbit strongfield approximation (CQSFA) [56][57][58][59][60] (see Ref. [61] for the foundations of the CQSFA approach) are recent trajectory-based models that are capable to reproduce interference structures in photoelectron momentum distributions of the ATI process.…”