Quantum versus semi-classical signatures of correlated triple ionization in Dalitz plots

We investigate correlated three-electron escape in Ne when driven by an intense, infrared laser field. We do so by employing a reduced-dimensionality quantum-mechanical model and two three-dimensional semi-classical models. One semi-classical model is a recently developed one that accounts with effective coulomb potentials for the interaction between two bound electrons (ECBB) while it fully accounts for all other interactions. The other semi-classical model is the Heisenberg one, which effectively accounts for the interaction of each electron with the core via a soft-core potential. We identify and compare the signatures of correlated three-electron escape for both quantum and semi-classical models on Dalitz plots and find a better agreement between the quantum and the ECBB model. We also show that a central spot'' on the Dalitz plots is reproduced by all models. Using the ECBB model we associate this spot’’ with the direct triple ionization pathway and argue this to be the case also for the quantum model. Devising a simple classical model that accounts for the direct pathway of triple ionization, we show that the width of this spot in the Dalitz plots solely depends on the time of tunnel-ionization.

💡 Research Summary

This paper investigates the correlated escape of three electrons from a neon atom driven by an intense infrared laser field, focusing on the signatures of non‑sequential multiple ionization (NSMI) as visualized in Dalitz plots. Three theoretical approaches are employed: a reduced‑dimensionality quantum‑mechanical model and two three‑dimensional semi‑classical models, namely the Effective Coulomb‑Potential for Bound‑Bound (ECBB) model and the Heisenberg (H) model.

The ECBB model treats the electron‑core interaction with the full Coulomb potential for all electrons, while the interaction between two bound electrons is replaced by an effective Coulomb potential that remains finite at zero separation. A set of on‑the‑fly criteria determines whether a given electron is “bound” or “quasifree,” thereby preventing artificial auto‑ionization. The Heisenberg model, in contrast, softens the electron‑core Coulomb singularity by adding a Heisenberg‑type repulsive potential, which eliminates auto‑ionization but also softens recollisions, leading to less efficient energy transfer during electron‑electron collisions.

The quantum model confines each electron to a one‑dimensional track inclined at a fixed angle to the laser polarization axis; the three tracks are spaced by π/6. The Hamiltonian includes full Coulomb electron‑electron and electron‑core terms, softened by a small regularisation parameter ε and an effective charge q_ee chosen to reproduce neon’s triple‑ionization potential (Ip = 4.63 a.u.). The laser pulse is 800 nm, 25 fs (full‑width at half‑maximum), with peak intensities of 1.0, 1.3, and 1.6 PW cm⁻². The first electron tunnel‑ionizes according to the ADK rate (including high‑intensity corrections), its exit point is obtained analytically, and the transverse momentum follows a Gaussian distribution derived from tunnelling theory. The initially bound electrons are sampled from a micro‑canonical distribution.

All three models generate Dalitz plots of the final electron momenta. A pronounced central “spot” appears in every plot. The ECBB and quantum results show an almost identical spot in terms of position, shape, and density, indicating that the ECBB model captures the essential quantum dynamics of the direct triple‑ionization pathway. The Heisenberg model also reproduces the spot but with a broader, noisier distribution, reflecting its softened recollisions and reduced direct‑ionization probability.

To interpret the spot, the authors devise a simple classical picture: the width of the central spot depends solely on the distribution of the tunnelling time t₀ of the first electron. Since the tunnelling instant determines the subsequent recollision timing and the amount of energy transferred to the two bound electrons, variations in t₀ translate directly into variations of the final momentum sharing among the three electrons, which manifests as the horizontal spread of the spot in the Dalitz plot. Consequently, measuring the spot width provides a diagnostic of the tunnelling‑time distribution under given laser parameters.

The paper concludes that (i) the ECBB semi‑classical model offers quantum‑level accuracy for triple ionization while being computationally cheaper than full quantum simulations, (ii) the central spot in Dalitz plots is a robust fingerprint of direct triple ionization, observable across different theoretical frameworks, and (iii) the spot’s width is a sensitive probe of the tunnelling dynamics. These findings supply a concrete benchmark for future experimental studies of three‑electron dynamics and guide the development of efficient yet accurate theoretical tools for strong‑field multi‑electron processes.