Resonant photoionization and time delay

Resonances leave prominent signatures in atomic and molecular ionization triggered by the absorption of single or multiple photons. These signatures reveal various aspects of the ionization process, characterizing both the initial and final states of the target. Resonant spectral features are typically associated with sharp variations in the photoionization phase, providing an opportunity for laser-assisted interferometric techniques to measure this phase and convert it into a photoemission time delay. This time delay offers a precise characterization of the timing of the photoemission process. In this review, a unified approach to resonant photoionization is presented by examining the analytic properties of ionization amplitude in the complex photoelectron energy plane. This approach establishes a connection between the resonant photoemission time delay and the corresponding photoionization cross-section. Numerical illustrations of this method include: (i) giant or shape resonances, where the photoelectron is spatially confined within a potential barrier, (ii) Fano resonances, where bound states are embedded in the continuum, (iii) Cooper minima (anti-resonances) arising from kinematic nodes in the dipole transition matrix elements, and (iv) confinement resonances in atoms encapsulated within a fullerene cage. The second part of this review focuses on two-photon resonant ionization processes, where the photon energies can be tuned to a resonance in either the intermediate or final state of the atomic target. Our examples include one- or two-electron discrete excitations both below and above the ionization threshold. These resonant states are probed using laser-assisted interferometric techniques. Additionally, we employ laser-assisted photoemission to measure the lifetimes of several atomic autoionizing states.

💡 Research Summary

This topical review presents a unified theoretical framework for resonant photoionization in atoms and molecules, linking the analytic properties of the ionization amplitude in the complex photoelectron‑energy plane to observable quantities such as the photoionization cross‑section and the Wigner time delay. The authors first treat single‑photon processes, demonstrating that the amplitude’s poles (or resonant zeros) give rise to characteristic phase variations that can be directly translated into time delays via τ_W = dδ/dE. They illustrate this connection for four archetypal resonances.

Shape resonances, arising from a quasi‑bound electron trapped behind a centrifugal‑plus‑potential barrier, are described using a scattering‑matrix formalism. The dipole matrix element is approximated by D(E) ≈ d(E) e^{2iδ(E)}, leading to σ(E)=σ_max sin²δ(E) and τ_W = ∂δ/∂E. Numerical calculations for Xe 4d→εf and I⁻ 4d→εf transitions show that time delays obtained from the phase and those derived from the cross‑section derivative are essentially identical, confirming the analytic relation.

Fano resonances, where a discrete state is embedded in a continuum, are treated with the classic Fano formula σ(ε) ∝ (ε+q)²/(ε²+1) and the corresponding time delay τ_W(ε)=2Γ/(ε²+1), independent of the asymmetry parameter q. By expressing the amplitude as D(ε) ∝