Lorentz Meets Fano in Spectral Line Shapes: A Universal Phase and Its Laser Control

TLDR

Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. The study introduces a universal temporal‑phase formalism that maps the Fano asymmetry parameter q to a phase of the time‑dependent dipole‑response function and demonstrates its use in amplifying resonantly interacting EUV light via quantum‑phase control. The authors develop a universal temporal‑phase formalism that maps the Fano asymmetry parameter q to a phase of the time‑dependent dipole‑response function. Experimentally, the formalism converts Fano absorption lines of autoionizing helium into Lorentzian lines and vice versa, amplifies resonantly interacting EUV light, and enables extraction of the quantum phase of excited states from line‑shape analysis.

Abstract

Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase {\phi} of the time-dependent dipole-response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also prove the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism amplifies resonantly interacting extreme-ultraviolet light by quantum-phase control. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with scientific applications in many branches of spectroscopy.