  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.
