Fig. 2: The results of transient complex refraction spectroscopy in argon.

a, b Schematic diagram of the transient complex refraction spectroscopy with double attosecond pulses (DAPs) having different \({\tau }_{{DAPs}}\) delays of 5 and 10 fs to characterize nonlinear complex dipole phase in autoionizing states of Ar. The blue solid and dotted lines represent the dipole oscillations due to resonant excitation of autoionization states by DAPs. Near-infrared (NIR) induced changes due to re-excitation to the Ar*+ state is also shown by the red solid line. c, d Measured transient spectrograms with \({\tau }_{{DAPs}}=\) 5 fs and \({\tau }_{{DAPs}}=\)10 fs. e, f Reconstructed relative amplitudes with τDAPs = 5 fs and τDAPs = 10 fs. g, h Reconstructed relative phase with \({\tau }_{{DAPs}}=\) 5 fs and \({\tau }_{{DAPs}}=\)10 fs.