Fig. 1: Experimental setup of transient complex refraction spectroscopy with double attosecond pulses (DAPs).

a Schematic illustration of transient refraction spectroscopy with DAPs. BSM: beam-splitting mirror. Mo/Si: Mo/Si multilayer-coated spherical mirror. Grating: diffraction grating. XCCD: X-ray CCD camera. b The energy level diagram of an Ar atom. Blue arrows represent excitations via DAPs from the 3s²3p⁶ ground state to the 3s3p⁶4p, 3s3p⁶5p, and 3s3p⁶6p autoionizing states. Red arrows show the excitations via the near-infrared (NIR) pulse to the 3s3p⁶ state. Γ is the decay time of each autoionization state⁶. c The spectral interferogram with/without Ar gas using only DAPs. The dashed lines represent the transitions from the ground state to the autoionizing states of Ar. The inset shows the isolated attosecond pulse (IAP) spectrum, which was obtained by integrating the spatially resolved spectral interference waveforms over the entire spatial range. d Optical density spectrum of Ar gas. This spectrum is obtained from (c). These waveforms were obtained by averaging 30 measurements. The error bars indicate the root mean square error.