Fig. 1: Experimental setup and concept illustration.

a Schematic of the experimental setup. Argon gas in a gas cell is excited by a sequential preparation and control pulse pair with a time delay of τ. The free induction decay (FID) emission from the excited argon atoms is recorded by an XUV spectrometer composed of a grating and an XUV charge-coupled device (CCD) camera. The preparation and control pulses are blocked by an indium thin film. b Schematic of the energy level diagram of argon. The initial states (\({|i}\rangle\), 4s₁ and 4s₂) of the five-level system is first prepared by a strong laser pulse (green) with a five-photon process. The two-photon transitions from the initial states to the final states (\({|f}\rangle\), 5s and 3d) are then driven by a weak control pulse (red) under the near-resonant condition, facilitated by the intermediate states (\({|m}\rangle\), 4p). The relaxation from |f〉 to the ground state (\({|g}\rangle\), 3p) leads to the emission of FID (purple) with intensity of \({I}_{f}^{{{{{{\rm{FID}}}}}}}\). Inset: Simplified illustration of the two-photon transitions from 4s₁ and 4s₂ to the 5s and 3d final states, leading to quantum-path interferometry (QPI) on the final states. c The XUV spectra of the FID emission with (blue line) and without (red line) control-pulse excitation. The peaks of different initial and final states are labeled. The transmission spectrum of the indium thin film is also plotted⁶². d The FID intensity of the 5s and 3d states as a function of the relative time delay between the prepare and control pulses τ. The relative phase between the two oscillation traces is labeled as Δϕ. The low-intensity regions are labeled by the white color for illustration purpose.