Fig. 3: Transition amplitudes and phases involved in quantum-path interferometry of 5s.

a Model results of the populations on different states under varying control-pulse intensity, I_c. b The model results of the transition amplitudes between the initial states and the 5s final state (a_i4), and the interference visibility M₄ as a function of the control pulse intensity, I_c. c The symbols represent the experimental results of the oscillating phase of the 5s state, δϕ₄. The error bars are determined by considering both the fitting errors and the standard deviations of experimental results, extracted from 5 individual scans. The solid lines show the model results of the phases of two-photon channels to the 5s state, φ_i4, and the dashed line represents the model results of the corresponding oscillating phase. d Illustration of the QPI on the 5s state under different control-laser intensity, I_c, showing the jump of the oscillating phase when the paths reach the “2π condition”. e The time evolution of the transition amplitude a₁₄ under different control-laser intensity, I_c. f Same as e for the transition amplitude a₂₄.