Fig. 1. (a) Temporal profile of attosecond XUV pulse in the z-direction. τ_d is the time interval between the two pulses. (b) Sketch of interference pathways. Impulsive excitation (¹U) forms a coherent superposition of bound states (|1⟩, |b⟩, |j⟩, ...) and continuum (|q⟩). A second attosecond XUV pulse (²U) transfers the coherent population to the continuum |p⟩. The dynamical quantum beat is determined by the shaded areas in the energy–time diagram enclosed by different pathways. The quantum beat phase of path 1 is the red shaded area, |ε_j − ε_b|t_d, and the phase of path 2 is the purple shaded area, |q22−εj|td.

Fig. 2. Populations of bound states driven by the pump pulse.

Fig. 3. (a) Photoelectron’s momentum distribution in the laser field’s polarized direction with different time delay. (b) Frequency-resolved photon-electronic spectroscopy G(p, Ω). The laser parameters of the first pulse are λ₁ = 100 nm and T₁ = 2.5 optical cycles.

Fig. 4. Populations of the first four bound states calculated by TDSE and reconstructed by our scheme. The laser parameters of the pump pulse are (a) λ₁ = 100 nm, T₁ = 2.5 optical cycles, (b) λ₁ = 120 nm, T₁ = 2.5 optical cycles, (c) λ₁ = 100 nm, T₁ = 1.5 optical cycles, and (d) λ₁ = 120 nm, T₁ = 1.5 optical cycles, respectively. Here, dΩ = 0.00178 a.u.

Fig. 5. The frequency-resolved photoelectron yield at the momentum p = 0.04455 a.u. for (a) dΩ = 0.00102 a.u., (b) dΩ = 0.0018 a.u., and (c) dΩ = 0.00204 a.u. L₁, L₂, L₃, L₄ correspond to the horizontal lines in Fig. 3. The first pulse is 100 nm, and the pulse duration is 2.5 optical cycles.