Fig. 1. Coherent photoelectron spectroscopy of optical dressing.

a Three-dimensional ITR-4PP movie of the three-photon resonant IP1←SS transition (ħω_l = 1.54−eV). Each frame of Supplementary Movie 1, from which the data is taken, records the photoelectron signal counts vs. E_f (relative to the Fermi level, E_F), and k_|| in ~100 as steps (sample movie frames are shown in 15 fs intervals). The back panel shows a cross section through the movie for k_|| = 0 Å⁻¹. b Time-integrated 4PP spectrum showing the SS and IP1 bands for resonant excitation at k_|| = 0 Å⁻¹. c Selection of data from a for k_|| = 0 Å⁻¹ showing an E_f(τ)-interferogram; the profiles show I2PC trace for E_f = 5.65 eV (orange) and a 4PP spectrum for τ = 0 fs (black); the inset expands the E_f(τ)-data around τ = 0 fs (the dashed box). The dressing is evident in the dip in I2PC intensity at τ = 0 fs that is caused by the subfemtosecond splitting of the interference fringes, when the pump and probe fields are in-phase and $\mathcal{E}$(τ) is maximum, but not in the τ = 0 fs E_f-profile. d The unperturbed surface-projected band structure of Cu(111). The SS and IP1 bands (black lines) in the surface-projected band gap between the lower and upper sp-bands, L_sp and U_sp (gray shading), are coupled by the three-photon resonant laser field (blue); the fourth photon induces the photoemission (dashed blue). The excitation is resonant at k_|| = 0 Å⁻¹ producing one peak with enhanced 4PP yield in b; the different m_eff of the SS and IP1 bands, however, cause their detuning for increasing k_|| and consequent detection of two bands. e The optical dressing of the SS and IP1 bands: the increasing electric field $\mathcal{E}$ (right arrow) causes AC Stark effect shifts of the SS and IP1 bands to E_± (blue), while the Floquet effect replicates E_± at integer multiples of nħω_l are (violet). The optical dressing is revealed by Mollow-Triplet structures in the resonant coherent polarizations at 3ω_l (brown arrows), and Autler–Townes doublets in the nonresonant coherent polarizations at 2ω_l (red arrows).