Coherent Two-Dimensional Multiphoton Photoelectron Spectroscopy of Metal Surfaces

Light interacting with high-electron-density materials elicits an ultrafast coherent many-body screening response on sub-to few-femtosecond timescales, which makes its experimental observation challenging. Here, we describe the coherent two-dimensional (2D) multiphoton photoemission (mPP; m = 2-5) study of the Shockley surface (SS) state of Ag(111) as a benchmark for spectroscopy of the coherent nonlinear responses of metals to intense optical fields in the perturbative regime; similar 2D signatures can be expected for coherent responses in other materials like low-dimensional semiconductors and strongly correlated materials. Employing interferometric time-resolved multiphoton photoemission spectroscopy (ITR-mPP), we correlate the coherent polarizations excited in the sample with photoelectron energy distributions where the interaction terminates and photoelectrons carry away the information on their excitation. By measuring the nonresonant three-and four-photon photoemission of the SS state, as well as its replicas in above-threshold photoemission (ATP), we record the coherent response of the Ag(111) surface by 2D photoemission spectroscopy and relate it to its band structure. A 2D analysis of the SS state and its ATP replicas shows similar behavior, indicating that they are mth- and mth + 1-order coherent processes in a contradiction of the common attribution of ATP as a sequential process where a photoelectron excited above the vacuum level absorbs one or more additional photons. We interpret the mPP process by an optical Bloch equation model, which reproduces the main features of the surface state coherent polarization dynamics in ITR-mPP experiments: The distributions of spectroscopic components in 2D photoelectron spectra of coherent mPP are shown to follow systematically the n=m ratio, where n and m are orders of the induced coherence and the photoemission process contributing to the signal.