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  • M. Reutzel, A. Li, Z. Wang, H. Petek, Probing Nonlinear Light–Matter Interaction in Momentum Space: Coherent Multiphoton Photoemission Spectroscopy, in Nonlinear X-Ray Spectroscopy for Materials Science (Springer, 2023), pp. 57.

    Optical fields interacting with metal surfaces can drive collective free electron plasma currents and single-particle dipole excitations. The outcome of these coherent interactions is immediately evident in nearly perfect images that appear in metal mirrors. Yet, performing quantum state-resolved measurements and electronic charge/spin actuations of metals is extremely challenging because of interaction-driven decoherence of the polarization of the electronic system. In this chapter, we describe interferometrically time-resolved multiphoton photoemission spectroscopy as a quantum state-resolved method for investigating coherent responses of solids. We perform 3D (energy, momentum, and time)-resolved nonlinear photoelectron spectroscopy to record the coherent response of single crystal surfaces with attosecond accuracy. The measurements resolve the coherent polarization oscillations in response to the driving light field, the resonant frequencies of the metal sample, and the optical field-induced dressing of the electronic band structure. As a model system, we focus on the coherent responses of single crystal silver and copper surfaces to intense ~20 fs laser pulses in the IR-UV spectral range. Noble metals provide well-known band structures, deeply studied attosecond collective responses, and simple surface preparation methods that guide the development of experimental and theoretical extension of coherent nonlinear photoemission spectroscopy to more complex materials. To photoexcite electrons above the vacuum level in a nonlinear manner, the excitation creates Floquet ladders of quasi-energy states up to fifth order in the driving light field, including signatures of above threshold photoemission. Finally, we show that at high driving field amplitudes, electrons follow both the space and optical field-dependent periodic potentials causing non-perturbative modifications of metal crystal electronic structures. Hence, nonlinear interferometric photoelectron spectroscopy enables to quantify, as well as to transiently modify, the coherent responses of solid-state materials.

    DOI: 10.1007/978-981-99-6714-8_3