The energy-time uncertainty is an intrinsic limit for time-resolved experiments imposing a tradeoff between the duration of the light pulses used in experiments and their frequency content. In standard time-resolved photoemission, this limitation maps directly onto a tradeoff between the time resolution of the experiment and the energy resolution that can be achieved on the electronic spectral function. Here we propose a protocol to disentangle the energy and time resolutions in photoemission. We demonstrate that dynamical information on all time scales can be retrieved from time-resolved photoemission experiments using suitably shaped light pulses of quantum or classical nature. As a paradigmatic example, we study the dynamical buildup of the Kondo peak, a narrow feature in the electronic response function arising from the screening of a magnetic impurity by the conduction electrons. After a quench, the electronic screening builds up on timescales shorter than the inverse width of the Kondo peak and we demonstrate that the proposed experimental scheme could be used to measure the intrinsic time scales of such electronic screening. The proposed approach provides an experimental framework to access the nonequilibrium response of collective electronic properties beyond the spectral uncertainty limit and will enable the direct measurement of phenomena such as excited Higgs modes and, possibly, the retarded interactions in superconducting systems.
