  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.
