  Coherent wave control exploits the interference among multiple waves
impinging on a system to suppress or enhance outgoing signals based on their
relative phase and amplitude. This process inherently requires non-Hermiticity,
in order to enable energy exchanges among the waves, and spatial interfaces in
order to tailor their scattering. Here we explore the temporal analogue of this
phenomenon, based on time-interfaces that support instantaneous non-Hermitian
scattering events for photons analogous to mechanical collisions. Based on this
mechanism, we demonstrate ultra-broadband temporal coherent wave control and
photonic collisions with phase-tunable elastic features, and apply them to
erase, enhance and reshape arbitrary pulses by suitably tailoring the amplitude
and phase of counterpropagating signals. Our findings provide a pathway to
effectively sculpt broadband light with light without requiring spatial
boundaries, within an ultrafast and low-energy platform.
