Shot noise limited characterization of ultraweak femtosecond pulse trains

Probing the evolution of physical systems at the femto- or attosecond timescale with light requires accurate characterization of ultrashort optical pulses. The time profiles of such pulses are usually retrieved by methods utilizing optical nonlinearities, which require significant signal powers and operate in a limited spectral range\cite{Trebino_Review_of_Scientific_Instruments97,Walmsley_Review_09}. We present a linear self-referencing characterization technique based on time domain localization of the pulse spectral components, operated in the single-photon regime. Accurate timing of the spectral slices is achieved with standard single photon detectors, rendering the technique applicable in any spectral range from near infrared to deep UV. Using detection electronics with about $70$ ps response, we retrieve the temporal profile of a picowatt pulse train with $\sim10$ fs resolution, setting a new scale of sensitivity in ultrashort pulse characterization.