  Attosecond pulses in the soft-X-ray (SXR) to water-window energy region offer
the tools for creating and studying target specific localized inner-shell
electrons or holes in materials, enable monitoring or controlling charge and
energy flows in a dynamic system on attosecond timescales. Recently, a number
of laboratories have reported generation of continuum harmonics in the
hundred-electron-volt to kilovolt region with few-cycle long-wavelength
mid-infrared lasers. These harmonics have the bandwidth to support pulses with
duration of few- to few-ten attoseconds. But harmonics generated in a gas
medium have attochirps that cannot be fully compensated by materials over a
broad spectral range; thus, realistically what are the typical shortest
attosecond pulses that one can generate? To answer this question, it is
essential that the temporal attosecond pulses be accurately characterized. By
re-analyzing the soft X-ray harmonics reported in three recent experiments
\cite{chang_natcom2017,Thomas_OE2017,Bieger_2017PRX} using a newly developed
broadband phase retrieval algorithm, we show that their generated attosecond
pulses are all longer than about 60 as. Since broadband pulses tend to have
high-order chirps away from the spectral center of the pulse, the algorithm has
to be able to retrieve accurately the phase over the whole bandwidth. Our
re-evaluated pulse durations are found to be longer than those previously
reported. We also introduce the autocorrelation (AC) of the streaking
spectrogram. By comparing the ACs from the experiments and from the retrieved
SXR pulses, the accuracy of the retrieved results can be directly visualized to
ensure that correct phases have been obtained. Our retrieval method is fast and
accurate, and it shall provide a powerful tool for the metrology of
few-ten-attosecond pulses in the future.
