  The paper describes a new concept of visible pump/X-ray probe/slow detector
experiments that could be performed at third-generation synchrotron light
sources. We propose a technique that would allow time resolution up to
femtosecond capabilities to be recovered from a long (100 ps) X-ray probe
pulse. The visible pump pulse must be as short as the desired time resolution.
The principle of operation of the proposed pump-probe scheme is essentially
based on the statistical properties of the synchrotron radiation. These
properties are well known in statistical optics as properties of completely
chaotic polarized light. Our technique utilizes the fact that, for any
synchrotron light beam there exist some characteristic time (coherence time),
which determines the time-scale of the random fluctuations. The typical
coherence time of soft X-ray synchrotron light at the exit of monochromator is
in the femtosecond range. An excited state is prepared with a pump pulse and
then projected with a probe pulse onto a final ion state. The first statistical
quantity of interest is the variance of the number of photoelectrons detected
during synchrotron radiation pulse. The statistics of concern are defined over
an ensemble of synchrotron radiation pulses. From a set of variances measured
as a function of coherence time (inversely proportional to monochromator
bandwidth) it is possible to reconstruct the femtosecond dynamical process.
