  The phasing problem of heterodyne-detected nonlinear spectroscopy states that
the relative time delay between the exciting pulses and a local oscillator must
be known with subcycle precision to separate absorptive and dispersive
contributions. Here, a solution to this problem is presented which is the
time-domain analogue of holographic interferometry, in which the comparison of
two holograms reveals changes of an objects size and position with
interferometric precision (i.e. to fractions of a wavelength of light). The
introduced method, called nonlinear polarization holography, provides
equivalent information as attosecond nonlinear polarization spectroscopy but
has the advantage of being all-optical instead of using an attosecond streak
camera. Nonlinear polarization holography is used here to retrieve the
time-domain nonlinear response of a nanoscale iridium film to an ultrashort
femtosecond pulse. Using density matrix calculations it is shown that the
knowledge of the nonlinear response with subcycle precision allows to
distinguish excitation and relaxation mechanisms of low-energetic electrons
that depend on the nanoscale structure of the iridium film.
