  We show how cross-correlating a high redshift external tracer field, such as
the 21cm neutral hydrogen distribution and product maps involving Cosmic
Microwave Background (CMB) temperature and polarisation fields, that probe
mixed bispectrum involving these fields, can help to determine the reionization
history of the Universe, beyond what can be achieved from cross-spectrum
analysis. Taking clues from recent studies for the detection of primordial
non-Gaussianity (Munshi & Heavens 2010), we develop a set of estimators that
can study reionization using a power spectrum associated with the bispectrum
(or skew-spectrum). We use the matched filtering inherent in this method to
investigate different reionization histories. We check to what extent they can
be used to rule out various models of reionization and study cross
contamination from different sources such as the lensing of the CMB. The
estimators can be fine-tuned to optimize study of a specific reionization
history. We consider three different types of tracers in our study, namely:
proto-galaxies; 21cm maps of neutral hydrogen; quasars. We also consider four
alternative models of reionization. We find that the cumulative signal-to-noise
(S/N) for detection at $\ell_{max}=2000$ can reach $\mathcal{O}(70)$ for cosmic
variance limited all-sky experiments. Combining 100GHz, 143GHz and 217GHz
channels of the Planck experiment, we find that the (S/N) lies in the range
$\mathcal{O}(5)-\mathcal{O}(35)$. The (S/N) depends on the specific choice of a
tracer field, and multiple tracers can be effectively used to map out the
entire reionization history with reasonable S/N. Contamination from weak
lensing is investigated and found to be negligible, and the effects of Thomson
scattering from patchy reionizationare also considered.
