  We develop an ultrafast frequency-resolved Raman spectroscopy with entangled
photons for polyatomic molecules in condensed phases, to probe the electronic
and vibrational coherences. Using quantum correlation between the photons, the
signal shows the capability of both temporal and spectral resolutions that are
not accessible by either classical pulses or the fields without entanglement.
We develop a microscopic theory for this Raman spectroscopy, revealing the
electronic coherence dynamics which often shows a rapid decay within
$\sim$50fs. The heterodyne-detected Raman signal is further developed to
capture the phases of electronic coherence and emission in real-time domain.
