  We present an analytical quantum theoretic model for non-resonant molecular
two-photon absorption (TPA) of broadband, spectrally multi-mode squeezed
vacuum, including low-gain (isolated entangled photon pairs or EPP) and
high-gain (bright squeezed vacuum or BSV) regimes. The results are relevant to
the potential use of entangled-light TPA as a spectroscopic and imaging method.
We treat the scenario that the exciting light is spatially single-mode and is
non-resonant with all intermediate molecular states. In the case of high gain,
we find that in the case that the linewidth of the final molecular state is
much narrower than the bandwidth of the exciting light, bright squeezed vacuum
is found to be equally (but no more) effective in driving TPA as is a
quasi-monochromatic coherent-state (classical) pulse of the same temporal
shape, duration and mean photon number. Therefore, in this case the sought-for
advantage of observing TPA at extremely low optical flux is not provided by
broadband bright squeezed vacuum. In the opposite case that the final-state
linewidth is much broader than the bandwidth of the BSV exciting light, we show
that the TPA rate is proportional to the second-order intensity autocorrelation
function at zero time delay g^(2)(0), as expected. We derive and evaluate
formulas describing the transition between these two limiting cases, that is,
including the regime where the molecular linewidth and optical bandwidth are
comparable, as is often the case in experimental studies. We also show that for
g^(2)(0) to reach the idealized form g^(2)(0) = 3 + 1/n, with n being the mean
number of photons per temporal mode, it is required to compensate the
dispersion inherent in the nonlinear-optical crystal used to generate the BSV.
