  We closely replicated and extended a recent experiment ("Spatial properties
of entangled two-photon absorption," Phys. Rev. Lett. 129, 183601, 2022) that
reportedly observed enhancement of two-photon absorption rates in molecular
samples by using time-frequency-entangled photon pairs, and we found that in
the low-flux regime, where such enhancement is theoretically predicted
in-principle, the two-photon fluorescence signal is below detection threshold
using current state-of-the-art methods. The results are important in the
context of efforts to enable quantum-enhanced molecular spectroscopy and
imaging at ultra-low optical flux. Using an optical parametric down-conversion
photon-pair source that can be varied from the low-gain spontaneous regime to
the high-gain squeezing regime, we observed two-photon-induced fluorescence in
the high-gain regime but in the low-gain regime any fluorescence was below
detection threshold. We supplemented the molecular fluorescence experiments
with a study of nonlinear-optical sum-frequency generation, for which we are
able to observe the low-to-high-gain crossover, thereby verifying our
theoretical models and experimental techniques. The observed rates (or lack
thereof) in both experiments are consistent with theoretical predictions and
with our previous experiments, and indicate that time-frequency photon
entanglement does not provide a practical means to enhance in-solution
molecular two-photon fluorescence spectroscopy or imaging with current
techniques.
