  We systematically studied the temporal profile of biphotons, i.e., pairs of
time-correlated single photons, generated from a hot atomic vapor via the
spontaneous four-wave mixing process. The measured temporal width of biphoton
wave packet or two-photon correlation function against the coupling power was
varied from about 70 to 580 ns. We derived an analytical expression of the
biphoton's spectral profile in the Doppler-broadened medium. The analytical
expression reveals that the spectral profile is mainly determined by the effect
of electromagnetically induced transparency (EIT), and behaves like a
Lorentzian function with a linewidth approximately equal to the EIT linewidth.
Consequently, the biphoton's temporal profile influenced by the Doppler
broadening is an exponential-decay function, which was consistent with the
experimental data. Employing a weak input probe field of classical light, we
further measured the EIT spectra under the same experimental conditions as
those in the biphoton measurements. The theoretical predictions of the biphoton
wave packets calculated with the parameters determined by the classical-light
EIT spectra are consistent with the experimental data. The consistency
demonstrates that in the Doppler-broadened medium, the classical-light EIT
spectrum is a good indicator for the biphoton's temporal profile. Besides, the
measured biphoton's temporal widths well approximated to the predictions of the
analytical formula based on the biphoton's EIT effect. This study provides an
analytical way to quantitatively understand the biphoton's spectral and
temporal profiles in the Doppler-broadened medium.
