  We report the observation of symmetry protected two-photon coherence time of
biphotons generated from backward spontaneous four-wave mixing in laser-cooled
$^{87}$Rb atoms. When biphotons are nondegenerate, non-symmetric photonic
absorption loss results in exponential decay of the temporal waveform of the
two-photon joint probability amplitude, leading to shortened coherence time. In
contrast, in the case of degenerate biphotons, when both paired photons
propagate with the same group velocity and absorption coefficient, the
two-photon coherence time, protected by space-time symmetry, remains unaffected
by medium absorptive losses. Our experimental results validate these
theoretical predictions. This outcome highlights the pivotal role of symmetry
in manipulating and controlling photonic quantum states.
