  We theoretically investigate the spectral property of biphoton state from the
cascade emissions from a Doppler-broadened atomic ensemble. This biphoton state
is spontaneously created in the four-wave-mixing process. The upper transition
of the emissions lies in telecom bandwidth, which prevails in fiber-based
quantum communication for low-loss transmission. We obtain the spectral
property in terms of superradiant decay rates of the lower transition,
excitation pulse durations, and temperature of the medium. We quantify their
frequency entanglement by Schmidt decomposition and find that more entangled
source can be generated with longer excitation pulses, enhanced decay rates,
and significant Doppler broadening. A minimally entangled biphoton source can
also be located at some optimal temperature of the atoms. This allows spectral
shaping of continuous frequency entanglement, which is useful in multimode
long-distance quantum communication.
