  The cascaded biphoton state generated from a cold atomic ensemble presents
one of the strongly correlated resources that can preserve and relay quantum
information. Under the four-wave mixing condition, the emitted signal and idler
photons from the upper and lower excited states become highly correlated in
their traveling directions and entangled in continuous frequency spaces. In
this system, we theoretically study the spectral compression of the biphoton
source using an external cavity and show the reduction in its frequency
entanglement entropy. This indicates, respectively, an improved light
absorption efficiency for the idler photon as well as an almost pure biphoton
source which is useful in optical quantum networks. We further investigate the
limit of the spectral compression that can be achieved by using multiple
cavities. Our results show the capability and potential of the biphoton source
with external cavities, where the performance of atom-based quantum memory can
be enhanced and the entanglement property can be manipulated by tailoring the
spectral compression.
