  Generating nonclassical light offers a benchmark tool for the fundamental
research and potential applications in quantum optics. Conventionally, it has
become a standard technique to produce the nonclassical light through the
nonlinear optical processes occurring in nonlinear crystals. In this review we
describe using cold atomic-gas media to generate such nonclassical light,
especially focusing on narrow-band biphoton generation. Compared with the
standard procedure, the new biphoton source has such properties as long
coherence time, long coherence length, high spectral brightness, and high
conversion efficiency. In this paper we concentrate on the theoretical aspect
of the entangled two-photon state produced from the four-wave mixing in a
multilevel atomic ensemble. We show that both linear and nonlinear optical
responses to the generated fields play an important role in determining the
biphoton waveform and, consequently on the two-photon temporal correlation.
There are two characteristic regimes determined by whether the linear or
nonlinear coherence time is dominant. In addition, our model provides a clear
physical picture that brings insight into understanding biphoton optics with
this new source. We apply our model to recent work on generating narrow-band
(and even subnatural linewidth) paired photons using the technique of
electromagnetically induced transparency and slow-light effect in cold atoms,
and find good agreements with experimental results.
