  We perform a quantum-theoretical treatment of cavity linewidth narrowing with
intracavity electromagnetically induced transparency (EIT). By means of
intracavity EIT, the photons in the cavity are in the form of cavity
polaritons: bright-state polariton and dark-state polariton. Strong coupling of
the bright-state polariton to the excited state induces an effect known as
vacuum Rabi splitting, whereas the dark-state polariton decoupled from the
excited state induce a narrow cavity transmission window. Our analysis would
provide a quantum theory of linewidth narrowing with a quantum field pulse at
the single-photon level.
