  We present an experimental proposal to achieve a strong photon blockade by
employing electromagnetically induced transparency (EIT) with single
alkaline-earth-metal atom trapped in an optical cavity. In the presence of
optical Stark shift, both second-order correlation function and cavity
transmission exhibit asymmetric structures between the red and blue sidebands
of the cavity. For a weak control field, the photon quantum statistics for the
coherent transparency window (i.e. atomic quasi-dark state resonance) are
insensitive to the Stark shift, which should also be immune to the spontaneous
emission of the excited state by taking advantage of the intrinsic dark-state
polariton of EIT. Interestingly, by exploiting the interplay between Stark
shift and control field, the strong photon blockade at atomic quasi-dark state
resonance has an optimal second-order correlation function
$g^{(2)}(0)\sim10^{-4}$ and a high cavity transmission simultaneously. The
underlying physical mechanism is ascribed to the Stark shift enhanced spectrum
anharmonicity and the EIT hosted strong nonlinearity with loss-insensitive
atomic quasi-dark state resonance, which is essentially different from the
conventional proposal with emerging Kerr nonlinearity in cavity-EIT. Our
results reveal a new strategy to realize high-quality single photon sources,
which could open up a new avenue for engineering nonclassical quantum states in
cavity quantum electrodynamics.
