Photonic band-gap properties for two-component slow light

We consider two-component "spinor" slow light in an ensemble of atoms coherently driven by two pairs of counterpropagating control laser fields in a double tripod-type linkage scheme. We derive an equation of motion for the spinor slow light (SSL) representing an effective Dirac equation for a massive particle with the mass determined by the two-photon detuning. By changing the detuning the atomic medium acts as a photonic crystal with a controllable band gap. If the frequency of the incident probe light lies within the band gap, the light tunnels through the sample. For frequencies outside the band gap, the transmission probability oscillates with increasing length of the sample. In both cases the reflection takes place into the complementary mode of the probe field. We investigate the influence of the finite excited state lifetime on the transmission and reflection coefficients of the probe light. We discuss possible experimental implementations of the SSL using alkali atoms such as Rubidium or Sodium.