Quantum Optical Spin-Glass State of Impurity Two-Level Atoms in a Photonic Band Gap

We describe the collective optical properties of impurity two-level atoms in a photonic band gap interacting by resonance dipole-dipole interaction (RDDI) and coupled to a localized cavity mode. The random impurity atom positions are modeled by means of a Gaussian random distribution of RDDI's with variance $J$ and atomic line fluctuation with variance $\delta$. We demonstrate the occurrence of a new collective atomic steady state, the optical analog of a spin-1/2 dipolar glass, and an associated Bose-glass state of photons in the cavity mode.