Photonic band gap in an imperfect atomic diamond lattice: penetration depth and effects of finite size and vacancies

Mauro Antezza (1) , Yvan Castin (2)

1 L2C - Laboratoire Charles Coulomb
2 LKB (Lhomond) - Laboratoire Kastler Brossel

We study the effects of finite size and of vacancies on the photonic band gap recently predicted for an atomic diamond lattice. Close to a $J_g=0\to J_e=1$ atomic transition, and for atomic lattices containing up to $N\approx 3\times10^4$ atoms, we show how the density of states can be affected by both the shape of the system and the possible presence of a fraction of unoccupied lattice sites. We numerically predict and theoretically explain the presence of shape-induced border states and of vacancy-induced localized states appearing in the gap. We also investigate the penetration depth of the electromagnetic field which we compare to the case of an infinite system.

Mots clés: photonic band gap; optical lattices; Mott phase; light penetration depth; optical band structure; in-gap states; vacancies

Domaines: Gaz Quantiques [cond-mat.quant-gas]

Mauro Antezza, Yvan Castin. Photonic band gap in an imperfect atomic diamond lattice: penetration depth and effects of finite size and vacancies. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2013, 88 (033844), pp.033844. ⟨10.1103/PhysRevA.88.033844⟩. ⟨hal-00818327⟩