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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 $J_g=0to J_e=1$ atomic transition, and for atomic lattices containing up to $Napprox 3times10^4$ 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.
We investigate finite-size quantum effects in the dynamics of $N$ bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACS) we extend the standard mean-field
The quantum anomalies at the edges correspond to the topological phases in the system, and the chiral edge states can reflect bulk bands topological properties. In this paper, we demonstrate a simulation of Floquet systems chiral edge states in posit
We address the challenge of realizing a Floquet-engineered Hofstadter Bose-Einstein condensate (BEC) in an ultracold atomic gas, as a general prototype for Floquet engineering. Motivated by evidence that such a BEC has been observed experimentally, w
We introduce and investigate a system that uses temporal resonance-induced phase space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both th
Spatial gaps correspond to the projection in position space of the gaps of a periodic structure whose envelope varies spatially. They can be easily generated in cold atomic physics using finite-size optical lattice, and provide a new kind of tunnel b