  We propose a scheme involving cold atoms trapped in optical lattices to
observe different phenomena traditionally linked to quantum-optical systems.
The basic idea consists of connecting the trapped atomic state to a non-trapped
state through a Raman scheme. The coupling between these two types of atoms
(trapped and free) turns out to be similar to that describing light-matter
interaction within the rotating-wave approximation, the role of matter and
photons being played by the trapped and free atoms, respectively. We explain in
particular how to observe phenomena arising from the collective spontaneous
emission of atomic and harmonic oscillator samples such as superradiance and
directional emission. We also show how the same setup can simulate Bose-Hubbard
Hamiltonians with extended hopping as well as Ising models with long-range
interactions. We believe that this system can be realized with state of the art
technology.

Quantum Physics