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

Simulating quantum-optical phenomena with cold atoms in optical lattices