Quantum simulators are setups which are designed to mimic the interactions and dynamics of other relevant many-body systems whose behaviour is very difficult to understand with current numerical methods. When such interactions are obtained in a continuous and global way, one talks about analog quantum simulators, which are generally more resilient to noise and easier to implement.

Among the different implementations, cold atoms in optical lattices is one of most mature implementation for such analog quantum simulators, that allow engineering many-body models in a versatile way and in 1, 2, and 3 dimensions. These systems, however, also have some limitations, such as the limited kinetic energy as they hop through the lattice, setting stringent temperature requirements, or the fact that they interact mostly locally.

Along the years, we have proposed several implementations to either increase interaction strength (using photonic crystals) or to increase the range of the interactions (e.g, to simulate quantum chemistry problems). Below we sketch some of our main contributions to the field with some selected publications in each topic (see Publications for a complete list of the publications)