Quantum simulation based on ultracold atoms in a lattice

We review the history of quantum simulation from the“bottom- up”approach with ultracold atoms. Considered as a macroscopic quantum state, ultracold atoms have the advantage of all the degrees of freedom being precisely controlled. They are a perfect platform for quantum simulation. An optical lattice is one of the most important techniques in this field because it connects ultracold atom physics with condensed matter physics, and provides a perfect example to show the scientific value of quantum simulation with ultracold atoms. Recently, quantum simulation for topological physics has become a hot topic attracting more and more attention from the ultracold atoms community. We will present a brief review, then share some thoughts about quantum simulation with ultracold atoms.