中文摘要：

Graphene has attracted enormous attention over the past years in condensed matter physics.The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions.Such feature is the origin of many topological properties in graphene-like physics.On the other hand,ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics.Here,we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice,including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels.We also present the related experimental advances.

英文摘要：

Graphene has attracted enormous attention over the past years in condensed matter physics. The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions. Such feature is the origin of many topological properties in graphene-like physics. On the other hand, ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics. Here, we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice, including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels. We also present the related experimental advances.