I will discuss how to engineer laser-atom interactions for creating synthetic topological defects and synthetic spaces. Engineered couplings between internal states of ultracold atoms have allowed experimentalists to deliver a Yang monopole in laboratories. I will show that interactions lead to topological defects beyond the descriptions of single particle physics. Discrete defects may even be turned into continuous ones, a new type of “more is different” phenomena. I will also discuss a recent progress of creating a synthetic Hall cylinder, a cylindrical surface penetrated by a net effective magnetic flux. A Bose-Einstein condensate on such Hall cylinder has a range of properties unattainable by its counterparts living in planar spaces. This progress shows that synthetic spaces allow physicists to bypass many constraints and access intriguing quantum phenomena inherent to the topology of spaces
