Understanding the behavior of interacting electrons in solids or liquids is at the heart
of modern quantum science and necessary for technological advances.
However, the complexity of their interactions generally prevents us from coming up
with an exact mathematical description of their behavior. Precisely engineered
ultracold gases are emerging as a powerful tool for unraveling these challenging physical
problems. In this talk, I will present recent developments at JILA on using atoms in crystals
of light for the investigation of complex many-body phenomena and magnetism. I will
also discuss a new research direction of using atomic clocks not only as precise time
keepers but also as unique quantum laboratories for the investigation of new forms of
matter with no known
counterpart in nature.