A charged quantum system subjected to high magnetic fields often exhibits unusual phenomena such as integer and fractional quantum Hall effect. Although atoms are neutral, a synthetic gauge field for atoms can be generated by engineering atom-light interaction. A pioneering experiment by Ian Speilman’s group in NIST has successfully implemented this scheme in Rb-87 Bose-Einstein condensates (Nature, 462, 628 (2009)). This method potentially can create a sufficient large magnetic field to generate quantum Hall state in cold atoms. Combining with optical lattices, one can study a wide range of ultra-high field phenomena not accessible by real magnetic field in solids, namely, the magnetic flux through a unit cell is a sizable fraction of flux quanta. The properties of quantum many-body systems in such regime are barely explored and will surely lead to many fascinating phenomena. We shall give couple such examples.