supported by the National Natural Science Foundation of China (10934010, 60978019 and 11104064);the National Basic Research Program of China (2009CB930701, 2010CB922904,2011CB921502 and 2012CB821300);the Research Grants Council of Hong Kong (11061160490 and 1386-N-HKU748/10);Zhang X F is also supported by the China Postdoctoral Science Foundation (2011M500032)
We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and...