The study of topological phases has been a central topic of condensed matter physics since the observations of the quantum Hall effect. In this talk, I will describe the physics of two-component bosons or fermions in synthetic magnetic field where the field strengths for the two components may be tuned independently. A variety of states, including topologically ordered states and symmetry-protected topological states, are proposed and characterized using trial wave functions and Chern-Simons field theories. It is confirmed by numerical calculations that these states can be realized using simple Hamiltonians defined in continuum or lattice. Our work suggests that a rich set of topological states can be created using specially designed artificial gauge fields.

Dr. Ying-Hai Wu graduated from University of Science and Technology of China with a Bachelor degree in 2009. He obtained his Ph.D. degree in physics in 2014 from Pennsylvania State University under the supervision of Prof. J. K. Jain. He has been a postdoc in the theory group led by Prof. J. I. Cirac at the Max Planck Institute of Quantum Optics since 2014. His main research interests are topological states, strongly correlated systems, and quantum optics.