Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, I show that a synthetic cylinder could be threaded by a net effective magnetic flux through its surface. The surface of the synthetic cylinder is spun by one real dimension and another synthetic dimension consists of internal states of atoms. Due to the periodic boundary condition in the synthetic dimension and magnetic flux, such a synthetic Hall cylinder gives rise to a periodic lattice in real dimensions. The BEC’s transport in the band structure, i.e., the Bloch oscillation, is analogous to traveling on a Mobius strip in the momentum space. Adding an extra external incommensurate optical lattice would introduce a localization-delocalization transition. Near the transition point, the physical observables are sensitive to the axial magnetic flux. In experiments, this flux could drift. The flux sensitivity could be utilized for precision measurements.
Dr. Yangqian Yan is currently a postdoctoral scholar with a research interest in theoretical cold atomic gases in the Department of Physics and Astronomy at the Purdue Univerisity. He will be joining the department of physics of the Chinese University of Hong Kong as an assistant professor. Dr. Yan received his PhD at Washington State University in 2016 and bachelor's degree at University of Science and Technology of China in 2010.
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