Conduction Bands of Atomic Tunneling Ring in Artificial Gauge Field Assisted Opened Optical Traps

We show conduction bands of artificial gauge field assisted atom flow in triangle optical lattice. The conduction bands are result from periodicity boundary condition of artificial magnetic flux induced phases of atoms. The positions of conduction bands depend on geometry of the atom trajectory. We consider a cell of the triangle optical lattice which is a opened system connected to its environment of Fermion atom clouds. The chemical potentials of the atom clouds are the same and the atom flow is absolutely created by a clock laser induced spin-orbit coupling. Our results are important for the control of atom flow in quantum circuits.