Quantum tunneling of magnetization in dipolar spin-1 condensates under   external fields
  We study the macroscopic quantum tunneling of magnetization of the F=1 spinor condensate interacting through dipole-dipole interaction with an external magnetic field applied along the longitudinal or transverse direction. We show that the ground state energy and the effective magnetic moment of the system exhibit an interesting macroscopic quantum oscillation phenomenon originating from the oscillating dependence of thermodynamic properties of the system on the vacuum angle. Tunneling between two degenerate minima are analyzed by means of an effective potential method and the periodic instanton method. 
Limin Yang, Yunbo Zhang