Irregular Spin Tunnelling for Spin-1 Bose-Einstein Condensates in a   Sweeping Magnetic Field
  We investigate the spin tunnelling of spin-1 Bose-Einstein condensates in a linearly sweeping magnetic field with a mean-field treatment. We focus on the two typical alkali Bose atoms $^{87}Rb$ and $^{23}Na$ condensates and study their tunnelling dynamics according to different sweeping rates of external magnetic fields. In the adiabatic (i.e., slowly sweeping) and sudden (i.e., fast sweeping) limits, no tunnelling is observed. For the case of moderate sweeping rates, the tunnelling dynamics is found to be very sensitive on the sweeping rates with showing a chaotic-like tunnelling regime. With magnifying the regime, however, we find interestedly that the plottings become resolvable under a resolution of $10^{-4}$ G/s where the tunnelling probability with respect to the sweeping rate shows a regular periodic-like pattern. Moreover, a conserved quantity standing for the magnetization in experiments is found can dramatically affect the above picture of the spin tunnelling. Theoretically we have given a reasonable interpretation to the above findings and hope our studies would bring more attention to spin tunnelling experimentally. 
Guan-Fang Wang, Li-Bin Fu and Jie Liu