超冷原子在光晶格中量子輸運的計算:In this reference we present details of the calculation in our paper \K. Henderson, H. Kelkar, B.
Guti?errez-Medina, T. C. Li, M. G. Raizen. Experimental study of the role of atomic interactions on quantum transport. Phys. Rev. Lett. 96, 150401(2006) ". We calculate the dipole potential and band structure of sodium atoms in an optical lattice. We also calculate the evolution of atomic distribution in an optical lattice with a single-particle band theory. The calculated expansion velocities and density proˉles are in excellent agreement with the experimental results of thermal atoms. They also agree with the experimental result of Bose-Einstein condensation (BEC) atoms in low well depth. For high well depth, however, the expansion of BEC is slower than the single- particle prediction, indicating the importance of interactions on quantum transport.