Numerical Simulation of Ultracold Atoms Trapped in Optical Lattices
Optical Science Laboratory
Ultracold atoms have been stimulating many researchers’ interest after a successful realization of Bose-Einstein condensation in 1995. Recent noteworthy progress on atom manipulation techniques has led to unprecedented experiments demonstrating an extremely high controllability. An optical lattice, formed by a standing wave of counter-propagating laser lights as shown in Fig. 1, is a typical example that allows us to investigate fundamental quantum many-body problems found in condensed matter physics via atomic gases.
We have developed a highly efficient numerical method based on the Gutzwiller approximation and analyzed the ground state properties of ultracold atoms trapped in optical lattices . To examine the quantitative ability of our method, we numerically simulated the recent experiment performed by MIT group  which precisely observed the quantum phase transition of bosonic atoms in a three-dimensional optical lattice. Figure 2(a) shows the average number distribution of atoms over the lattice sites in the y=0 plane for the superfluid phase where the depth of optical lattice is relatively shallow. Note that 560,000 lattice sites and 300,000 atoms are assumed in our calculations. The smooth and convex atom distribution is obtained reflecting a weak magnetic confining potential in the experiment. Figure 2(b), on the other hand, shows the number distribution for the Mott-insulator phase where the lattice depth is deep enough. Due to the strong repulsive interactions between the atoms, the average number takes the discrete values ranging from n=1 to n=5, which leads to a stepwise distribution. From this result, we understand that ultracold atoms in the Mott-insulator phase form an intriguing shell structure in their spatial distribution. The calculated results in Fig. 2 agree well with the experimental observations of MIT group and we have confirmed an excellent quantitative performance of our numerical simulations.
This work was supported in part by Japan Science and Technology Agency, CREST.
 M. Yamashita and M. W. Jack, Phys. Rev. A 79 (2009) 023609.
 G. K. Campbell et al., Science 313 (2006) 649.
Fig. 1. Schematic diagram of ultracold atomic gas trapped in an optical lattice.
Fig. 2. Number distributions in the y=0 plane: (a) superfluid state and (b) Mott-insulator state.
[back] [Top] [Next]