1 The parameters of a system are well-controllable 2 measurable System Simulator
6 1 The parameters of a system are well-controllable 2 measurable System Simulator
Atoms at optical lattices Bose-Hubbard Hamiltonian H ∑ bb+∑6n+2 ∑(-1) D Jaksch et al(1998) 60 nm array of 1D tubes M. Greiner et al., Nature(2002) You can control almost all aspects of the periodic structure and the interactions between the atoms
7 Atoms at optical lattices You can control almost all aspects of the periodic structure and the interactions between the atoms M. Greiner et al. , Nature (2002) D.Jaksch et al (1998) + = − + + − i j i i i j i i ni ni U H J b b n ˆ (ˆ 1) 2 Bose ˆ -Hubbard Hamiltonian
Cold atomic systems Quantum information Ultra cold atoms Many-body system Few-body system (condensed matter physics Field theories
8 Cold atomic systems Ultra cold astoms Quantum information Many-body system (condensed matter physics) Few-body system Field theories
Real space or momentum distributions of the atoms Time of flight measurement time of flight 2 ms 6 ms 14 ms 18 ms Individual condensates in the lattice expand and interfere with each other, revealing the momentum distribution of the atoms in the lattice
9 Real space or momentum distributions of the atoms
33 103 Spin hall effects I Gauge fields in atomic systems 2 Spin Hall effects and Atomic spin Hall effects 3 Detection 4 Conclusions
10 Spin Hall Effects 1 Gauge fields in atomic systems 2 Spin Hall effects and Atomic spin Hall effects 3 Detection 4 Conclusions