1. 郑 公 平 河南师范大学 第五届全国冷原子物理和量子信息青年学者学术讨论会
Ground-state phases of ultracold spin-1 atoms
in a double-wells optical superlattice under the weak magnetic field
郑 公 平
河南师范大学

2. Ultracold atoms in an optical superlattice
In the array of the double-wells optical lattice, many identical instances of the experiment in parallel may be carried out in a single run.
S. Folling, et. al., 2007 Nature (London)

3. Spinless atoms in a double-wells
P. Cheinet, et. al., 2008 Phys. Rev. Lett

4. Spin-1 atoms in a deep double-wells optical superlattice
The effective two-site Bose-Hubbard-type model:

5. The Hamiltonian can be diagonalized exactly or pertubatively.
The eigenstates of are easy to be obtained.
The Hamiltonian can be diagonalized exactly or pertubatively.
Method: Only the states with the same z component of total spin have non-zero transition matrix elements and thus form a closed subspace.

6. The high-energy levels can be integrated out
Auerbach A ，Interacting Electrons and Quantum Magnetism
Comparing these eigen-energies we can obtain the lowest one, i.e., the ground states.

7. Result Two atoms trapped in one double-wells
For the ferromagnetic atomic interaction
ground state:

8. Result
For the antiferromagnetic atomic interaction

9. Result
The weak critical magnetic field is one-to-one with the tunneling parameter t, which is easy to be controlled exactly in experiments.
This may be useful for the detection of the weak magnetic field if these quantum phases can be distinguished.

10. Result
Three atoms trapped in one double-wells

11. Thanks for your attention!