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

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) 448 1029.

Spinless atoms in a double-wells P. Cheinet, et. al., 2008 Phys. Rev. Lett. 101 090404.

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

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.

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.

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

Result For the antiferromagnetic atomic interaction

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.

Result Three atoms trapped in one double-wells

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