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arXiv 1507.04740cond-mat.quant-gas
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双阱光晶格中的大有效三体相互作用

Large effective three-body interaction in a double-well optical lattice

Saurabh Paul, Eite Tiesinga

摘要:

研究了具有两个局部极小的光晶格中的超冷原子,证明了仅存在两两相互作用的多带玻色-哈伯德(BH)哈密顿量的低能态等价于存在强三体相互作用的有效单带哈密顿量.我们研究了双阱光晶格,它具有沿$x$轴对称的双阱结构和沿垂直方向的单阱结构。通过精确的能带结构计算和数值构造的Wannier函数,得到了两体相互作用能,从而构造了最低两个能带的BH哈密顿量。我们的有效汉密尔顿量是从两个最低能带的Wannier函数所跨越的子空间内获得的每个单胞的$N$ -原子汉密尔顿量的基态构造的。该模型包括相邻晶胞的基态之间的跳跃。我们表明,这样一个有效的哈密顿量有很强的三体相互作用,可以很容易地调整通过改变晶格参数。最后,依靠数值平均场模拟,我们表明,有效的哈密顿量是一个很好的近似的两带BH哈密顿量在很宽的晶格参数范围内,无论是在超流和莫特绝缘体地区。

英文摘要:

We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions.

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