Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping
Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping
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DOI：
10.1103/physreva.76.053604
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发表时间：
2007-09
影响因子：
2.9
通讯作者：
I. Papadopoulos;P. Wagner;Günter Wunner;J. Main
中科院分区：
文献类型：
--
作者：
I. Papadopoulos;P. Wagner;Günter Wunner;J. Main
对O‘Dell等人的一项提议进行了放大。对于具有吸引1/r相互作用的中性原子的玻色-爱因斯坦凝聚体的实现，我们指出，通过引入适当的‘原子’单元，物理上最好地理解了凝聚体在没有外陷陷势的情况下的自陷。这揭示了一个显著的标度性质：凝聚体的物理只取决于两个参数N{sup 2}a/a{subu}和{Gamma}/N{sup 2}，其中N是粒子数，a是散射长度，a{subu}是‘玻尔’半径，{Gamma}是以原子为单位的陷阱频率。我们计算了自陷波函数和势能以及能量、尺寸和峰密度的精确数值结果，并与以前的变分结果进行了比较。我们指出了负散射长度的推广的Gross-Pitaevskii方程的第二解的存在性，它与基态一起产生于切线分叉中。这表明，对于负散射长度，凝聚态存在不稳定的集体激发态。
Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive 1/r interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate 'atomic' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters N{sup 2}a/a{sub u} and {gamma}/N{sup 2}, where N is the particle number, a the scattering length, a{sub u} the 'Bohr' radius, and {gamma} the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.