以第一原理研究非等向性阱中玻色-愛因斯坦凝結在接觸與偶極交互作用下的特性

Ab initio study of the properties of Bose-Einstein condensates with dipolar interactions in an anisotropic Trap

廖聖侖(Shein-Lun Liao)

指導教授 ： 朱時宜

國立臺灣大學/理學院/物理研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.01242

摘要

無資料

關鍵字

玻色愛因斯坦凝結 ； 廣義擬似譜法 ； Gross-Pitaevskii 方程 ； 散射長度 ； 偶極

並列摘要

We present an ab initio numerical method to study the properties of Bose-Einstein condensates (BECs) which include both interactions via contact and magnetic dipole-dipole forces. We efficiently solve the nonlocal and anisotropic interaction potential between dipoles which are represented in a differential form. The BEC Hamiltonian is discretized and solved accurately through the generalized pseudospectral method (GPS method). Using the iteration minimization technique, we obtain the solutions of the non-linear Gross-Pitaevskii equation with non-local dipolar interaction. We find that the density profiles strongly depend upon the geometry of trapping potentials. We determine that the maximum density is not always located at the center of a trap due to the interaction between dipoles. Experiments have shown that the stability of dipolar BECs strongly depends on the geometry of trapping potentials and the scattering length. As the scattering length decreases under certain critical values acrit , BECs are no longer stable. Using the GPS method, the critical scattering length corresponding to different trap geometries is accurately determined with a minimum number of grid points. In addition, we show that the
Thomas-Fermi approximation is not good enough to describe condensates before BECs collapse, and the double-peaks feature of density profiles is an important characteristic in such condition. In the near future, the dynamics of dipolar BECs will be studied employing the GPS method.

並列關鍵字

BEC ； dipole ； GPS method ； Gross-Pitaevskii equation ； double peaks

參考文獻

[6] C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet. Evidence of boseeinstein

[10] T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell,

of a purely dipolar quantum gas against collapse. Nat Phys, 4(3):218–222, March

[2] Eric Cornell. Very cold indeed: The nanokelvin physics of bose-einstein condensation.

J. Res. Natl. Inst. Stand. Technol., 101:419, 1996.