二維雙偶極晶體的物理性質

Abstract

對於具備偶極-偶極交互作用的準二維玻色愛因斯坦凝體，本文以高斯波包作為晶體相的試驗波函數。在高粒子密度的情形下，可將此波函數合理地當作偶極晶格點上的波函數。考慮非正交波函數基底的疊加效應，修正Hartree-Fock平均場近似，再透過數值計算找出晶體相的能量極小值。最後，經由聲子頻譜分析，以及切變模數與壓縮模數恆為正值的結果，證實高粒子密度條件下系統呈現晶體相的可能性。

The current work designs a Gassian trial wavefuntion for Bose-einstein condensates (BEC) with dipole-dipole interaction. The wavefunction is reasonably regarded as that of the dipole crystal under high particle density condition. Hartree-Fock mean field approximation has been modified under the consideration of the overlaping effect of non-orthogonal wavefunction. The minimum energy of crystalline phase can therefore be found by numerical computations and phonon spectrum evaluation. These shear and compression modulus are shown to be definitely positive. Thus, it is concluded that quasi-2D dipolar crystal is a stable state under high condensed density.