论文标题
完全各向异性限制中两个超电原子光谱的分析溶液
Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement
论文作者
论文摘要
我们研究了三维（3D）或二维（2D）完全各向异性谐波陷阱中两个超低原子的系统。我们得出该系统的eigen-Energy e的代数j_ {3d}（e）= 1/a__ {3d}（j_ {2d}（e）= ln a_ {2d}）在3D（2d）情况下，该系统的特征性Egen-Energy e具有3D（2D）的情况，带有A_ {3D}和A _ emplactiontions and A _ _ _ {2d} at _ _ {2D} weptions ands and santipss，and and a _ {2d} weeptions和a _ {2d s-{2d s-{2d s- {2d}功能J_ {3D}（E）和J_ {2D}（E）。在先前的研究中，对于球形或轴向对称的谐波陷阱获得了此类方程（T. Busch等，发现物理学28，549（1998）; Z.Idziaszek和T. Calarco，Phys。Ang。A74，022712（2006））。但是，对于我们完全各向异性陷阱的病例，仅得出了某些情况下的基础能量方程（J. Liang和C. Zhang，Phys。Scr。77，025302（2008））。我们在这项工作中的结果适用于该系统的任意特征能量，可用于研究该陷阱中相互作用的超低原子的动力学和热动力学，例如，第二个病毒系数的计算或两体波函数的演化计算。另外，我们的上述方程式推导方法也可以用于超低原子的其他两体问题。
We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the algebraic equation J_{3D}(E) = 1/a_{3D} (J_{2D}(E) = ln a_{2D}) for the eigen-energy E of this system in the 3D (2D) case, with a_{3D} and a_{2D} being the corresponding s-wave scattering lengths, and provide the analytical expressions of the functions J_{3D}(E) and J_{2D}(E). In previous researches this type of equation was obtained for spherically or axially symmetric harmonic traps (T. Busch, et. al., Found. Phys. 28, 549 (1998); Z. Idziaszek and T. Calarco, Phys. Rev. A 74, 022712 (2006)). However, for our cases with a completely anisotropic trap, only the equation for the ground-state energy of some cases has been derived (J. Liang and C. Zhang, Phys. Scr. 77, 025302 (2008)). Our results in this work are applicable for arbitrary eigen-energy of this system, and can be used for the studies of dynamics and thermal-dynamics of interacting ultracold atoms in this trap, e.g., the calculation of the 2nd virial coefficient or the evolution of two-body wave functions. In addition, our approach for the derivation of the above equations can also be used for other two-body problems of ultracold atoms.
