Suppression of quantum collapse in an anisotropic gas of dipolar bosons
Suppression of quantum collapse in an anisotropic gas of dipolar bosons
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DOI：
10.1103/physreva.84.033616
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发表时间：
2011-09
影响因子：
2.9
通讯作者：
H. Sakaguchi;B. Malomed
中科院分区：
文献类型：
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作者：
H. Sakaguchi;B. Malomed
在最近的工作[Sakaguchi和Malomed，Phys.Rev.A83，013607（2011）]中，量子坍缩问题的解决方案（落在中心）在三维空间的吸引力潜力-提出了（U{sub 0}/2）r{sup-2}，基于用具有排斥立方项的Gross-Pitaevskii（GP）方程代替线性Schroedinger方程。该模型适用于携带永久电偶极矩的分子的量子气体，吸引中心代表固定电荷。结果表明，排斥非线性抑制量子坍缩，并创建相应的球对称基态（GS），这是在线性薛定谔方程的情况下失踪。在这里，我们的目标是扩展到圆柱形的几何形状和携带角动量的本征态的分析。圆柱形各向异性是由一个均匀的直流电场施加的，它固定了偶极矩的方向，从而改变了吸引力的潜力。首先，我们分析了在具有柱对称势的线性薛定谔方程的框架下，对于方位量子数m=0（GS）和m=1，2的态，量子坍缩开始的条件的修改。得到了相应的吸引势强度（U{sub 0}）{sub cr}（m）的临界值，并给出了非线性GP方程的数值解，证明了在m= 0，1，2时，量子坍缩被原来缺失的本征态所取代.通过数值模拟扰动演化，验证了它们的动力学稳定性。当m=0时，也给出了解析形式的M-Fermi近似。对于解来说至关重要的是在r{yields}0处正确选择边界条件。«少
In recent work [Sakaguchi and Malomed, Phys. Rev. A 83, 013607 (2011)], a solution to the problem of the quantum collapse (fall onto the center) in the three-dimensional space with the attractive potential -(U{sub 0}/2)r{sup -2} was proposed, based on the replacement of the linear Schroedinger equation by the Gross-Pitaevskii (GP) equation with the repulsive cubic term. The model applies to a quantum gas of molecules carrying permanent electric dipole moments, with the attraction center representing a fixed electric charge. It was demonstrated that the repulsive nonlinearity suppresses the quantum collapse and creates the corresponding spherically symmetric ground state (GS), which was missing in the case of the linear Schroedinger equation. Here, we aim to extend the analysis to the cylindrical geometry and to eigenstates carrying angular momentum. The cylindrical anisotropy is imposed by a uniform dc field, which fixes the orientation of the dipole moments, thus altering the potential of the attraction to the center. First, we analyze the modification of the condition for the onset of the quantum collapse in the framework of the linear Schroedinger equation with the cylindrically symmetric potential for the states with azimuthal quantum numbers m=0 (the GS) and m=1, 2. The corresponding criticalmore » values of the strength of the attractive potential (U{sub 0}){sub cr}(m) are found. Next, a numerical solution of the nonlinear GP equation is developed, which demonstrates the replacement of the quantum collapse by the originally missing eigenstates with m=0,1,2. Their dynamical stability is verified by means of numerical simulations of the perturbed evolution. For m=0, the Thomas-Fermi approximation is presented too, in an analytical form. Crucially important for the solution is the proper choice of the boundary conditions at r{yields}0.« less