Creation and Stability of Vortices in a Dilute Trapped Bose Gas

9971518 FetterThis grant will support the theoretical research which investigates the connections between concepts developed for superfluid helium and stationary and rotating Bose-Einstein condensates formed from cold alkali atoms.该基金将支持研究超流氦概念与冷碱金属原子形成的静止和旋转玻色-爱因斯坦凝聚之间的联系的理论研究。 目前该领域的主要问题之一是单连通凝聚体中量子化涡旋和多连通凝聚体中量子化环流的产生、稳定性和检测。 本研究将利用已知的低温下稀玻色气体的一般理论描述，研究在旋转的非轴对称凝聚体中产生涡旋的临界角速度，其中旋转的阱壁赋予原子角动量，无论是在小凝聚体的接近理想极限还是在大凝聚体的相反极限。 这引入了大量新的概念特征。 对于非旋转的轴对称凝聚体，当凝聚体中含有一个单量子化涡旋时，其中一个简正模的频率为负，这表明凝聚体存在潜在的不稳定性. 外部旋转提高了这个频率，并最终使其为正（从而稳定了漩涡）。 这种情况已经详细分析了一个小的接近理想的冷凝物，其中的负频率正常模式涉及的涡核相对于冷凝物的质心的运动的旋涡。 本文用几种不同的方法研究了大尺度轴对称凝聚体中涡旋的反向极限。 对于旋转的非轴对称凝聚体，无论是在小凝聚体还是大凝聚体极限下，涡线都变成了简单的二维饼状涡。 这种行为使得研究具有极端轴对称性的近二维凝聚体中的饼状涡的行为变得有趣。 此外，还有一个有趣的问题，即这种被困系统是否能够达到严格的二维极限。该补助金将支持理论研究，研究超流氦（一种无阻力流动的流体）概念与冷碱原子形成的静止和旋转玻色-爱因斯坦凝聚体之间的联系。 玻色-爱因斯坦凝聚在许多年前就被预测到了，但直到最近才在实验室中被观察到。 目前该领域的主要问题之一是单连通凝聚体中量子化涡旋和多连通凝聚体中量子化环流的产生、稳定性和检测。 本研究将研究这些冷凝物的各种构型。*

9971518FetterThis grant will support theoretical research which investigates the connections between concepts developed for superfluid helium and stationary and rotating Bose-Einstein condensates formed from cold alkali atoms. One of the major current issues in this field is the creation, stability, and detection of quantized vortices in a simply connected condensate and quantized circulation in a multiply connected condensate. This research will use the known general theoretical description of a dilute Bose gas at low tempertaure to study the critical angular velocity for the creation of a vortex in rotating nonaxisymmetric condensates, where the rotating trap walls impart angular momentum to the atom, both in the nearly ideal limit of a small condensate and in the opposite limit of a large condensate. This introduces seveal new conceptual features. The analysis will be extended to include the creation of quantized circulation in a similar doubly connected nonaxisymmetric condensate.For a nonrotating axisymmetric condensate containing a singly quantized vortex, one single normal mode has a negative frequency, which indicates a potential instability. An external rotation raises this frequency and eventually makes it positive (thus stabilizing the vortex). This situation has been analyzed in detail for a vortex in a small nearly ideal condensate, where the negative-frequency normal mode involves a motion of the vortex core relative to the center of mass of the condensate. The opposite limit of a vortex in a large axisymmetric condensate has been studied with several different methods. The proposed generalization to a rotating nonaxisymmetric condensate is especially important in connection with possible experimental schemes for vortex creation, both in the small-condensate and large-condensate limits.For this superfluid helium films, the vortex lines become simply two-dimensional pancake vortices. This behavior makes it interesting to investigate the behavior of pancake vortices in a nearly two-dimensional condensate with extreme axial symmetry. In addition, there is the intriguing question whether such trapped systems can ever attain the strict two-dimensional limit.%%%This grant will support theoretical research which investigates the connections between concepts developed for superfluid helium (a fluid which flows without resistance) and stationary and rotating Bose-Einstein condensates formed from cold alkali atoms. Bose-Einstein condensates were predicted many years ago, but only recently have been observed in the laboratory. One of the major current issues in this field is the creation, stability, and detection of quantized vortices in a simply connected condensate and quantized circulation in a multiply connected condensate. This research will study various configurations of these condensates.***