2017年泛珠三角与中华名校物理奥林匹克邀请赛试题与答案test2_solution.pdf

Pan Pearl River Delta Physics Olympiad 2017 2017 年泛珠三角及中华名校物理奥林匹克邀请赛 Sponsored by Institute for Advanced Study, HKUST 香港科技大学高等研究院赞助 Simplified Chinese Part-2 (Total 2 Problems, 55 Points) 简体版卷-2 （共2题，55分） (2:00 pm – 5:00 pm, 3 February, 2017) Problem 1: Bose Einstein Condensation (22 points) 玻色-爱因斯坦凝聚 （22 分） -34 Planck’s constant 普朗克常数h = 6.626  10 Js -23 -1 Boltzmann constant 波尔兹曼常数kB = 1.381  10 JK In nature, particles are classified into two different kinds: bosons and fermions. Bosons (e.g. photons) are particles that like to be together in the same state. In contrast, fermions (e.g. electrons, protons and neutrons) are unlikely to go into an already occupied state according to the Pauli exclusion principle. Statistical mechanics tells us that when a system of bosons reaches a critical density in a trap it undergoes a transition that a large number of bosons will have a tendency to occupy the same lowest-energy state. This phenomenon is called Bose-Einstein condensation. The following figure shows how bosons and fermions occupy energy states when the temperature approaches 0 K. 在自然界中，粒子可以分为两种不同的类型：玻色子和费米子。玻色子（例如光子）是喜 欢一起处于相同状态的粒子。相反，根据泡利不相容原理，费米子（例如电子、质子和中 子）不可能进入已经被占据的状态。统计力学告诉我们，当一个玻色子系统在阱中达到临 界密度时，它会经历相变，令大量的玻色子倾向占据相同的最低能阶。这种现象称为玻色 -爱因斯坦凝聚。下图显示当温度接近0 K 时，玻色子和费米子如何占据能阶。 Recent development of trapping and cooling ultracold atoms (e.g. Sodium, Rubidium and Lithium atoms) paved the way for the observation of Bose-Einstein condensation of atomic gases in ultracold temperature (Nobel prize in physics 2001), which had been t