过去人们都用电偶极的作用来解释分子、原子间力，原子由核和电子组成，核和电子构成偶极是合理的。 A、B两个原子相互作用示意图，原子核位于a和d处，电子绕核运动，当B原子的电子位于c处时受到A原子的最大偶极作用为：按照库仑定律，A原子的电子在b处时c处电子受到最大排斥力(用负值表示)，A原子的电子在f处时，c处电子受到a处核的最大吸引力(用正值表示)，净剩力F B c 为该两力之差(k是系数，r是原子半径，R是原子间距)： F B c = f Ab +f Af =-k/(r bc ) 2 +k/(r + r bc ) 2 当B原子的电子位于e处时受到A原子的最大偶极作用为：A原子的电子在b处时d处B核受到最大吸引力(用正值表示)，A原子的电子在f处时，d处B核受到a处A核最大排斥力(用负值表示)，净剩力 F Be 为该两力之差： F Be = f ' Ab +f ' Af = +k/(r + r bc ) 2 -k/(r bc +2r ) 2 总的净剩力：F= F B c + F Be =2 k/(r + r bc ) 2 - k/(r bc ) 2 -k/(r bc +2r ) 2 r bc远大于 r 时, F=0。 r bc = r时， F=-11k/(18 r 2 ) 原 子 越接 近 排 斥 力 越 大, 这是理论计算 的 最大值。 两个原子外面是电子，用静电力的库仑定律来计算只能得出净剩力是排斥力的结论。 实际值应 接近零才能符合气体的电中性。 中外都有人用偶极作用来推导分子间力，但都是错误的推导。用任何数学方法都不可能合符逻地得出吸引力。 那么还有什么力使原子相互吸引？我们知道两块磁铁靠近会自动吸在一起，南北磁极吸在一起是最低能态（稳定态）。原子中电子绕核运动也能产生磁场(还有磁矩)，依靠电子运动产生的磁场相吸使体系处于 最 低 能 态 使原子凝聚在一起 。 斯特恩-盖拉赫实验是让原子束穿过不均匀磁场，结果发现有单电子的H、Li、Cs、Ag等原子束分裂为两束，有成对电子(两电子的运动方向相反)的Sn、Pb、Cd、Hg原子束不分裂仍为一束。这个实验首先发现核外电子产生的磁场与外磁场的作用。 H、Li、Cs、Ag等原子束中部分原子的单电子向某方向运动产生的磁场方向与外磁场相反时，原子受到吸引力向上偏转；同时原子束中部分原子的单电子向反方向运动产生的磁场方向与外磁场相同，原子受到排斥力向下偏转；这就是原子束分裂的原因。在Sn、Pb、Cd、Hg原子束中成对电子(两电子的运动方向相反)的磁场相互抵消，在外磁场中几乎不受力，所以Sn、Pb、Cd、Hg原子束不分裂。 原子的单电子会顺应外磁场，这类原子叫顺磁性原子，例如H、Li、Na、K、Cs、Cu、Ag等原子。原子的成对的电子总是反抗外磁场，这类原子叫抗磁性原子，例如Sn、Pb、Cd、Hg、He、Ne、Ar、Kr、Xe等原子。 由于抗磁性原子的电子成对使其磁场大部分相消(磁矩反平行)，剩余磁场较弱导致这类原子对其他同类原子的相互作用比较弱，所以这类原子要在更低的温度才凝聚，它们的熔点较低，例如Sn、Pb、Cd、Hg、He、Ne、Ar、Kr、Xe等。反之，那些有不成对电子的顺磁性原子对其他 同 类 原子的 相 互 作用 比较强，它们容易凝聚有较高的熔点。当然要在相近状态下比较 熔 点 ： HHe， LiNe, NaAr, KKr, RbXe CuZn, AgCd, AuHg 氢原子的单电子有较強磁场，形成氢分子后的剩余磁场仍比氦原子 的 剩余 磁 场 強，所以氢的熔点比氦的 熔 点 高。 Li、Na、K、Rb形成晶胞 后的剩余磁场仍比 Ne、Ar、Kr、Xe 原子 的 剩余 磁 场 強，所以 Li 、 Na 、 K 、 Rb 的熔点比 Ne 、 Ar 、 Kr 、 Xe 的 熔 点 高。但是 影响熔点的原因很多，这里是初步探索。
谁来讲十分钟： Photo finish in race for strontium condensate Nov 18, 2009 An expanding field An Austrian group has beaten its US counterpart by a matter of days in a race to create a Bose-Einstein condensate (BEC) of strontium atoms. Researchers at the Institute of Quantum Optics and Information (IQOQI) at the Austrian Academy of Sciences submitted their paper on a strontium BEC a mass of ultracold atoms all in the same quantum state just 10 days before those at Rice University in Houston, Texas. The breakthrough makes way for more precise quantum timekeeping and new studies of the quantum nature of matter. We have been in a race to get this done, and once some big unknowns were figured out a couple of years ago it was no mystery how to get here, says Rice Universitys Tom Killian, who adds that the IQOQI is a great lab. Rudi Grimm of the IQOQI says he and his colleagues learnt a lot from the Rice University group, but were just quicker with the final cooling stage. A single state Bose-Einstein condensation occurs when atoms of integer spin are cooled below a critical temperature. The atoms settle in the same quantum state and move coherently as though they are a single entity. The first BECs were made in 1995 from alkali metal atoms, such as rubidium, which have one electron in their outer shell. Over the past few years BECs have also come made from atoms that have two outer electrons ytterbium and more recently calcium. The real prize, however, is strontium another atom with two outer electrons that has already proved very useful in extremely accurate optical clocks. Two electron atoms are interesting because they have no magnetic moment in their ground state. This means that a BEC of strontium would not have to be shielded from stray magnetic fields making it easier to use in applications such as an atom interferometer that could be used to detect tiny changes in the local gravitational field. Breaking with convention However, the conventional way of cooling atoms to create a BEC involves trapping them with a magnetic field, and then lowering the fields potential so the hottest atoms tend to collide with others and are ejected from the trap a process called evaporative cooling. Some researchers had found that lasers could perform both the trapping and evaporative cooling of non-magnetic atoms, but this has proven problematic. The trouble is related to the scattering length, which effectively marks the distance at which atoms collide. The most abundant isotope of strontium, Sr-88, has a very small scattering length, so the collision rate is too low and evaporative cooling fails. On the other hand, the next most abundant isotope, Sr-86, has a very big scattering length, so collisions occur among too many atoms. The breakthrough of the two groups was to opt for a much rarer isotope, Sr-84, which has a scattering length somewhere between Sr-88 and Sr-86 making it just right. The IQOQI group used it to create a BEC of about 1.5 10 5 atoms, while the Rice University group used it to create a larger BEC of 3 10 5 atoms. I think it is impressive how the field has matured and that we can now condense atoms which have small natural abundance, and which cannot be magnetically trapped in the ground state, says Wolfgang Ketterle of the Massachusetts Institute of Technology, who won the Nobel Prize for Physics in 2001 for being one of the first to create a BEC. The strontium experiment demonstrated an amazing combination of advanced techniques. Robust and well defined Strontium is advantageous because it forms fairly robust condensates that can last longer and be made larger. This makes it easier for studies of quantum degeneracy, in which atomic interactions are tuned, for example, to create novel quantum fluids. Another advantage is that it has several well defined electronic-transition frequencies, which makes it attractive as an atomic clock for more precise metrology studies. Tilman Pfau, a physicist at the University of Stuttgart who used similar techniques to condense chromium five years ago, called the new work an interesting addition to the BECs of ytterbium and calcium. What is maybe also interesting is that people talked about condensing strontium for years, and now within days two groups have achieved this goal almost simultaneously, he adds. Science is a nonlinear process. The strontium BECs comes hot on the heels of the first calcium condensate, which was reported in September by Sebastian Kraft and colleagues at Germanys PTB metrology lab in Braunschweig. Kraft told physicsworld.com long term goal of the PTB team is to create an optical lattice of calcium atoms in which each lattice site holds precisely one atom. Such a Mott insulator could in principle be used as part of an atomic clock that is extremely precise because individual atoms are isolated from each other. The research is reported in three papers in Physical Review Letters (see restricted links). About the author Jon Cartwright is a freelance journalist based in Bristol, UK
半年前刘全慧老师在他的博文 《学一回苏格拉底如何？》 中谈到有学生问光子是否存在BEC。由于自己才疏学浅，对这个问题没有深刻的理解，只是隐约记得当年去北大偷听《量子光学》这门课的时候老师似乎说过激光就是光子的BEC。因此当时就在该博文下面留言激光就是光子的BEC。在刘老师和众博友的细心教导下，我终于放弃了这个观念。但是心里一直有点残念，既然光子没有BEC，那我总要想个办法弄出点类似BEC的东西，哪怕是等效的或者是在某一个维度上也好，由此写下这篇博文，请各位大侠斧正。 我的方案如下： 往一卷光缆中打一束激光，如图所示。光缆直径为a，激光的入射位置d、激光的频率以及光缆的卷曲半径R都是可以调节的。在光缆上建立新的正交坐标{u, }，那么在{u, }坐标下看整个系统则如下图所示， 光线就像乒乓球一样在光纤中弹跳。 既然光线的运动可以等效于重力场中的乒乓球，那么如果我们只关注{u, }坐标中的u维度，那么光线运动就等效为一维的重力场中的粒子，其势能如下图所示 而光遵循的麦克斯韦方程可以等效的化为薛定谔方程，那么光线在u轴上的运动完全就是一维重力场中的量子粒子，其波函数也由上图给出（Airy函数）。那么光线在各个分立能级上的分布函数就可以求出，如下图所示 我总是可以通过调节激光的入射位置d、激光的频率以及光缆的卷曲半径R让能量主要集中在基态（n=1）上。那么按照爱因斯坦给出来的BEC的定义，我就完成了光线在某一特定维度（u轴）上的等效BEC。而且实现该等效BEC还不需要超低温，只需要在常温下通过非常简单的手段就可以实现。（哈哈，本博主得意地笑一下！） 当然这究竟是不是BEC，当然不是。鄙人的恩师经常告诫我们，麦克斯韦方程化成薛定谔方程再怎么像，它毕竟不是薛定谔方程。麦克斯韦方程它本身还是经典的，而薛定谔方程是量子的。BEC是一个量子概念，它不可能在经典体系里得出。 顺便插一个故事，当年Berry重新提出几何相位的概念，大家都想用实验验证几何相位，第一个实验就是让偏正光在卷曲的光纤里绕几圈射出后偏正角度与入射时有个偏差，这样人们就说这是几何相位。但是很多人（包括Berry本人）也反对将量子的几何相位用这种经典的薛定谔方程来得出。 Berry's phase in Optical Fiber As is seen in fig below, photon in the fiber is in helicity states i.e. circularly polarized and the helix k(t) undergoes a loop in the k space with the same initial k and final k i.e. k(T) = k(0). The helicity state is set up of optical fiber experiment to measure Berry's pahse. They Berry's phase is where l is the number of the loop and (C) is the solid angle enclosed by the k in one loop as in fig below. And the rotation of linear polarization of the photon is C is the path of the k in one loop, and (C) is the solidangle in one loop. 反正不才也不想发什么文章，就把一点想法曝在博客上，与众博友哈喇一番，就用来消遣消遣，还望各位大侠不吝赐教。 注：本文部分插图摘自网络，部分插图摘自PRL,102, 180402
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