玻色-爱因斯坦凝聚

专题三：玻色爱因斯坦凝聚1. 经典统计分布函数2. 量子统计分布函数3. 玻色爱因斯坦凝聚1. 经典统计分布函数一绝热系统处在势场中：一个服从经典统计的系统处于温度 T的热平衡中，其能量的每一独立的平方项都有平均值 1/2kT.与 b无关！如粒子动力学只容许分立能量：普朗克能量均分定理利用它可推导出黑体辐射公式2. 量子统计分布函数两个全同粒子，推广到 n个全同粒子（玻色子）， n 个玻色子处于相同状态的几率 n！ 倍于其经典几率 。问题：将一个玻色子放在一个状态上去的几率和状态原有的玻色子数目有何关系？再放一个的几率是相应经典几率的 (n+1)倍，增强因子（ 1+n）费米子： 为得量子统计分布，还需精细平衡原理。在处于平衡的体系中考虑两个能级 i与 j,上面分别有 ni及 nj个粒子。令 Ri-j代表从 i到 j的跃迁几率。精细平衡：经典统计，有：对玻色子，有增强因子 1+n:对所有能级成立。费米子： 1 n取代 1+n玻色爱因斯坦分布函数费米狄拉克分布函数Quantum StatisticsPredicted 1924Created 19953. 玻色爱因斯坦凝聚Q1: What Is Bose-Einstein Condensation?De Broglie 德布罗意 (1929 Nobel Prize winner) proposed that all matter is composed of waves. Their wavelengths are given byl = de Broglie wavelengthh = Plancks constant 普朗克 常数m = massv = velocityAgainst Our Intuition?! In most everyday matter, the de Broglie wavelength is much shorter than the distance separating the atoms. In this case, the wave nature of atoms cannot be noticed, and they behave as particles. The wave nature of atoms become noticeable when the de Broglie wavelength is roughly the same as the atomic distance. This happens when the temperature is low enough, so that they have low velocities. In this case, the wave nature of atoms will be described by quantum physics, e.g. they can only stay at discrete energy states (energy quantization). Bose and Einstein In 1924 an Indian physicist named Bose studied the quantum behaviour of a collection of photons. Bose sent his work to Einstein, who realized that it was important. Einstein generalized the idea to atoms, considering them as quantum particles with mass. Einstein found that when the temperature is high, they behave like ordinary gases. However, when the temperature is very low, they will gather together at the lowest quantum state. This is called Bose-Einstein condensation.Fermions (費米子 ) and Bosons (玻色子 ) Not all particles can have BEC. This is related to the spin of the particles. The spin quantum number of a particle can be an integer or a half-integer. Single protons, neutrons and electrons have a spin of . They are called fermions. They cannot appear in the same quantum state. BEC cannot take place. Some atoms contain an even number of fermions. They have a total spin of whole number. They are called bosons. Bosons show strong “social” behaviour, and can have BEC. Example: A 23Na atom has 11 protons, 12 neutrons and 11 electrons.The Material For BEC BEC was found in alkali metals e.g. 87Rb (铷 ), 23Na (钠 ), 7Li (锂 ) because:They are bosons.Each atom is a small magnetic compass, so that a cooling technique called magnetic cooling can work.The atoms have a small repulsion, so that they do not liquefy or solidify down to a very low temperature.Cooling Down the Atoms See the animation: /physics/2000/bec/what_is_it.html When the temperature is high, the atoms have high energies on average. The energy levels are almost continuous. It is sufficient to describe the system by classical physics. When the temperature is low, the atoms have low energies on average. It is necessary to describe the system by quantum physics. When the temperature is very low, a large fraction of atoms suddenly crash into the lowest energy state. This is called Bose-Einstein condensation.The Strange State of BEC When all the atoms stay in the condensate, all the atoms are absolutely identical. There is no possible measurement that can tell them apart. Before condensation, the atoms look like fuzzy balls. After consdensation, the atoms lie exactly on top of each other (a superatom).Q2: How Is BEC Made?Laser beamOther equipment: laser equipment, computer, electronicsCost less than US$100,000Laser Cooling (激光冷卻 ) The technique of laser cooling was developed by the winners of the 1997 Nobel Prize winners. In the physical world, the lowest temperatures approach a limit of 273oC. This is called the absolute zero. Nothing can be as cold as the absolute zero because all atomic and subatomic motions stop. Laser cooling can get to the low temperature of 0.18K (1 K微開 = 10-6K).Chu 朱棣文 Cohen-Tannoundji PhillipsPing-pong Balls Photons are particles. They carry momenta like ping-pong balls. You can slow the motion of an atom by bouncing laser light off the atoms. See the animation /physics/2000/bec/lascool1.html. Tuning the Laser Only laser light with the correct colour (frequency) can be absorbed by the atoms. If the colour is wrong, the atoms cannot absorb the photons. See the animation /physics/2000/bec/lascool2.htmlUsing the Doppler Effect Problem: The laser can slow the approaching atoms, but it can also blast off the receding ones. Solution: Use Doppler shift. When the atom is receding from the laser source, the wavelength is lengthened and there is a redshift. When the atom is approaching the laser source, the wavelength is shortened and there is a blueshift. See the animation: http:/www.astro.ubc.ca/scharein/a311/Sim.htmlLaser Trapping (激光陷阱 ) Suppose the laser has the right colour for the photons to be absorbed by an approaching atom, then the atom will be slowed down. However, the laser will not have the right colour for the photons to be absorbed by the receding atom because of Doppler effect. Hence the atom will not