高等固体物理波色爱因斯坦凝聚省公共课一等奖全国赛课获奖课件.pptx
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1、专题三:玻色爱因斯坦凝聚专题三:玻色爱因斯坦凝聚1.经典统计分布函数经典统计分布函数2.量子统计分布函数量子统计分布函数3.玻色爱因斯坦凝聚玻色爱因斯坦凝聚第1页1.1.经典统计分布函数经典统计分布函数一绝热系统处于势场中:一绝热系统处于势场中:第2页第3页一个服从经典统计系统处于温度一个服从经典统计系统处于温度T热平衡中,其能量每一热平衡中,其能量每一独立平方项都有平均值独立平方项都有平均值1/2kT.与与b无关!无关!第4页如粒子动力学只允许分立能量:如粒子动力学只允许分立能量:普朗克能量均分定理普朗克能量均分定理利用它可推导出黑体辐射公式利用它可推导出黑体辐射公式第5页2.2.量子统计分
2、布函数量子统计分布函数两个全同粒子,两个全同粒子,推广到推广到n个全同粒子(玻色子),个全同粒子(玻色子),n 个玻色子处于相同状态个玻色子处于相同状态几率几率n!倍于其经典几率!倍于其经典几率。第6页问题:将一个玻色子放在一个状态上去几率和状态原有玻色子问题:将一个玻色子放在一个状态上去几率和状态原有玻色子数目有何关系?数目有何关系?再放一个几率是对应经典几率再放一个几率是对应经典几率(n+1)(n+1)倍,增强因子(倍,增强因子(1+n1+n)费米子:费米子:为得量子统计分布,还需精细平衡原理。为得量子统计分布,还需精细平衡原理。第7页在处于平衡体系中考虑两个能级在处于平衡体系中考虑两个能
3、级i i与与j,j,上面分别有上面分别有n ni i及及n nj j个个粒子。令粒子。令R Ri-ji-j代表从代表从i i到到j j跃迁几率。跃迁几率。精细平衡:精细平衡:经典统计,有:经典统计,有:对玻色子,有增强因子对玻色子,有增强因子1+n:1+n:对全部能级成立。对全部能级成立。第8页费米子:费米子:1 1n n取代取代1+n1+n玻色爱因斯坦分布函数玻色爱因斯坦分布函数费米狄拉克分布函数费米狄拉克分布函数第9页Quantum Statistics第10页Predicted 1924Created 19953.3.玻色爱因斯坦凝聚玻色爱因斯坦凝聚第11页Q1:What Is Bose
4、-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=velocity第12页Against Our Intuition?!In most everyday matter,the de Broglie wavelength is much shorter than
5、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 hav
6、e 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).第13页第14页Bose and EinsteinIn 1924 an Indian physicist named Bose studied the quantum behaviour of a collection of photons.Bose sent his wor
7、k 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 qu
8、antum state.This is called Bose-Einstein condensation.第15页第16页Fermions(費米子費米子)and Bosons(玻色子玻色子)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.T
9、hey 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 a
10、nd 11 electrons.第17页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 t
11、o a very low temperature.第18页第19页第20页第21页第22页Cooling Down the AtomsSee the animation:http:/www.colorado.edu/physics/bec/what_is_it.htmlWhen 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 phy
12、sics.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.第23页The Strange State of
13、BECWhen 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).第24页Q2:How Is BEC Made?Laser b
14、eamOther equipment:laser equipment,computer,electronicsCost less than US$100,000第25页Laser Cooling(激光冷卻激光冷卻)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 z
15、ero.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-TannoundjiPhillips第26页Ping-pong BallsPhotons are particles.They carry momenta like ping-pong balls.You can slow the motion of
16、an atom by bouncing laser light off the atoms.See the animation http:/www.colorado.edu/physics/bec/lascool1.html.第27页Tuning the LaserOnly 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 http:/www.
17、colorado.edu/physics/bec/lascool2.html第28页Using the Doppler EffectProblem: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
18、 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.html第29页Laser Trapping(激光陷阱激光陷阱)Suppose the laser has the right colour for the photons to be absorbed by an approaching atom,then the atom will be slowed d
19、own.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 change in this case.When lasers are sent in from all the different directions,the atoms can get cold very quickly.This is called laser trapping,a
20、nd the trapped atoms form an optical molass(光學粘膠).See the animation:http:/www.colorado.edu/physics/bec/lascool4.html第30页Magnetic Trapping(磁性陷阱磁性陷阱)Problem:Laser cooling can cool the atoms down to 10K,because atoms can spontaneously emit the absorbed photon.This is still too hot for BEC.Solution:Evap
21、orative coolingThe atoms behave as tiny compasses.They can be pulled by magnetic fields.A magnetic field can be designed to push the atoms inwards from both sides,forming a magnetic trap.See the animation:http:/www.colorado.edu/physics/bec/mag_trap.html第31页Evaporative Cooling(挥发冷却挥发冷却)Principle:Evap
22、oration takes heat.A cup of tea gets cool after steam escapes,because faster atoms escape from the cup,leaving behind the slower ones.Technique:Lower the height of the trap quickly,so that there are still enough atoms left in the trap to get involved in BEC.Try to trap the largest number of atoms in
23、 BEC in the animation:http:/www.colorado.edu/physics/bec/evap_cool.html第32页Can You Break This Record?第33页Q3:What Does a Bose-Einstein Condensate Look Like?There is a drop of condensate at the centre.The condensate is surrounded by uncondensed gas atoms.The combination looks like a cherry with a pit.
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