毕业答辩ppt模板-华中师范大学汉口分校

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1.1. 经典统计分布函数经典统计分布函数一绝热系统处在势场中：一绝热系统处在势场中：玻尔兹曼分布玻尔兹曼分布单位体积内的粒子数单位体积内的粒子数对动量积分对动量积分势能势能动能；动能；处的单位体积内粒子数处的单位体积内粒子数：在：在kTEkTEzyxKpKpzyxKTEEzzzyyyxxxppPKeNNdxdydzeNdNdzzzdyyydxxxpppmEEEENdpdpdxdydzdpemkTNdNdpppdpppdpppdzzz

2、dyyydxxx 002220230:,)(21:0)2( 无无关关：能能量量以以外外的的能能量量，它它与与是是除除自自由由度度，自自由由度度：自自由由度度的的能能量量分分配配定定理理对对多多自自由由度度体体系系，有有按按称称为为正正则则分分布布中中的的粒粒子子数数是是在在相相空空间间体体积积元元坐坐标标、广广义义动动量量的的函函数数的的体体系系，其其能能量量是是广广义义一一个个自自由由度度为为ifiifiiiiikTppqqEffffffpiEppppqqEEbppiCeppqqddpdpdqdqdppqqEEfff111122/),.,;,.,(111111),.,.,;,.,(:),.,

3、;,.(.),.,;,.,(11 kTdpedppebdpedpeibpiibpikTiikTiiiii1,222/ 12bdpeibpi 分分母母：kTbbdpeiibpi21212112/32 分分子子：一个服从经典统计的系统处于温度一个服从经典统计的系统处于温度T的热平衡中，其能量的热平衡中，其能量的每一独立的平方项都有平均值的每一独立的平方项都有平均值1/2kT.与与b无关！无关！无关。无关。，与，与则则如如ckTcqiii21,2 其其平平均均势势能能也也相相同同。不不同同相相当当于于体体系系不不同同硬硬度度的的大大量量谐谐振振子子但但平平均均动动能能相相等等。不不同同相相当当于于质

4、质量量不不同同的的等等离离子子体体，虽虽然然它它们们考考虑虑由由电电子子和和质质子子组组成成),(),(cb20/20/0/)1()(11.1,/xxnkTnhxxxnkTnhnkTnheehedxdheeekThxeenhEnhE 分子：分子：分母：分母：令令对量子谐振子：对量子谐振子：1/ kThehE 如粒子动力学只容许分立能量：如粒子动力学只容许分立能量：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2. 2. 量子统计分布函数量子统计分布函数两个全同粒子，两个全同粒子， ,不不相相容容原原理理倍倍态态的的几几率率是是经经典典几几率率的的两两个

5、个玻玻色色子子处处于于相相同同状状PauliFBFB 0)2 , 1(2)1()1(2)2 , 1(:)1()2()2()1(21)2 , 1()1()2()2()1(21)2 , 1( 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的几率的几率n！倍于其经典几率！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？色子数目有何关系？ncnBnncnPnPnPPPn)( !)(11 量量子子：个个粒粒子子的的几几率率经经典典：在在态态上上放放BnBn

6、cnBnPPnPPnP1111)1()!1( 再放一个的几率是相应经典几率的再放一个的几率是相应经典几率的(n+1)(n+1)倍，增强因子（倍，增强因子（1+n1+n）费米子：费米子： )1 , 0( ,)1(1 nPn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。在处于平衡的体系中考虑两个能级在处于平衡的体系中考虑两个能级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的跃迁几率。的跃迁几率。jiiRnijjRnijjjiiRnRn 精细平衡：精细平衡：经典统计，有：经典统计，有：k

7、TEkTEcckTEEeeRRnnenn/211221/ )(212121 对玻色子，有增强因子对玻色子，有增强因子1+n:1+n:kTEkTEBBcBcBeennRRnnRnRRnR/2121122112112212212111)1()1( 对所有能级成立。对所有能级成立。 0/)(/)(/22/11)()(11)(1;1121总总粒粒子子数数只只与与温温度度有有关关的的常常数数NdEENEneeEneenneennennBkTEBTkTETkTEkTE 费米子：费米子：1 1n n取代取代1+n1+n)(21)(11)(:,11)(1/ )(/)(/化化学学势势的的分分布布能能量量化化学学

8、势势，对对自自由由电电子子，令令 FFkTEEFFkTkTEFTkTEneEnFermieeeeEneennFF 玻色爱因斯坦分布函数玻色爱因斯坦分布函数。且和系统能级密度有关且和系统能级密度有关有关的量，有关的量，是和粒子数密度和温度是和粒子数密度和温度 费米狄拉克分布函数费米狄拉克分布函数Quantum StatisticsPredicted 1924Created 19953. 3. 玻色爱因斯坦凝聚玻色爱因斯坦凝聚Q1: What Is Bose-Einstein Condensation?De Broglie 德布罗意 (1929 Nobel Prize winner) propos

9、ed that all matter is composed of waves. Their wavelengths are given byl = de Broglie wavelengthh = Plancks constant 普朗克常数m = massv = velocitymvhlAgainst Our Intuition?! In most everyday matter, the de Broglie wavelength is much shorter than the distance separating the atoms. In this case, the wave

10、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 atom

11、s 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. Eins

12、tein 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 conde

13、nsation.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 . They are called fermions. They cannot appear in

14、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 B

15、EC 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

16、Down the AtomsSee the animation: /physics/2000/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 physics.When the temperature is low, the atoms

17、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 BECWhen all the atoms stay in the condensate

18、, 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, compu

19、ter, electronicsCost less than US$100,000Laser 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 zero. Nothing can be as cold as the absol

20、ute 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-TannoundjiPhillipsPing-pong BallsPhotons are particles. They carry momenta like ping-pong balls.You can slow the motion of an atom by bouncing laser light off the

21、atoms.See the animation /physics/2000/bec/lascool1.html. 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 /physics/2000/bec/lasco

22、ol2.htmlUsing 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 is approaching the laser sour

23、ce, 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 no

24、t 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, and the trapped atoms form

25、an optical molass (光學粘膠).See the animation: /physics/2000/bec/lascool4.htmlMagnetic 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: Evaporative coolingThe

26、 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: /physics/2000/bec/mag_trap.htmlEvaporative Cooling (挥发冷却挥发冷却)Principle: Evaporation take

27、s 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 BEC in

28、 the animation:/physics/2000/bec/evap_cool.htmlCan You Break This Record?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.See the m

29、ovie when it cools from 400 nK to 50 nK (1 nK= 10-9K). : /physics/2000/bec/what_it_looks_like.htmlThe Nobel Prize in Physics 2001USA(Eric A.Cornell,1961)Germany(Wolfgang Kettlerle,1957)USA(Carl E.Wieman,1951)“for the achievement of Bose-Einstein condensation in dilute gases of

30、alkali atoms, and for early fundamental studies of the properties of the condensatesWhat is an atom laser?An atom laser is analogous to an optical laser, but it emits matter waves instead of electromagnetic waves.Its output is a coherent matter wave, a beam of atoms which can be focused to a pinpoin

31、t or can be collimated to travel large distances without spreading. The beam is coherent, which means, for instance, that atom laser beams can interfere with each other. Compared to an ordinary beam of atoms, the beam of an atom laser is extremely bright. One can describe laser-like atoms as atoms m

32、arching in lockstep.Although there is no rigorous definition for the atom laser (or, for that matter, an optical laser), all people agree that brightness and coherence are the essential features. Ketterles home pageAtomic trapATOMIC TRAP cools by means of two different mechanisms. First, six laser b

33、eams (red) cool atoms, initially at room temperature, while corralling them toward the cen-ter of an evacuated glass box. Next, the laser beams are turned off, and the magnetic coils (copper) are ener-gized. Current flowing through the coils generates a magnetic field that further confines most of t

34、he atoms while allowing the energetic ones to escape. Thus, the average energy of the remaining atoms decreases, mak-ing the sample colder and even more closely confined to the center of the trap. Ultimately, many of the atoms attain the lowest possible energy state allowed by quan-tum mechanics and

35、 become a single entity known as a Bose-Einstein condensate.Sci. Am., March 1998, p. 27.The parts of an atom laserA laser requires a cavity (resonator), an active medium, and an output coupler. In the MIT atom laser, the resonator is a magnetic trap in which the atoms are confined by magnetic mirror

36、s. The active medium is a thermal cloud of ultracold atoms, and the output coupler is an rf pulse which controls the reflectivity of the magnetic mirrors. Ketterles homepageThe gain process in an atom laserThe analogy to spontaneous emission in the optical laser is elastic scattering of atoms (colli

37、sions similar to those between billiard balls). In a laser, stimulated emission of photons causes the radiation field to build up in a single mode. In an atom laser, the presence of a Bose-Einstein condensate (atoms that occupy a single mode of the system, the lowest energy state) causes stimulated

38、scattering by atoms into that mode.More precisely, the presence of a condensate with N atoms enhances the probability that an atom will be scattered into the condensate by N+1. Ketterles homepageThe gain process in an atom laserIn a normal gas, atoms scatter among the many modes of the system. But w

39、hen the critical temperature for Bose-Einstein condensation is reached, they scatter predominantly into the lowest energy state of the system, a single one of the myriad of possible quantum states. This abrupt process is closely analogous to the threshold for operating a laser, when the laser sudden

40、ly switches on as the supply of radiating atoms is increased.In an atom laser, the excitation of the active medium is done by evaporative cooling - the evaporation process creates a cloud which is not in thermal equilibrium and relaxes towards colder temperatures. This results in growth of the conde

41、nsate. After equilibration, the net gain of the atom laser is zero, i.e., the condensate fraction remains constant until further cooling is applied. Ketterles homepageThe gain process in an atom laserUnlike optical lasers, which sometimes radiate in several modes (i.e. at several nearby frequencies)

42、 the matter wave laser always operates in a single mode. The formation of the Bose condensate actually involves mode competition: the first excited state cannot be macroscopically populated because the ground state eats up all the pie. Ketterles homepageThe output of an atom laserThe output of an op

43、tical laser is a collimated beam of light. For an atom laser, it is a beam of atoms. Either laser can be continuous or pulsed - but so far, the atom laser has only been realized in the pulsed mode.Both light and atoms propagate according to a wave equation. Light is governed by Maxwells equations, a

44、nd matter is described by the Schroedinger equation. The diffraction limit in optics corresponds to the Heisenberg uncertainty limit for atoms. In an ideal case, the atom laser emits a Heisenberg uncertainty limited beam. Ketterles homepageOptical versus atom laser: differencesPhotons can be created

45、, but not atoms. The number of atoms in an atom laser is not amplified. What is amplified is the number of atoms in the ground state, while the number of atoms in other states decreases. Atoms interact with each other - that creates additional spreading of the output beam. Unlike light, a matter wav

46、e cannot travel far through air. Atoms are massive particles. They are therefore accelerated by gravity. A matter wave beam will fall like a beam of ordinary atoms. A Bose condensates occupies the lowest mode (ground state) of the system, whereas lasers usually operate on very high modes of the laser resonator. A Bose condensed system is in thermal equilibrium and characterized by extremely low temperature. In contrast, the optical laser operates in a non-equilibrium situation which can be characterized by a negative te