Atoms in Unison in the Coolest Gas in

Atoms in Unison in the Coolest Gas in the Universe 超冷世界的原子大合唱 K. Y. Michael Wong 王國彝 Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China. 香港科技大學物理系 What is the significance of the 2001 Nobel Prize in Physics?

The Prize “for the achievement of Bose-Einstein condensation (玻色-愛因斯坦凝聚態) in dilute gases of alkali atoms (碱原子) , and for early fundamental studies of the properties of the condensates"

The Winners Eric A. Cornell Wolfgang Ketterle Carl E. Wieman 康奈爾 克特勒 維曼 JILA & NIST, Boulder, Colorado. MIT JILA & University of Colorado, Boulder. 1961 - 1957 - 1951 -

The Godfather Ramsey (1989) Kleppner (1 H) The Sons Chu (1997) Phillips (1997) Pritchard The Grandsons Wieman (87 Rb) Ketterle (23 Na) Hulet (7 Li) Cornell (87 Rb)

Q 1: What Is Bose-Einstein Condensation? De Broglie 德布羅意 (1929 Nobel Prize winner) proposed that all matter is composed of waves. Their wavelengths are given by l = de Broglie wavelength h = Planck’s constant 普朗克常數 m = mass v = velocity

Against 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. Ù The wave nature of atoms become noticeable when the de Broglie wavelength is roughly the same as the atomic distance. Ù This happens when the temperature is low enough, so that they have low velocities. Ù 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). Ù

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 ½. They are called fermions. They cannot appear in the same quantum state. BEC cannot take place. Ù Some atoms contain an even number of fermions. They have a total spin of whole number. They are called bosons. Ù Bosons show strong “social” behaviour, and can have BEC. Ù Example: A 23 Na atom has 11 protons, 12 neutrons and 11 electrons. Ù Ù Ù

The Material For BEC Ù BEC was found in alkali metals e. g. 87 Rb (金如), 23 Na (鈉), 7 Li (鋰) because: ÙThey are bosons. ÙEach atom is a small magnetic compass, so that a cooling technique called magnetic cooling can work. ÙThe 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: http: //www. colorado. edu/physics/2000/bec/what_is_it. html Ù 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. Ù When the temperature is low, the atoms have low energies on average. It is necessary to describe the system by quantum physics. Ù When the temperature is very low, a large fraction of atoms suddenly crash into the lowest energy state. This is called Bose-Einstein condensation. Ù

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. Ù Before condensation, the atoms look like fuzzy balls. Ù After consdensation, the atoms lie exactly on top of each other (a superatom). Ù

Q 2: How Is BEC Made? Laser beam Other equipment: laser equipment, computer, electronics Cost less than US$100, 000

Laser Cooling (激光冷卻) Chu 朱棣文 Cohen-Tannoundji Phillips The technique of laser cooling was developed by the winners of the 1997 Nobel Prize winners. Ù In the physical world, the lowest temperatures approach a limit of – 273 o. C. This is called the absolute zero. Nothing can be as cold as the absolute zero because all atomic and subatomic motions stop. Ù Laser cooling can get to the low temperature of 0. 18 K (1 K微開= 10 -6 K). Ù

Ping-pong Balls Ù Ù Ù 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 http: //www. colorado. edu/physics/2000/bec/lascool 1. html.

Tuning the Laser Only laser light with the correct colour (frequency) can be absorbed by the atoms. Ù If the colour is wrong, the atoms cannot absorb the photons. Ù See the animation http: //www. colorado. edu/physics/2000/bec/lascool 2. html Ù

Using the Doppler Effect (多普勒效應) Problem: The laser can slow the approaching atoms, but it can also blast off the receding ones. Ù Solution: Use Doppler shift. Ù When the atom is receding from the laser source, the wavelength is lengthened and there is a redshift. Ù When the atom is approaching the laser source, the wavelength is shortened and there is a blueshift. Ù See the animation: http: //www. astro. ubc. ca/~scharein/a 3 11/Sim. html Ù

Laser 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. Ù 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. Ù When lasers are sent in from all the different directions, the atoms can get cold very quickly. Ù This is called laser trapping, and the trapped atoms form an optical molass ( 光學粘膠). Ù See the animation: http: //www. colorado. edu/physics/2000/bec/lascool 4. html Ù

Magnetic Trapping (磁性陷阱) Problem: Laser cooling can cool the atoms down to 10 K, because atoms can spontaneously emit the absorbed photon. This is still too hot for BEC. Ù Solution: Evaporative cooling Ù The atoms behave as tiny compasses. They can be pulled by magnetic fields. Ù A magnetic field can be designed to push the atoms inwards from both sides, forming a magnetic trap. Ù See the animation: http: //www. colorado. edu/physics/2000/bec/mag_trap. html Ù

Evaporative Cooling (揮發冷卻) Principle: Evaporation takes heat. A cup of tea gets cool after steam escapes, because faster atoms escape from the cup, leaving behind the slower ones. Ù Technique: Lower the height of the trap quickly, so that there are still enough atoms left in the trap to get involved in BEC. Ù Try to trap the largest number of atoms in BEC in the animation: Ù http: //www. colorado. edu/physics/2000/bec/evap_cool. html Ù

Can You Break This Record?

Q 3: What Does a Bose-Einstein Condensate Look Like? There is a drop of condensate at the centre. Ù The condensate is surrounded by uncondensed gas atoms. Ù The combination looks like a cherry with a pit. Ù See the movie when it cools from 400 n. K to 50 n. K (1 n. K納開= 10 -9 K). : http: //www. colorado. edu/physics/2000/bec/what_it_looks_like. html Ù

Atom Laser (原子激射) Laser of light: all the photons are exactly the same in colour, direction and phase (positions of peaks and valleys). Ù Laser of atoms: all the atoms in the condensate are exactly the same. Ù See the animation: http: //cua. mit. edu/ketterle_group/Animation_folder/Atom_laser. htm Ù

Oscillations See the animation: http: //cua. mit. edu/ketterle_group/Animation_folder/Oscillations. htm Note the “shape” motion and “sloshing” motion.

Interference Pattern (干涉圖像) When two Bose-Einstein condensates spread out, the interference pattern reveals their wave nature. Ù See the animation: http: //cua. mit. edu/ketterle_group/Animation_folder/TOFsplit. htm Ù

Vortices (漩渦) When the condensate is rotated, vortices appear. The angular momentum of each of them has a discrete value.

Q 4: What Is Bose-Einstein Condensation Good For? This is a completely new area. Applications are too early to predict. The atom laser can be used in: Ù atom optics (studying the optical properties of atoms) Ù atom lithography 光刻 (fabricating extremely small circuits) Ù precision atomic clocks Ù other measurements of fundamental standards Ù hologram 全息圖 Ù communications and computation. Ù Fundamental understanding of quantum mechanics. Ù Model of supernova explosion 超新星爆炸. Ù Model of black holes 黑洞. Ù Ù

References Homepage of the Nobel e-Museum (http: //www. nobel. se/). BEC Homepage at the University of Colorado (http: //www. colorado. edu/physics/2000/bec/). Ù Ketterle Group Homepage (http: //www. cua. mit/ketterle_group/). Ù The Coolest Gas in the Universe (Scientific American, December 2000, 92 -99). Ù Atom Lasers (Physics World, August 1999, 31 -35). Ù Ù