1、Bose-Einstein Condensates,Brian Krausz Apr. 19th, 2005,Table of Contents,What is a BEC? How do you make one in lab? Laser cooling Magnetic trapping Evaporative cooling What are the properties of a BEC? Some history Applications, extra stuff,A BEC is a gaseous superfluid phase formed by atoms (mostly
2、 alkali metals) at very low temperatures Predicted by S. Bose and Einstein in the 1920s based on statistical mechanics Cooling bosonic atoms to low temps causes condensing into the lowest available quantum state (ground orbital) Particles in the condensate have the same wave function Bose-Einstein d
3、istribution function F(,) = exp(-)/)-1-1,Importance of Phase Space Density,For indistinguishable particles (i.e. bosons)g = ZNN! P(excited) ZN e-N P(ground) N! N! (2N)1/2NNe-N (Z/N)N 1/ (2N)1/2(nQ/n)N(2N)-1/2 Z = nQV,=,=,=,Results,If n nQ (quantum regime) , then most particles will be in the ground
4、stateIn a sense, here the Boltzmann factor dominates over the number of statesBEC comes from the loss of multiplicityLow temps ensure that this ideal gas model will work,Left: just before appearance of condensate Center: just after appearance Right: BEC after more evaporation,Velocity-distribution d
5、ata confirming the discovery of a new phase of matter, the Bose-Einstein condensate, out of a gas of rubidium atoms. The artificial colors indicate the number of atoms at each velocity, with red being the fewest and white being the most.,Laser Cooling,Optical molasses technique often used to slow at
6、oms (3 orthogonal pairs of counter-propagating lasers)there is also Chirp cooling, Zeeman slowingLaser is detuned just below transition frequency Atoms moving against laser beam see higher freq.Upon re-radiation, atom undergoes random walk in momentum spaceAtoms absorb more photons traveling in dire
7、ction opposite to its motion, resulting in slowing & cooling,Trapping,Radiation pressure opposes atoms tendency to drift away from center Often done with 6 laser beamsWeak B field tunes the resonance of the atom to absorb from the laser beam pointing to the centerCooling and trapping gets temp in ra
8、nge of 10-100K and 109 atoms This is still 100X too hot to form a BEChttp:/ Cooling,The most energetic particles escape the magnetic potentialThis reduces the average thermal energy of the sampleNumber of atoms reduces from 109 to 107http:/ A BEC,Ground state condensate contains 106 108 atomsBEC pro
9、vides a great example of coherent quantum phenomenaA macroscopic view of QM!,When exactly does this occur?,In terms of the Einstein condensation temperature:E = 22 . (n/2.6)2/3M derived in “Thermal Physics” Kittel, Kroemer Below this value, ground orbital occupancy is macroscopicIn terms of the numb
10、er density,n = N/V = 2.6/3DBDB = h (2M)-1/2“Atomic Physics” C. Foot,At low phase-space densities, particles have no reason to share the same stateBEC is a completely different phase transition from normal condensation of a vapor into liquidInstead, BEC occurs when occupation of quantum states approa
11、ches unity,BEC remarks,What properties does a BEC have?,Superfluidity A BEC is a gaseous superfluid with irrotational flow (curl = 0) Resists rotation until a vortex forms Similar to how a superconductor resists a magnetic fieldCoherence Condensates have well defined amplitude and phase represented
12、by a single wavefunction Makes possible the idea of matter waves with constructive/destructive interference (Ketterle, MIT),What helps make a good BEC?,Making KE small Making interactions large Having a good trap Types of traps include MOT, magnetic trap, Ioffe-Pritchard trap Having a large phase-sp
13、ace density,Phase Space Evolution During BEC Production,http:/www.ph.utexas.edu/dept/research/heinzen/bose.html,A Bit of History,Boses 1924 paper derived the Planck distribution for radiation in a new way Einstein applied the Bose method to particles, predicting BEC Steven Chu (Stanford) and colleag
14、ues won Nobel Prize in 1997 for optical molasses (discovered at Bell Labs in 1985) JILA group at Colorado, Boulder and at MIT successfully creates first BEC in 1995 Prof. Cornell & Wieman win 2001 Nobel Prize for creating BEC with Rubidium,Applications,Atom lasers Sensitive measurement instruments I
15、mproved ability to manipulate matter waves Laser gyroscopes, accelerators Stuff we cant even imagine yet!,Whats Going on Now?,Over 30 different groups worldwide working on different BEC projectsBEC is starting to be accomplished with Hydrogen and metastable 4HeProf. Stamper-Kurn is using Rb to study
16、 spinor condensates,What is a Spinor Condensate?,A spinor condensate is one which possesses a spin degree of freedom with full rotational symmetry He uses an optically trapped gas of atoms in the F=1 hyperfine level of 87Rb. A far-detuned optical trap, unlike the more common magnetic trap, provides
17、equal confinement for the three spin states. When a condensate is formed from atoms distributed among the various spin states, the result is three separate but coupled condensates, or equivalently a single multicomponent “spinor“ condensate.,Spinor condensate,http:/physics.berkeley.edu/research/ultracold/E1_spinor.html,
