Bose-Einstein Condensates

1. Bose-Einstein Condensates

2. 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

3. A BEC is a gaseous superfluid phase formed by atoms (mostly alkali metals) at very low temperatures • Predicted by S. Bose and Einstein in the 1920’s 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 Ψ • Bose-Einstein distribution function • F(ε,τ) = [exp((ε-μ)/τ)-1]-1

4. Importance of Phase Space Density • For indistinguishable particles (i.e. bosons) g = ZN N! P(excited)ZN e-N P(ground) N! N! ≈ (2πN)1/2NNe-N (Z/N)N·1/ (2πN)1/2 (nQ/n)N(2πN)-1/2 Z = nQV = = =

5. Results • If n > nQ(quantum regime) , then most particles will be in the ground state • In a sense, here the Boltzmann factor dominates over the number of states • BEC comes from the loss of multiplicity • Low temps ensure that this ideal gas model will work

6. Velocity-distribution data 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. • Left: just before appearance of condensate • Center: just after appearance • Right: BEC after more evaporation

7. Laser Cooling • Optical molasses technique often used to slow atoms (3 orthogonal pairs of counter-propagating lasers) • there is also Chirp cooling, Zeeman slowing • Laser is detuned just below transition frequency • Atoms moving against laser beam see higher freq. • Upon re-radiation, atom undergoes random walk in momentum space • Atoms absorb more photons traveling in direction opposite to its motion, resulting in slowing & cooling

8. Trapping • Radiation pressure opposes atom’s tendency to drift away from center • Often done with 6 laser beams • Weak B field tunes the resonance of the atom to absorb from the laser beam pointing to the center • Cooling and trapping gets temp in range of 10-100μK and 109 atoms • This is still ~100X too hot to form a BEC http://www.fortunecity.com/emachines/e11/86/bose.html

9. Evaporative Cooling • The most energetic particles escape the magnetic potential • This reduces the average thermal energy of the sample • Number of atoms reduces from ~109 to ~107 http://www.fortunecity.com/emachines/e11/86/bose.html

10. Finally, A BEC • Ground state condensate contains ~106 – 108 atoms • BEC provides a great example of coherent quantum phenomena • A macroscopic view of QM!

11. When exactly does this occur? • In terms of the Einstein condensation temperature: τE = 2πħ2 . (n/2.6)2/3 M derived in “Thermal Physics” Kittel, Kroemer • Below this value, ground orbital occupancy is macroscopic • In terms of the number density, n = N/V = 2.6/λ3DB λDB = h · (2πMτ)-1/2 “Atomic Physics” C. Foot

12. BEC remarks • At low phase-space densities, particles have no reason to share the same state • BEC is a completely different phase transition from normal condensation of a vapor into liquid • Instead, BEC occurs when occupation of quantum states approaches unity

13. 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 field • Coherence • Condensates have well defined amplitude and phase represented by a single wavefunction • Makes possible the idea of matter waves with constructive/destructive interference (Ketterle, MIT)

14. 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-space density

15. Phase Space Evolution During BEC Production http://www.ph.utexas.edu/dept/research/heinzen/bose.html

16. A Bit of History • Bose’s 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 colleagues 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

17. Applications • Atom lasers • Sensitive measurement instruments • Improved ability to manipulate matter waves • Laser gyroscopes, accelerators • Stuff we can’t even imagine yet!

18. What’s Going on Now? • Over 30 different groups worldwide working on different BEC projects • BEC is starting to be accomplished with Hydrogen and metastable 4He • Prof. Stamper-Kurn is using Rb to study spinor condensates

19. 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 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.

20. Spinor condensate