Bose-Einstein Condensates

Brian Krausz Apr. 19 th , 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 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

Importance of Phase Space Density

 For indistinguishable particles (i.e. bosons) g = Z N N!

P(excited) P(ground) = Z N e N N!

N! ≈ (2πN) 1/2 N N e -N = (Z/N) N ·1/ (2πN) 1/2 = (n Q /n) N (2πN) -1/2 Z = n Q V

Results

 If n > n Q (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

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

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

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 10 9 atoms • This is still ~100X too hot to form a BEC http://www.fortunecity.com/emachines/e11/86/bose.html

Evaporative Cooling

 The most energetic particles escape the magnetic potential  This reduces the average thermal energy of the sample  Number of atoms reduces from ~10 9 to ~10 7 http://www.fortunecity.com/emachines/e11/86/bose.html

Finally, A BEC

 Ground state condensate contains ~10 6 – 10 8 atoms  BEC provides a great example of coherent quantum phenomena  A macroscopic view of QM!

When exactly does this occur?

 In terms of the Einstein condensation temperature: τ E = 2 πħ 2 . (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/λ 3 DB λ DB = h · (2 π M τ ) -1/2 “Atomic Physics” C. Foot

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

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)

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

Phase Space Evolution During BEC Production

http://www.ph.utexas.edu/dept/research/heinzen/bose.html

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

Applications

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

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 4 He  Prof. Stamper-Kurn is using Rb to study 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 condensate. 87 Rb. 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"

Spinor condensate

http://physics.berkeley.edu/research/ultracold/E1_spinor.html