Bose-Einstein Bose-Einstein CondensatesCondensates

Brian KrauszBrian Krausz

Apr. 19Apr. 19thth, 2005, 2005

Table of ContentsTable of Contents

What is a BEC?What is a BEC? How do you make one in lab?How do you make one in lab?

• Laser coolingLaser cooling• Magnetic trappingMagnetic trapping• Evaporative coolingEvaporative cooling

What are the properties of a BEC?What are the properties of a BEC? Some historySome history Applications, extra stuffApplications, extra stuff

A BEC is a gaseous superfluid phase A BEC is a gaseous superfluid phase formed by atoms (mostly alkali metals) at formed by atoms (mostly alkali metals) at very low temperaturesvery low temperatures

Predicted by S. Bose and Einstein in the Predicted by S. Bose and Einstein in the 1920’s based on statistical mechanics1920’s based on statistical mechanics

Cooling bosonic atoms to low temps Cooling bosonic atoms to low temps causes condensing into the lowest causes condensing into the lowest available quantum state (ground orbital)available quantum state (ground orbital)• Particles in the condensate have the same Particles in the condensate have the same

wave function wave function ΨΨ Bose-Einstein distribution functionBose-Einstein distribution function

• F(F(εε,,ττ) = [exp(() = [exp((εε--μμ)/)/ττ)-1])-1]-1-1

Importance of Phase Space DensityImportance of Phase Space Density

For indistinguishable particles (i.e. bosons)For indistinguishable particles (i.e. bosons)g = g = ZZNN

N!N!P(excited)P(excited) ZZN N ee--NN

P(ground)P(ground) N! N! N! N! ≈ (2≈ (2ππN)N)1/21/2NNNNee-N-N

(Z/N)(Z/N)NN ·1/ (2·1/ (2ππN)N)1/21/2

(n(nQQ/n)/n)NN(2(2ππN)N)-1/2-1/2 Z = Z = nnQQVV

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ResultsResults

If n > nIf n > nQQ (quantum regime) , then most (quantum regime) , then most particles will be in the ground stateparticles will be in the ground state

In a sense, here the Boltzmann factor In a sense, here the Boltzmann factor dominates over the number of statesdominates over the number of states

BEC comes from the loss of multiplicityBEC comes from the loss of multiplicity

Low temps ensure that this ideal gas Low temps ensure that this ideal gas model will workmodel will work

Left: just before appearance of condensateLeft: just before appearance of condensate Center: just after appearanceCenter: just after appearance Right: BEC after more evaporationRight: BEC after more evaporation

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.

Laser CoolingLaser Cooling Optical molasses technique often used to slow Optical molasses technique often used to slow

atoms (3 orthogonal pairs of counter-propagating atoms (3 orthogonal pairs of counter-propagating lasers)lasers)• there is also Chirp cooling, Zeeman slowingthere is also Chirp cooling, Zeeman slowing

Laser is detuned just below transition frequencyLaser is detuned just below transition frequency• Atoms moving against laser beam see higher Atoms moving against laser beam see higher freq.freq.

Upon re-radiation, atom undergoes random walk Upon re-radiation, atom undergoes random walk in momentum spacein momentum space

Atoms absorb more photons traveling in direction Atoms absorb more photons traveling in direction opposite to its motion, resulting in slowing & opposite to its motion, resulting in slowing & coolingcooling

TrappingTrapping Radiation pressure opposes atom’s tendency to Radiation pressure opposes atom’s tendency to

drift away from centerdrift away from center• Often done with 6 laser beamsOften done with 6 laser beams

Weak B field tunes the resonance of the atom to Weak B field tunes the resonance of the atom to absorb from the laser beam pointing to the centerabsorb from the laser beam pointing to the center

Cooling and trapping gets temp in range of 10-Cooling and trapping gets temp in range of 10-100100μμK and 10K and 109 9 atomsatoms• This is still ~100X too hot to form a BECThis is still ~100X too hot to form a BEC

http://www.fortunecity.com/emachines/e11/86/bose.htmlhttp://www.fortunecity.com/emachines/e11/86/bose.html

Evaporative CoolingEvaporative Cooling

The most energetic particles The most energetic particles escape the magnetic potentialescape the magnetic potential

This reduces the average This reduces the average thermal energy of the samplethermal energy of the sample

Number of atoms reduces Number of atoms reduces from ~10from ~1099 to ~10 to ~1077

http://www.fortunecity.com/emachines/e11/86/bose.htmlhttp://www.fortunecity.com/emachines/e11/86/bose.html

Finally, A BECFinally, A BEC

Ground state condensate contains Ground state condensate contains ~10~1066 – 10 – 1088 atoms atoms

BEC provides a great example of BEC provides a great example of coherent quantum phenomenacoherent quantum phenomena

A macroscopic view of QM!A macroscopic view of QM!

When exactly does this occur?When exactly does this occur?

In terms of the Einstein condensation In terms of the Einstein condensation temperature:temperature:

ττEE = = 22ππħħ22 . (n/2.6) . (n/2.6)2/32/3

M M derived in “Thermal Physics” Kittel, Kroemerderived in “Thermal Physics” Kittel, Kroemer

• Below this value, ground orbital occupancy is Below this value, ground orbital occupancy is macroscopicmacroscopic

In terms of the number density,In terms of the number density,n = N/V = 2.6/n = N/V = 2.6/λλ33

DBDB

λλDBDB = h · (2 = h · (2ππMMττ))-1/2-1/2

““Atomic Physics” C. FootAtomic Physics” C. Foot

At low phase-space densities, particles At low phase-space densities, particles have no reason to share the same statehave no reason to share the same state

BEC is a completely different phase BEC is a completely different phase transition from normal condensation of a transition from normal condensation of a vapor into liquidvapor into liquid

Instead, BEC occurs when occupation of Instead, BEC occurs when occupation of quantum states approaches unityquantum states approaches unity

BEC remarksBEC remarks

What properties does a BEC have?What properties does a BEC have?

Superfluidity• A BEC is a gaseous superfluid with irrotational A BEC is a gaseous superfluid with irrotational

flow (curl = 0)flow (curl = 0)• Resists rotation until a vortex formsResists rotation until a vortex forms• Similar to how a superconductor resists a Similar to how a superconductor resists a

magnetic fieldmagnetic field

CoherenceCoherence• Condensates have well defined amplitude and Condensates have well defined amplitude and

phase represented by a single wavefunctionphase represented by a single wavefunction• Makes possible the idea of matter waves with Makes possible the idea of matter waves with

constructive/destructive interference constructive/destructive interference (Ketterle, MIT)(Ketterle, MIT)

What helps make a good BEC?What helps make a good BEC?

Making KE smallMaking KE small Making interactions largeMaking interactions large Having a good trapHaving a good trap

• Types of traps include MOT, magnetic Types of traps include MOT, magnetic trap, Ioffe-Pritchard traptrap, Ioffe-Pritchard trap

Having a large phase-space densityHaving a large phase-space density

Phase Space Evolution During Phase Space Evolution During BEC ProductionBEC Production

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

A Bit of HistoryA Bit of History

Bose’s 1924 paper derived the Planck distribution Bose’s 1924 paper derived the Planck distribution for radiation in a new wayfor radiation in a new way

Einstein applied the Bose method to particles, Einstein applied the Bose method to particles, predicting BECpredicting BEC

Steven Chu (Stanford) and colleagues won Nobel Steven Chu (Stanford) and colleagues won Nobel Prize in 1997 for optical molasses (discovered at Prize in 1997 for optical molasses (discovered at Bell Labs in 1985)Bell Labs in 1985)

JILA group at Colorado, Boulder and at MIT JILA group at Colorado, Boulder and at MIT successfully creates first BEC in 1995successfully creates first BEC in 1995

Prof. Cornell & Wieman win 2001 Nobel Prize for Prof. Cornell & Wieman win 2001 Nobel Prize for creating BEC with Rubidiumcreating 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?What’s Going on Now?

Over 30 different groups worldwide Over 30 different groups worldwide working on different BEC projectsworking on different BEC projects

BEC is starting to be accomplished BEC is starting to be accomplished with Hydrogen and metastable with Hydrogen and metastable 44HeHe

Prof. Stamper-Kurn is using Rb to Prof. Stamper-Kurn is using Rb to study spinor condensates study spinor condensates

What is a Spinor Condensate?What is a Spinor Condensate? A spinor condensate is one which possesses a A spinor condensate is one which possesses a

spin degree of freedom with full rotational spin degree of freedom with full rotational symmetrysymmetry

He uses an optically trapped gas of atoms in the He uses an optically trapped gas of atoms in the F=1 hyperfine level of F=1 hyperfine level of 8787Rb. A far-detuned optical Rb. A far-detuned optical trap, unlike the more common magnetic trap, trap, unlike the more common magnetic trap, provides equal confinement for the three spin provides equal confinement for the three spin states. When a condensate is formed from atoms states. When a condensate is formed from atoms distributed among the various spin states, the distributed among the various spin states, the result is three separate but coupled condensates, result is three separate but coupled condensates, or equivalently a single multicomponent "spinor" or equivalently a single multicomponent "spinor" condensate. condensate.

Spinor condensateSpinor condensate

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