Bose-Einstein Condensates Brian Krausz Apr. 19 th, 2005

Table 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 history Some history Applications, extra stuff Applications, extra stuff

A BEC is a gaseous superfluid phase formed by atoms (mostly alkali metals) at very low temperatures 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 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) 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 ΨParticles in the condensate have the same wave function Ψ Bose-Einstein distribution function Bose-Einstein distribution function F(ε,τ) = [exp((ε-μ)/τ)-1] -1F(ε,τ) = [exp((ε-μ)/τ)-1] -1

Importance of Phase Space Density For indistinguishable particles (i.e. bosons) For indistinguishable particles (i.e. bosons) g = Z N N! N! P(excited) Z N e - N P(ground) 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 (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 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 In a sense, here the Boltzmann factor dominates over the number of states BEC comes from the loss of multiplicity BEC comes from the loss of multiplicity Low temps ensure that this ideal gas model will work Low temps ensure that this ideal gas model will work

Left: just before appearance of condensate Left: just before appearance of condensate Center: just after appearance Center: just after appearance Right: BEC after more evaporation Right: 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 Cooling Optical molasses technique often used to slow atoms (3 orthogonal pairs of counter-propagating lasers) Optical molasses technique often used to slow atoms (3 orthogonal pairs of counter-propagating lasers) there is also Chirp cooling, Zeeman slowing there is also Chirp cooling, Zeeman slowing Laser is detuned just below transition frequency Laser is detuned just below transition frequency Atoms moving against laser beam see higher freq.Atoms moving against laser beam see higher freq. Upon re-radiation, atom undergoes random walk in momentum space 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 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 Radiation pressure opposes atom’s tendency to drift away from center Often done with 6 laser beamsOften done with 6 laser beams Weak B field tunes the resonance of the atom to absorb from the laser beam pointing to the center 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 μK and 10 9 atoms Cooling and trapping gets temp in range of μK and 10 9 atoms This is still ~100X too hot to form a BECThis is still ~100X too hot to form a BEChttp://

Evaporative Cooling The most energetic particles escape the magnetic potential The most energetic particles escape the magnetic potential This reduces the average thermal energy of the sample This reduces the average thermal energy of the sample Number of atoms reduces from ~10 9 to ~10 7 Number of atoms reduces from ~10 9 to ~10 7http://

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

When exactly does this occur? In terms of the Einstein condensation temperature: In terms of the Einstein condensation temperature: τ E = 2πħ 2. (n/2.6) 2/3 M derived in “Thermal Physics” Kittel, Kroemer M derived in “Thermal Physics” Kittel, Kroemer Below this value, ground orbital occupancy is macroscopicBelow this value, ground orbital occupancy is macroscopic In terms of the number density, In terms of the number density, n = N/V = 2.6/λ 3 DB λ DB = h · (2 π M τ ) -1/2 λ DB = h · (2 π M τ ) -1/2 “Atomic Physics” C. Foot

At low phase-space densities, particles have no reason to share the same state 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 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 Instead, BEC occurs when occupation of quantum states approaches unity BEC remarks

What properties does a BEC have? Superfluidity A BEC is a gaseous superfluid with irrotational flow (curl = 0)A BEC is a gaseous superfluid with irrotational flow (curl = 0) Resists rotation until a vortex formsResists rotation until a vortex forms Similar to how a superconductor resists a magnetic fieldSimilar to how a superconductor resists a magnetic field Coherence Coherence Condensates have well defined amplitude and phase represented by a single wavefunctionCondensates have well defined amplitude and phase represented by a single wavefunction Makes possible the idea of matter waves with constructive/destructive interference (Ketterle, MIT)Makes possible the idea of matter waves with constructive/destructive interference (Ketterle, MIT)

What helps make a good BEC? Making KE small Making KE small Making interactions large Making interactions large Having a good trap Having a good trap Types of traps include MOT, magnetic trap, Ioffe-Pritchard trapTypes of traps include MOT, magnetic trap, Ioffe-Pritchard trap Having a large phase-space density Having a large phase-space density

Phase Space Evolution During BEC Production

A Bit of History Bose’s 1924 paper derived the Planck distribution for radiation in a new way Bose’s 1924 paper derived the Planck distribution for radiation in a new way Einstein applied the Bose method to particles, predicting BEC 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) 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 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 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 Over 30 different groups worldwide working on different BEC projects BEC is starting to be accomplished with Hydrogen and metastable 4 He BEC is starting to be accomplished with Hydrogen and metastable 4 He Prof. Stamper-Kurn is using Rb to study spinor condensates 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 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 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" condensate. He uses an optically trapped gas of atoms in the F=1 hyperfine level of 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" condensate.

Spinor condensate