Transcript Bose-Einstein Condensates

Bose-Einstein
Condensates
Brian Krausz
Apr. 19th, 2005
Table of Contents
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What is a BEC?
How do you make one in lab?
• Laser cooling
• Magnetic trapping
• Evaporative cooling
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What are the properties of a BEC?
Some history
Applications, extra stuff
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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
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Bose-Einstein distribution function
• F(ε,τ) = [exp((ε-μ)/τ)-1]-1
Importance of Phase Space Density
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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 = n QV
Results
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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
Velocity-distribution data confirming the discovery of a new phase of matter, the BoseEinstein 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.
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Left: just before appearance of condensate
Center: just after appearance
Right: BEC after more evaporation
Laser Cooling
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Optical molasses technique often used to slow
atoms (3 orthogonal pairs of counter-propagating
lasers)
• there is also Chirp cooling, Zeeman slowing
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Laser is detuned just below transition frequency
• Atoms moving against laser beam see higher freq.
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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
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Radiation pressure opposes atom’s tendency to
drift away from center
• Often done with 6 laser beams
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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 10100μK and 109 atoms
• This is still ~100X too hot to form a BEC
http://www.fortunecity.com/emachines/e11/86/bose.html
Evaporative Cooling
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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
Finally, A BEC
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Ground state condensate contains
~106 – 108 atoms
BEC provides a great example of
coherent quantum phenomena
A macroscopic view of QM!
When exactly does this occur?
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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
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In terms of the number density,
n = N/V = 2.6/λ3DB
λDB = h · (2πMτ)-1/2
“Atomic Physics” C. Foot
BEC remarks
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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?
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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
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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?
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Making KE small
Making interactions large
Having a good trap
• Types of traps include MOT, magnetic
trap, Ioffe-Pritchard trap
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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
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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?
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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
What is a Spinor Condensate?
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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.
Spinor condensate
http://physics.berkeley.edu/research/ultracold/E1_spinor.html