A review of atomic-gas Bose-Einstein condensation experiments for

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A review of atomic-gas Bose-Einstein condensation
experiments for Workshop Hawking Radiation
in condensed-matter systems Eric Cornell
JILA Boulder, Colorado
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.
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The basic loop.(once every minute) Cooling.
Minimum temperature. Stray heating. Confinement.
Magnetic. Optical. Reduced dimensions.
Arrays Observables. Images. Shot noise. Atom
counting. Interactions. The G-P equation. Speed
of sound. Time-varying interactions.
feshbach resonance. Reduced dimensions. Therma
l fluctuations. A range of numbers.
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MOT
Laser cooling
2.5 cm
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.
Basic cooling idea leads to Basic cooling
limit. Heating happens.
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V(x)
m
x
Self-interacting condensate expands to fill
confining potential to height m
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V(x)
m
x
Self-interacting condensate expands to fill
confining potential to height m
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n(x)
V(x)
kT
x
Cloud of thermal excitations made up of atoms on
trajectories that go roughly to where the
confining potential reaches kT
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V(x)
m
kT
x
When kT lt m then there are very few thermal
excitations extending outside of condensate.
Thus evaporation cooling power is small.
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BEC experiments must be completed within limited
time.
Bang!
Three-body molecular-formation process causes
condensate to decay, and heat! Lifetime longer at
lower density, but physics goes more slowly at
lower density!
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Dominant source of heat
Bang!
Decay products from three-body recombination can
collide as they depart, leaving behind excess
energy in still-trapped atoms.
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Bose-Einstein Condensation in a Dilute Gas
Measurement of Energy and Ground-State
Occupation, J. R. Ensher, D. S. Jin, M. R.
Matthews, C. E. Wieman, and E. A. Cornell, Phys.
Rev. Lett. 77, 4984 (1996)
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.
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m2
m-2
Energy
m-1
m0
m1
Typical single-atom energy level diagram in the
presence of a magnetic field. Note Zeeman
splitting.
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m-1
U(B)
m0
B
m1
B(x)
x
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m-1
U(B)
m0
B
m1
B(x)
x
U(x)
m-1
m0
x
m1
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Gravity (real gravity!) often is important force
in experiments
U(z)
m-1
m0
Why do atoms rest at equilibrium here?
z
m1
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Gravity (real gravity!) often is important force
in experiments
U(z)
m-1
m0
Why do atoms rest at equilibrium here?
z
m1
m-1
UB(z)mgz
m0
z
m1
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Shape of magnetic potential. U a x2 b y2 g
z2 Why?
electromagnet coils typically much larger,
farther apart, than size of atom cloud
R
L
D
D, L gtgt R so, order x3 terms are small. Magnetic
confining potential typically quadratic
only, except
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Cross-section of tiny wire patterned on chip
Atom chip substrate
If electromagnets are based on Atom
chip design, one can have sharper, more
structured magnetic potentials.
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If electromagnets are based on Atom
chip design, one can have sharper, more
structured magnetic potentials. But there is a
way to escape entirely from the boring rules of
magnetostatics.
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Interaction of light and atoms.
Laser beam
nlaser
Laser too blue atom diffracts light light
provides conservative, repulsive potential
Laser quasi-resonant atom absorbs light light
can provide dissipative (heating, cooling) forces
Laser too red atom diffracts light light
provides conservative, attractive potential
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One pair of beams standing wave in
intensity Can provide tight confinement in 1-D
with almost free motion in 2-d. (pancakes) This
is a one-D array of quasi-2d condensates
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Two pairs of beams Can provide tight
confinement in 2-D, almost-free motion in 1-d
(tubes) Can have a two-D array of quasi-1d
condensates
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• Why K-T on a lattice?
• Ease of quantitative comparison.
• Makes it easier to get a quasi-2d system
• This is the Frontier in Lattices Session!!!
• (come on!)

Our aspect ratio, (2.81), is modest,
but... addition of 2-d lattice makes phase
fluctuations much cheaper in 2 of 3 dimensions.
z, the thin dimension
x, y, the two large dimemsions.
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Three pairs of beams Can provide tight
confinement in 3-D, (dots) Can have a three-D
array of quasi-0d condensates
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Single laser beam brought to a focus.
Rayleigh range
Can provide a single potential (not an array of
potentials) with extreme, quasi-1D aspect
ratio. Additional, weaker beams can change
free-particle dispersion relation.
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.
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Observables Its all about images. Temperature,
pressure, viscosity, all these quantities are
inferred from images of the atomic density.
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Near-resonant imaging absorption.
signal-noise typically good, but sample is
destroyed.
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Watching a shock coming into existence
110 ms
V2003102764, 110 ms expansion
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Bigger beam now 12.4 pixel, 7.2 mW
using a bigger beam
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Absorption imaging one usually interprets images
as of a continuous density distribution, but
density distribution actually os made up
discrete quanta of mass known, (in my
subdiscipline of physics) as atoms.. Hard to
see an individual atom, but can see effects of
the discrete nature.
Absorption depth observed in a given box of area
A is OD (N0 /- N01/2) s /A The N01/2 term
is theatom shot noise. and it can
dominate technical noise in the image.
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Absorption depth observed in a given box of area
A is OD (N0 /- N01/2) s /A The N01/2 term is
theatom shot noise. and it can
dominate technical noise in the image.
Atom shot noise will likely be an important
background effect which can obscure Hawking
radiation unless experiment is designed well.
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Atom shot noise limited imaging
Data from lab of Debbie Jin.
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N.B imaging atoms with light is not the only
way to detect them I think we will hear from
Chris Westbrook about detecting individual
metastable atoms.
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.
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Why are BECs so interesting?
QM Particle described by Schrödinger equation
BEC many weakly interacting particles ?
Gross-Pitaevskii equation
The condensate is self-interacting (usually
self-repulsive)
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BEC many weakly interacting particles ?
Gross-Pitaevskii equation
Can be solved in various approximations. The
Thomas-Fermi approximation ignore KE term, look
for stationary states
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BEC many weakly interacting particles ?
Gross-Pitaevskii equation
m
Can be solved in various approximations. The
Thomas-Fermi approximation ignore KE term, look
for stationary states
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The Thomas-Fermi approximation ignore KE term,
look for stationary states
V(x)
m
x
Self-interacting condensate expands to fill
confining potential to height m
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BEC many weakly interacting particles ?
Gross-Pitaevskii equation
Can be solved in various approximations. Ignore
external potential, look for plane-wave excitatio
ns
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BEC many weakly interacting particles ?
Gross-Pitaevskii equation
Can be solved in various approximations. Ignore
external potential, look for plane-wave excitatio
ns
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speed of sound
c (m/m)1/2
Healing length
x (hbar2/m)1/2
Chemical potential
Data from Nir Davidson
m 4 p hbar2 a n /m
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Long wavelength excitations (k ltlt
1/x) relatively little density
fluctuation, large phase fluctuation (which we
cant directly image).
n(x)
f(x)
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But, if we turn off interactions suddenly (m
goes to zero), and wait a little bit
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But, if we turn off interactions suddenly (m
goes to zero), and wait a little bit
m goes to zero, x gets large now (k gt 1/x) the
same excitation now evolves much larger
density fluctuations.
n(x)
f(x)
Can you DO that?
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.
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Magnetic-field Feshbach resonance
repulsive
free atoms
DB
gt
attractive
molecules
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Single laser beam brought to a focus.
Suddenly turn off laser beam.
Data example from e.g. Ertmer.
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations.(a serious
problem) A range of numbers.
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The basic loop. Cooling. Minimum temperature.
Stray heating. Confinement. Magnetic. Optical.
Reduced dimensions. Arrays Observables. Images.
Shot noise. Atom counting. Interactions. The
G-P equation. Speed of sound. Time-varying
interactions. feshbach resonance. Reduced
dimensions. Thermal fluctuations. A range of
numbers.(coming later)