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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. The basic loop . Cooling . Minimum temperature. Stray heating. Confinement . Magnetic. Optical. Reduced dimensions. Arrays - PowerPoint PPT Presentation
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A review of atomic-gas Bose-Einstein condensation experiments for
Workshop: “Hawking Radiation in condensed-matter systems”
Eric Cornell JILABoulder, Colorado
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.
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.
Thermal fluctuations.
A range of numbers.
2.5 cm
Laser cooling
Basic cooling idea leads to Basic cooling limit.Heating happens.
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.
V(x)
x
Self-interacting condensate expands to fill confining potential to height
V(x)
x
n(x)
Self-interacting condensate expands to fill confining potential to height
V(x)
x
n(x)
kT
Cloud of thermal excitations made up of atoms on trajectoriesthat go roughly to where the confining potential reaches kT
V(x)
x
n(x)
When kT < then there are very few thermal excitations extending outside of condensate. Thus evaporation cooling power is small.
kT
BEC experiments must be completedwithin limited time.
Bang!
Three-body molecular-formation processcauses condensate to decay, and heat!Lifetime longer at lower density, but physics goes more slowly at lower density!
Dominant source of heat:
Bang!
Decay products from three-body recombinationcan collide “as they depart”, leaving behind excess energy in still-trapped atoms.
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)
The basic loop.
Cooling. Minimum temperature. Stray heating.
Confinement. Magnetic. Optical. Reduced dimensions. ArraysObservables. 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.
F=2
F=1m=1
m=-1m=0
m=2
m=-2Energy
Typical single-atom energy level diagramin the presence of a magnetic field.Note Zeeman splitting.
U(B)
B
m=-1
m=0
m=+1
B(x)
x
U(B)
B
m=-1
m=0
m=+1
B(x)
x
U(x)
x
m=-1
m=0
m=+1
U(z)
z
m=-1
m=0
m=+1
Why do atomsrest at equilibriumhere?
Gravity (real gravity!) often is important force in experiments
U(z)
z
m=-1
m=0
m=+1
Why do atomsrest at equilibriumhere?
UB(z)+mgz
z
m=-1
m=0
m=+1
Gravity (real gravity!) often is important force in experiments
Shape of magnetic potential.
U= x2 + y2 + z2 Why?
D
L
R electromagnet coilstypically much larger, farther apart, than size of atomcloud
D, L >> R
so, order x3 terms are small.Magnetic confining potential typically quadratic only,except…
Atom chip substrate
Cross-section of tiny wire patterned on chip
If electromagnets are based on “Atom chip”design, one can have sharper, more structuredmagnetic potentials.
If electromagnets are based on “Atom chip”design, one can have sharper, more structuredmagnetic potentials.But there is a way to escape entirelyfrom the boring rules of magnetostatics….
Laser beam
laser
Laser too red+atom diffracts light+light provides conservative,attractive potential
Laser too blue+atom diffracts light+light provides conservative,repulsive potential
Laser quasi-resonant+atom absorbs light+light can providedissipative (heating,cooling) forces
Interaction oflight and atoms.
One pair of beams: standing wave in intensity
Can provide tight confinement in 1-D with almostfree motion in 2-d. (pancakes)
This is a one-D array of quasi-2d condensates
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
Why K-T on a lattice?
1.Ease of quantitative comparison.2. Makes it easier to get a quasi-2d system3.This is the Frontier in Lattices Session!!! (come on!)Our aspect ratio, (2.8:1), 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”.
Three pairs of beams:
Can provide tight confinement in 3-D, (dots)
Can have a three-D array of quasi-0d condensates
Single laser beam brought to a focus.
Rayleighrange
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.
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.
Observables: It’s all about images.Temperature, pressure, viscosity,all these quantities are inferred from images of the atomic density.
Near-resonant imaging:absorption. signal-noisetypically good, but sampleis destroyed.
Off-resonant imaging:index of refraction mapping. Signal-noise typically less good, but (mostly) nondestructive..
Watching a shock coming into existence110 ms
using a bigger beam
Absorption imaging: one usuallyinterprets images as of a continuousdensity 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 +/- N0
1/2) /A
The N01/2 term is the”atom
shot noise”. and it can dominatetechnical noise in the image.
Absorption depth observed in a given box of area A is OD= (N0 +/- N0
1/2) /AThe N0
1/2 term is the”atomshot noise”. and it can dominatetechnical noise in the image.
Atom shot noise will likely be an important backgroundeffect which can obscure Hawking radiation unlessexperiment is designed well.
Atom shot noise limited imaging
Data from lab of Debbie Jin.
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.
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.
QM: Particle described by Schrödinger equation
rErVm2 extern
2
BEC: many weakly interacting particles Gross-Pitaevskii equation
rrrm
a4V
m22
2
extern
2
Why are BECs so interesting?
The condensate isself-interacting (usually self-repulsive)
BEC: many weakly interacting particles Gross-Pitaevskii equation
t
rirr
m
aV
m extern
222 4
2
Can be solved in various approximations.
The Thomas-Fermi approximation:ignore KE term, look for stationary states
BEC: many weakly interacting particles Gross-Pitaevskii equation
t
rirr
m
aV
m extern
222 4
2
Can be solved in various approximations.
The Thomas-Fermi approximation:ignore KE term, look for stationary states
externVrm
a 2
24
The Thomas-Fermi approximation:ignore KE term, look for stationary states
externVrm
a 2
24
V(x)
x
n(x)
Self-interacting condensate expands to fill confining potential to height
BEC: many weakly interacting particles Gross-Pitaevskii equation
t
rirr
m
aV
m extern
222 4
2
Can be solved in various approximations.
Ignore external potential, look for plane-waveexcitations
BEC: many weakly interacting particles Gross-Pitaevskii equation
t
rirr
m
aV
m extern
222 4
2
Can be solved in various approximations.
Ignore external potential, look for plane-waveexcitations
Data from Nir Davidson
c = (/m)1/2
= (hbar2/m)1/2
speed of sound:
Healing length:
Chemical potential:
= 4 hbar2 a n /m
n(x)
(x)
Long wavelengthexcitations(k << 1/)
relatively little density fluctuation,large phase fluctuation(which we can’t directly image).
n(x)
(x) But, if we turn offinteractions suddenly ( goes to zero), and wait a little bit:
n(x)
(x)
n(x)
(x)
m goes to zero, gets largenow (k > 1/)
the same excitation nowevolves much larger densityfluctuations.
But, if we turn offinteractions suddenly ( goes to zero), and wait a little bit:
Can you DO that?
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.
Magnetic-field Feshbach resonance
molecules
→ ←
attractive
repulsive
B>
free atoms
Single laser beam brought to a focus.
Suddenly turn off laser beam….
Data example from e.g. Ertmer.
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.
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)