laser cooling, atom traps - max planck societymotivation cooling atom traps arne fischer laser...

Arne Fischer Laser Cooling, Atom Traps

Arne Fischer

Seminar für mittlere Semester„Experimental Methods in Atomic Physics“

Universität Heidelberg

12.06.07

Laser Cooling, Atom Traps

Overview

• Motivation

• Cooling

• Atom Traps


www.mpiwww.mpi--hd.mpg.de/kellerbauerhd.mpg.de/kellerbauer

MotivationCooling

Atom Traps


Nobel Price

„for development of

methods to cool and

trap atoms with

laser light“

Physics Nobel Price 1997

MotivationCooling

Atom Traps


Advantages of cold atoms

room temperature : velocities on the order of 300 m/s

=> only short observation time

=> too fast for trapping

=> disturbing effects:

• Doppler shift• relativistic time dilation

=> displacement and broadening of the spectral lines

=> for exact observation slow/cold atoms are needed

MotivationCooling

Atom Traps


Doppler CoolingPG CoolingVSCPT

Basics : Two level atom

ħδ = ħωL - ħωA

δ < 0 => detuned to the red

δ > 0 => detuned to the blue

Γ

ħδ

ħωL

ħωA

ground state

excited state

MotivationCooling

Atom Traps



Basics : Photon Absorption / Emission

Absorption : one direction

Emission : spontaneous, isotropic

0

0 momentum

in change total

==>

=

=>

v

p

Δ

Δ

cmω

nmk

n Δv

cn

L

⋅⋅⋅−=⋅−==>

⋅⋅−=⋅−==>

hh

hh Ln kpω

Δ

atoms are moving towards the laser beam

after absorption atom is slowed down

=> Cooling

MotivationCooling

Atom Traps



Doppler Effect

Atom moves towards the laser beam => Doppler effect

=> Shifted resonance frequency :

Ideal laser detuning :

Problem: changes, atom goes out of resonance

Example: Sodium (Na): natural linewidth: Γ/2π = 10Mhz, λres ~ 600nm=> out of resonance after absorbing 200 photonscorresponds to a change in velocity of ~ 6 m/s

Solution: „frequency chirp“, Zeeman Slower

kvAA −= ωω '

'AL ωω =

'Aω

MotivationCooling

Atom Traps



Zeeman Slower

Idea:

Zeeman energy of stateswith m > 0 decreases withthe drecreasing fieldΔE ~ ΔB

for reaching this energy states σ+ light is used

=> the increasing of ω‘A is compensated by the

decreasing of the Zeeman energy.=> the atoms don‘t get out of resonance

Zeeman slower and frequency chirp methodsare used for precooling atoms

MotivationCooling

Atom Traps



Doppler Cooling / Optical Molasses

Two counterpropagating laser beams

no atomic beam => no special direction of movement

aim: atoms absorb mainly photons moving towards them

MotivationCooling

Atom Traps




AL ωω <AL ωω < v,ωA

Two counterpropagating laser beams

doppler effect

=> the resonance frequency for the laser in front of the atom isshifted downwards

=> if the lasers are detuned to the red the laser in front of the atom iscloser to resonance

=> mainly counterpropagating photons are absorbed

MotivationCooling

Atom Traps




Normalized velocity 2kv/Γ

Fo

rce (

arb

itra

ry u

nit

s)

ideal detuning : δ ≈ -Γ/2

=> net force is nearly linearin velocity and always opposes the velocityF = -α v

=> atoms are viscously confined

3 dimensional cooling:

6 beams arranged as 3orthogonal pairs

MotivationCooling

Atom Traps



Doppler Limit

Problem: every spontaneous emission causes random velocity change Δv=> random walk in velocity space=> heating=> temperature limit

lowest possible temperature:cooling is balanced by heating

kBTD = ħΓ/2

Sodium: TD ≈ 240μK C.J.FootC.J.Foot

MotivationCooling

Atom Traps



AC – Stark - Effect

Changing electromagnetic field creates an induced dipolemoment which interacts with the field

=> atomic energy levels are shifted

ΔE ~ Ω²/δ

Rabi – Frequency:

Ω ~ Xge

=> ΔE ~ intensity of a transitionΔE < 0 if the laser is detuned to the red

MotivationCooling

Atom Traps



Polarization – Gradient Cooling

σ- σ-σ+

Two counterpropagating laserbeams with orthogonalpolarization

=> total field has circularpolarization every λ/4

Example

ground state g with Jg = 1/2

exited state e with Je = 3/2

1/3 1/32/3 2/3

MotivationCooling

Atom Traps




En

erg

yg+1/2 g-1/2

g-1/2

σ- σ-σ+

σ- : atoms are optically pumped into the g-1/2 state

σ+ : atoms are optically pumped into the g+1/2 state

ΔE ~ intensity of a transitionΔE < 0

=> σ-:potential valleys for g-1/2

potential hills for g+1/2

σ+:potential valleys for g+1/2

potential hills for g-1/2

1/3 1/32/3 2/3

MotivationCooling

Atom Traps




Sysiphus-Effect:

pumping takes finite time τP

- atom starts in g-1/2

- looses kinetic energy by climbingthe potential hill

- after τP (ideal: on top) atom ispumped into lower state g+1/2

- energy loss trough emission ofblue shifted photon

g+1/2g-1/2g-1/2

MotivationCooling

Atom Traps




Sysiphus-Effect:

pumping takes finite time τP

- atom starts in g-1/2

- looses kinetic energy by climbingthe potential hill

- after τP (ideal: on top) atom ispumped into lower state g+1/2

- energy loss trough emission ofblue shifted photon

g+1/2g-1/2g-1/2

Limit : Recoil Limit recoil of a single photon

E = ħ²k²/2m=> Sodium: TR ≈ 0,77 μK

MotivationCooling

Atom Traps



Velocity Selective Coherence Population Trapping

Idea:

Between two counterpropagating laser beams atoms make a random walk in velocity space

=> sometimes an atom has v = 0

those atoms are optically pumped into a nonabsorbing„dark state“

=> the longer you wait the more atoms have v = 0

MotivationCooling

Atom Traps




2

1−

2

1+

v = 0=> due to stimulated emissionthe |e0> state can change intoa superpostion of |g+> and |g->

because of the destructively interferingtransition intensities this is adark state for the light

v ≠ 0=> due to doppler shifting the twobeams have not the same intensity from die view of the atom=> the dark state can not be reached

( )−+ +=Ψ ggSP2

1

MotivationCooling

Atom Traps




v = 0=> due to stimulated emissionthe |e0> state can change intoa superpostion of |g+> and |g->

because of the destructively interferingtransition intensities this is adark state for the light

v ≠ 0=> due to doppler shifting the twobeams have not the same intensity from die view of the atom=> the dark state can not be reached

( )−+ +=Ψ ggSP2

1

MotivationCooling

Atom Traps


Quadrupole TrapMOTDipole Force Trap

Atom Traps

Problem:atoms are neutral=> electric fields can not be used for catching atoms=> for cooling them laser cooling is necessary

the first trapping experiments were done with ions.-> in contrast ions can easily be slowed down and catched

with electric fields

trapping atoms was not achieved until after the inventionof laser cooling (first proposed in 1975 by Hänsch and Schawlow and Wineland and Dehmelt)

MotivationCooling

Atom Traps



Quadrupole Trap

Idea:Zeeman energy of quantum states with m > 0 increases with increasing magnetic field (low field seekers)=> atoms can be caught in field

minimaΔE = gμBm ΔB

typical dept < 0.1Tcorresponds to 0.05K and 7m/s (Na)

Problem:-the trap only works with the right quantum states

-no further cooling

W.D.PhillipsW.D.Phillips

MotivationCooling

Atom Traps



Magneto – Optical Trap

C.J.FootC.J.Foot

Idea:

The Quadrupole field shifts theZeeman energy levels

=> imbalance between theradiation forces

=> atoms are pushed back to the center

MotivationCooling

Atom Traps



Magneto – Optical Trap

MM

σ+

1

1 -1

-1

0 0

Energy

+zB(z)>0

σ-ωL

J = 0

J = 1

-zB(z)<0

Example:

atom moves in +z direction

=> the lasers come into resonance with theM = -1 state

because of the selection rules only the σ- lightinteracts with the atom

=> the atom is pushed backto the centre

=> trapping combined withcooling

MotivationCooling

Atom Traps



Dipole Force

Based on the AC Stark effect

=> energy levels are shifted in a laser beam

=> dipole force

Fdipole = Χ I

Χ = atomic polarizabilityI = laser intensity

=> for detuning to the red atoms areattracted into the regions with highintensity

ωL < ωA

ωL > ωA Energ

yEn

ergy

Laser Beam

MotivationCooling

Atom Traps



Dipole Force Trap

C.J.FootC.J.Foot

a focused laser beam confinesatoms in all directions

=> dipole force trap

Optical tweezers:

Atoms or even moleculescan be trapped in the focusof a laser beam. If the focus is moved thetrapped particals follow

MotivationCooling

Atom Traps


Bose Einstein CondensationAtom Laser

Bose Einstein Condensation

A BEC is a State of matter formed by bosons near the absolute 0

Due to cooling T falls below a critical temperature Tc

λ(Tc) ≈ d(Tc),

=> a large number of atoms collapses into the lowest quantum state

in this state the atoms are fully delocated in the area of the condensate

=> the state of the whole condensate can be described as a singlematter wave

231 nmTC ⋅∝

MotivationCooling

Atom Traps




Physics WorldPhysics World

1.) temperature sharply over Tcalmost classical distribution of atoms

2.) phase transition => sharp peak of atoms in the trap centre

3.) further cooling increases the condensatefraction to almost 100%

MotivationCooling

Atom Traps




Physics WorldPhysics World

1.) temperature sharply over Tcalmost classical distribution of atoms

2.) phase transition => sharp peak of atoms in the trap centre

3.) further cooling increases the condensatefraction to almost 100%

MITMIT

MotivationCooling

Atom Traps



BEC Application : Atom Laser

Idea:

Bose Einstein Condensate is hold in a magnetic trap

=> only states with M > 0 are trapped

=> if M is changed to a value =<0 atoms are no longer trapped (done with radio frequency pulses)

=> atoms leave the trap due to gravitational force

=> source of moving clouds of atoms in the samequantum state = atom laser

atom laseratom laserat the MITat the MIT

BEC

MotivationCooling

Atom Traps



Conclusion

Both laser cooling and atom traps made it possible toobservate atoms more exactly.Makes high precision spectroscopy of atoms possible.

Effects like Bose Einstein Condensation / fermi Condensationcould only be shown with these mechanisms.

In future lots of applications of ultracold atoms are thinkable for example•atom interferometry

-> an atom interferometer would be more precisely than onewith light because of the smaller wavelenght

•atom holography-> projection of electronic circuits onto semiconductors-> would also profit of the smaller wavelenght compared to light


www.mpiwww.mpi--hd.mpg.de/kellerbauerhd.mpg.de/kellerbauer

laser cooling, atom traps - max planck societymotivation cooling atom traps arne fischer laser...

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