Lecture II Non dissipative traps Evaporative cooling Bose-Einstein condensation.
Laser Cooling, Atom Traps - Max Planck SocietyMotivation Cooling Atom Traps Arne Fischer Laser...
Transcript of 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
Arne Fischer Laser Cooling, Atom Traps
www.mpiwww.mpi--hd.mpg.de/kellerbauerhd.mpg.de/kellerbauer
MotivationCooling
Atom Traps
Arne Fischer Laser Cooling, Atom Traps
Nobel Price
„for development of
methods to cool and
trap atoms with
laser light“
Physics Nobel Price 1997
MotivationCooling
Atom Traps
Arne Fischer Laser Cooling, 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
Arne Fischer Laser Cooling, 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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Doppler Cooling / Optical Molasses
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Doppler Cooling / Optical Molasses
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Polarization – Gradient Cooling
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Polarization – Gradient Cooling
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Polarization – Gradient Cooling
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Velocity Selective Coherence Population Trapping
2
1−
2
1+
2 Laser beams with the sameintensity
3 state atom:2 ground states |g-> and |g+>1 excited state |e0>
the intensities of the two transitions |g±> -> |e0> have to interfer destructively
MotivationCooling
Atom Traps
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Velocity Selective Coherence Population Trapping
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
Arne Fischer Laser Cooling, Atom Traps
Doppler CoolingPG CoolingVSCPT
Velocity Selective Coherence Population Trapping
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
Arne Fischer Laser Cooling, 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
Arne Fischer Laser Cooling, Atom Traps
Quadrupole TrapMOTDipole Force Trap
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
Arne Fischer Laser Cooling, Atom Traps
Quadrupole TrapMOTDipole Force Trap
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
Arne Fischer Laser Cooling, Atom Traps
Quadrupole TrapMOTDipole Force Trap
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
Arne Fischer Laser Cooling, Atom Traps
Quadrupole TrapMOTDipole Force Trap
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
Arne Fischer Laser Cooling, Atom Traps
Quadrupole TrapMOTDipole Force Trap
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
Arne Fischer Laser Cooling, 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
Arne Fischer Laser Cooling, Atom Traps
Bose Einstein CondensationAtom Laser
Bose Einstein Condensation
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
Arne Fischer Laser Cooling, Atom Traps
Bose Einstein CondensationAtom Laser
Bose Einstein Condensation
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
Arne Fischer Laser Cooling, Atom Traps
Bose Einstein CondensationAtom Laser
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
Arne Fischer Laser Cooling, Atom Traps
Bose Einstein CondensationAtom Laser
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
Arne Fischer Laser Cooling, Atom Traps
www.mpiwww.mpi--hd.mpg.de/kellerbauerhd.mpg.de/kellerbauer