Atom meets Photon

Atom traps(Atomfallen)

Alexander Späh

http://etc.usf.edu/clipart/4400/4465/hand_9.htm

Atom trap MOT Dipole Magnetic Electric Summary

1. atom trap

2. four different atom traps

3. summary

Atom trap MOT Dipole Magnetic Electric Summary

TkE Bkin 2

3=

?=potE

Atom trap MOT Dipole Magnetic Electric Summary

UF −∇=

depth of the trap

Forces:

radiation pressure trap

optical dipole trap

magnetic trap

electric trap

trap frequency

~kBT

heating rate T&

(only consider neutral atoms) time constant of the trap

size of the trap

Atom trap MOT Dipole Magnetic Electric Summary

Magneto-optical trap

Chu The manipulation of neutral particles 1998

• ~1010 atoms• diameter of a few mm

(Raab, Chu „Trapping of neutral sodium atoms with radiation pressure“ 1987)

Atom trap MOT Dipole Magnetic Electric Summary

xy

z

Optical molasses Hypothetical atom

Atom trap MOT Dipole Magnetic Electric Summary

1dim case:

z

inhomogeneous magnetic field

bzzB =)(

B(z)

Energy1

0

-1

−σ+σ

0

3dim case:

zµbmBmE ss ==∆ µ

Laserωh

Atom trap MOT Dipole Magnetic Electric Summary

advantages:

heating:

disadvantages:

• cooling and trapping• cooling down to ~10µK• capture velocity of a few K

• near resonant light � perturbed internal dynamics• achievable density limited by photonreemission and reabsorbtion

• certain requirements to atom sturcture

• temperature limited by doppler effects• background pressure

Atom trap MOT Dipole Magnetic Electric Summary

Chu Experimental observation of optically trapped atoms 1986

Dipole trap

• ~500 Na atoms• ~10µm diameter

Atom trap MOT Dipole Magnetic Electric Summary

ω0 = transition frequency

atom

ground state

excited state

ω < ω0 = red detuned

ω > ω0 = blue detuned

driving field E

E

pE

p

E

p

EpUdip 2

1−=

Atom trap MOT Dipole Magnetic Electric Summary

driving field E

EpUdip 2

1−=

IU reddip −∝

IU bluedip +∝

( ) ( )rUrF dipdip −∇=

IF reddip ∇∝

IF bluedip −∇∝

blue-detuned trap repels atomsout of intensity maximum

Atom trap MOT Dipole Magnetic Electric Summary

red-detuned trap attracts atomstowards the max. of intensity

( ) ( )∆

∝ rIrUdip

( ) ( )2∆

∝Γ rIrsc

dipole potential

scatteringrate

large detunings and high intensities for large potential depth andlow scatteringrate

0ωω −=∆

IF reddip ∇∝ IF blue

dip −∇∝

Atom trap MOT Dipole Magnetic Electric Summary

first dipol-trap 1986 Chu (Nobel prize 1997)

optical molasses

• sodium atoms cooled in optical molasses below 10-3K• laserbeam tuned far away from resonance• ~500 atoms confined in a volume of 103 µm3

• trap lifetimes of several seconds

(Chu „Experimental observation of optically trapped atoms“ 1986)

Atom trap MOT Dipole Magnetic Electric Summary

kBT

Udepth

focusd-beam trap

crossed-beam trap

standing-wave trap

optical-lattice trap

Atom trap MOT Dipole Magnetic Electric Summary

advantages:

heating:

disadvantages:

• far-detuned light causes weak interacion and therefore optical excitation can be kept very low

• trapping times of many seconds• great variety of different trapping geometries• easily moveable

• loading with precooled atoms• no cooling

• scattering processes• red-detuned trap: atoms at intensity maximum• blue-detuned trap: atoms at intensity minimum• background pressure

Atom trap MOT Dipole Magnetic Electric Summary

Magnetic trap

T. Bergeman magnetostatic trapping fields for neutral atoms 1987

(Alan „First observation of magnetically trapped neutral atoms“ 1985)

Atom trap MOT Dipole Magnetic Electric Summary

1dim:

BµUmag =

BµUF magmag ∇−=−∇=

magnetic potential

magnetic force

Maxwell: only low-field seekers are possible0=⋅∇ B

z

Energy

state at B=0

(e.g. Na 3S1/2 mF=2)

Atom trap MOT Dipole Magnetic Electric Summary

configurations of the inhomogeneous magnetic field in 3dim

(a) magn. quadrupol trap (b) spherical hexapole trap (c) ioffe trapp

T. Bergeman magnetostatic trapping fields for neutral atoms 1987

Atom trap MOT Dipole Magnetic Electric Summary

advantages:

heating:

disadvantages:

• trap depths of ~100mK• excellent tools for evaporative cooling and Bose-Einstein condensation

• trapping mechanism relies on the internal atomic state(only low-field seeker)

• complicated geometries of the magnetic field

• background pressure• Majorana transitions

Atom trap MOT Dipole Magnetic Electric Summary

Electric trap

Rieger Trapping of Neutral Rubidium with a Macroscopic Three-Phase Electric Trap 2007

(Rieger, Rempe „Trapping of neutral rubidium with a macroscopic three-phase electric trap“ 2007)

quadratic Strark shift α is the atom‘s static polarizability2

2

1EWs α−=

with vanish in time average

Atom trap MOT Dipole Magnetic Electric Summary

force EEEEWF sel ∇≅∇=−∇= 0αα

induced micromotion

( )txm ωsin=&&

( )tx ωsin−∝

non-linear potential and micromotioncause net force towards the trap center

( )2220 2

1zybbxEE +−+=

Ws

x- direction

y-z-plane

micromotion

Atom trap MOT Dipole Magnetic Electric Summary

advantages:

heating:

disadvantages:

• confining molecules and atoms• trap size of 0.3mm in diameter

• ~20µK trap depth• need precooled atoms

• background preassure

Atom trap MOT Dipole Magnetic Electric Summaryhe

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gdi

sadv

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ges

adva

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MOT Dipole Magnetic Electric

• cooling• trapping fromthermal gases

• near resonantlight

• temperaturelimited bydoppler effects

• far-detuned light• many trappinggeometries

• red and bluedetuning

• loading withprecooled atoms

• scatteringprocesses

• different heatingfor red and bluedetuning

• depths of ~100mK• Bose-Einsteincondensation

• only low-fieldseeker

• Majoranatransitions

• moleculesand atoms

• ~20µK trapdepth

• backgroundpressure