Trapping and cooling of atoms and ions

13.01.2015

• Laser cooling of atoms

• Magneto-optical trap

• Trapping, detection of single ions

• Single atom as mirror

Single versus many atoms• Single trapped atom: ideal isolated quantum system

• E. Schrödinger: we will never experiment with a single atom

• In 50th-60th technology was not at the proper level

• Many atoms: control of atomic motion or temperature

• Ashkin, Letokhov (1978): Laser cooling of atoms: velocity ~1-10 cm/sec

• Hansch, Shawlow, Wineland, Dehmelt: Laser cooling of ions and atoms

Doppler cooling of atoms with laseraa vmp

= kpph

=

kvmp aa

−=

1.

2.

3.

1. The transferred momentum to atom is averagedover many absorption/emission events

Γ−= kF

22ρ

( ) ( )222

02

2

22 /212/

2/

4/Γ++

=Γ+⋅+−+Ω

Ω=

δωωωρ

SS

vk aR

R

Laser photon

Spontaneous emission in random direction

av ω

vk ⋅+ω

2. Doppler effect

3. To cool down tune the laser below resonance(red detuning)

Doppler cooling of atoms with laser

av

Two counter-propagating red-detuned laser beams creates a viscous force vF α−=

Right beamLeft beam

1. Energy balance: cooling vs heating

CoolHeat EE −=

2. Doppler limit for cooling

vvFEmkE

Cool

Heat

)(2 22

22

=

Γ=

ρΓ−=− 0ωω

BD k

T2Γ

=

mvD 2

Γ=

133Cs: 62S1/2-62P3/2 , E1-transition

λ=852nm and Г = 2π x 5.2 MHz

TD = 0.12 mK, vD = 8 cm/sec

Magneto-Optical Trap

1. Slowing down atoms is not confining

2. Need trapping potential

3. Anti-Helmholtz coils create a magneticfield with minimum at the center

Magneto-Optical Trap

0=J

1+=Jm

0=Jm

1−=Jm

x

Energy

0

0ω ω

1. Force balance: confining due to the magnetic gradient and recoil of photons

xDxxF

Bxgvk B

α

µωωδω

−−=

∇±⋅±−=

)(

0

2. Load the trap with 108-1010 atoms. Doppler cooling. MOT is off, then Sisyphus cooling.

Magneto-Optical Trap

40Ca MOT in PTB, λ = 432 nm

88Sr MOT in Colorado, λ = 461 nm

Show movie!http://greiner.physics.harvard.edu/

87Rb MOT in PTB, λ = 780 nm

Sisyphus cooling below Doppler limit

• Jean Dalibard and Claude Cohen-Tannoudji (1989)

• Atoms moves along strong polarization gradient

• Atoms travels up the potential hill and loose energy

• http://www.nobelprize.org (Physics 1997)

Sisyphus cooling below Doppler limit

av Right beam: horizontally polarizedLeft beam: verticaly polarized

z8/λ 8/3λ 8/5λ

2/1±=em

2/1+=gm

2/1−=gm

Standing wave modulatesthe energy sublevels:AC-Stark shift

mkTSD 2

22≈

133Cs:

TD = 0.12 mK

TSD = 0.2 μK

+σ−σ −σ

How to trap a single neutral atom: Optical dipole trap

0.65 mK

V. Rosenfeld, PhD-Thesis, München 2008

Trapping of single atom: apparatus

• Dipole trap: P = 30 mW at 854 nm, NA=0.38

• Simultaneous MOT and DT operation

• Fluorescence detection: MOT is off

• Atom is confined within 3-4 sec

Trapping charged particles

1. Trapping charged particles? Ions for instance: Be+, Ca+, Mg+, Al+, Sr+, Ba+, Yb+

2. Need trapping potential. Easy: 4 electrods – DC potential.

Earnshaw Theorem (1842): Collection of point charges can not be maintained in a stablestationary equilibrium configuration solely by the electrostaticinteraction of the charges.

Trapping potential

Paul trap for trapping charged particles

Wolfgang Paul (1913-1993)

1. Need RF potential super-imposed with DC potential

Ring and linear Paul traps for single ions

Ring trap for 138Ba+ ions Linear trap for 40Ca+ ions

http://heart-c704.ibk.ac.at/

Ring Paul trap description

00),,(

)()()(222

=++→=∆Φ++∝Φ

−∝Φ∇⋅−==

cbacybyaxzyx

rrereErF 1. Linear trap: a = 1, b = -1, c = 0

2. Ring trap: a = b= 2, c = -2

( )2220

20

22

cos),( zrzr

tVUzr RFDC −+

+=Φ

ω 1. Trap size is about 1 mm

2. UDC = 5V, VRF = 500V, ω = 2π x 20 MHz

Pseudo-potential for the ion motion

)(21

4)~()~,~(

)~()~(

)~(2

)~()(1)~(

cos)~()~(cos)~()~(cos)~()(

cos~

~)(

2222

22

2

2

0

22

2

2

zrmm

xEeyx

xexFdx

xdEm

xEedttFT

xF

tdx

xdEm

xEeteExxdx

xdEetxeEtF

tm

Eextx

av

T

av

βαωω

ω

ωω

ωω

ωω

+==Ψ

Ψ∇⋅−=

−==

−≈−+=

−=

∫

Cooling of ion motion

Trapping 138Ba+

Ring diameter 1.2 mmView angle at 45 deg

Doppler cooling. TD ~ 1 mK

Amplitude ~ 40 nm

Averaging over many oscillations period results inmotion of ion in harmonic pseudo potential Ψ(r,z)with 3 oscillation modes

1 MHz 1.2 MHz

2.3 MHz

E

x,y,z

Resolved sideband coolingexcited

ground

λ = any nmГ < Ω

Ion displacement

Ener

gy

Ion’s vibrational states

Ωx/2π~ 1 MHz

v 1+v1−v

Resolved sideband cooling

Ion’s vibrational states

1 20 3

Laser probe frequency

Ω−0ω 0ω Ω+0ω

• The transition linewidth Г is less then trap frequency Ωx

• Absorption spectrum is different when ion is cooled: RedSideBand dissappear

• Minimum Temperature less than recoil of the photon (theory) ~ 10 μK

Abso

rptio

n

Resolved sideband cooling

Ion’s vibrational states

1 20 3

Laser probe frequency

Ω−0ω 0ω Ω+0ω

• The transition linewidth Г is less then trap frequency Ωx

• Absorption spectrum is different when ion is cooled: RedSideBand dissappear

• Minimum Temperature less than recoil of the photon (theory) ~ 10 μK

Abso

rptio

n

Sideband cooling of Hg+ ion

F. Diedrich et al, PRL 62, 403 (1989)

• Doppler cooling on S → P

• Sideband cooling on S→ D

• Electron shelving to detect population of S1/2 state

• Lower sideband is suppressed

• <nv> ≈ 0.05

• T ~ 10 μK