20.01.2016
Trapping and cooling of
atoms, ions and electrons
• Laser cooling of atoms
• Magneto-optical trap
• Trapping, detection of single ions
• Trapping and detection of single electrons
Single versus many atoms
• Single trapped atom: ideal isolated quantum system
• 1925: 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
• ~2000 - : quantum control on motion of trapped particles
Doppler cooling of atoms with laser


p ph  k


pa  mva
1. Laser photon



pa  mva  k
2. Spontaneous emission in random direction
1. The transferred momentum to atom is averaged
over many absorption/emission events


F    22 k 
 22 

 2R / 4

  2
 / 2     0  k  va   2
2
R
2. Doppler effect

va

S /2
2
1  S  2 /  

 
  k v
3. 3. To cool down tune the laser below resonance
(red detuning)
Doppler cooling of atoms with laser

va
Left beam
Right beam
Two counter‐propagating red‐detuned laser beams creates a viscous force


F   v
1. Energy balance: cooling vs heating
E Heat   E Cool
2
2
 k
E Heat 
 22
2m
E Cool  F (v)v
2. Doppler limit for cooling
TD 

2k B
133Cs: 62S
vD 
2
1/2‐6 P3/2

2m
, E1‐transition
λ=852nm and Г = 2π x 5.2 MHz
TD = 0.12 mK, vD = 8 cm/sec
   0  
Magneto-Optical Trap
1. Slowing down atoms is not confining
2. Need trapping potential
3. Anti‐Helmholtz coils create a magnetic
field with minimum at the center
Magneto-Optical Trap
Energy
mJ  1
mJ  0
mJ  1
0

J 0
0
x
1. Force balance: confining due to the magnetic gradient and recoil of photons
  g
    0  k  v  B Bx

F ( x)   Dx  x
2. Load the trap with 108‐1010 atoms. Doppler cooling. MOT is off, then Sisyphus cooling. Magneto-Optical Trap
88Sr MOT in Colorado, λ
= 461 nm
87Rb MOT in PTB, λ
= 780 nm
Students, ask Pavel to show the movie !
https://www.youtube.com/watch?v=eAIDL_2xN8M
40Ca MOT in PTB, λ
= 432 nm
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
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

va
Left beam: verticaly polarized
Right beam: horizontally polarized
me  1 / 2
TSD
 2k 2

2m
133Cs: TD = 0.12 mK
TSD = 0.2 μK
mg  1 / 2
Standing wave modulates
the energy sublevels:
AC‐Stark shift
mg  1 / 2
 /8


3 / 8


5 / 8


z
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.
Trapping potential
Earnshaw Theorem (1842): Collection of point charges can not be maintained in a stable
stationary equilibrium configuration solely by the electrostatic
interaction of the charges. 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




F (r )  eE (r )  e   (r )  r
1. Linear trap: a = 1, b = -1, c = 0
 ( x, y, z )  ax 2  by 2  cz 2
  0  a  b  c  0
U  V cos t 2
 (r , z )  DC 2 RF 2
r  2z 2
r0  2 z0

2. Ring trap: a = b= 2, c = -2

1. Trap size is about 1 mm
2. UDC = 5V, VRF = 500V, ω = 2π x 20 MHz Pseudo-potential for the ion motion
~
e
E
cos t
x(t )  ~
x
2
m
dE ( ~
x)
e2 E(~
x ) dE ( ~
x)
2
~
~
( x  x )  eE cos t 
cos
t
F (t )  eE ( x ) cos t  e
2
dx
m
dx
T
2
1
e
E(~
x ) dE ( ~
x)
~
Fav ( x )   F (t )dt  
2m 2 dx
T 0
F (~
x )   e   ( ~
x)
av
2 2 ~
e
E (x ) 1
2
2
2
~
~
( x , y ) 

m

(

r


z
)
2
4m
2
Cooling of ion motion
1 MHz
1.2 MHz
2.3 MHz
Averaging over many oscillations period results in
motion of ion in harmonic pseudo potential Ψ(r,z)
with 3 oscillation modes Trapping 138Ba+
Ring diameter 1.2 mm
View angle at 45 deg
E
 Doppler cooling. TD ~ 1 mK
x,y,z
 Amplitude ~ 40 nm
Resolved sideband cooling
excited
λ = any nm
Г<Ω
Energy
ground
Ωx/2π~ 1 MHz
Ion displacement
v 1
v
v 1
Ion’s vibrational states
Absorption
Resolved sideband cooling
0
1
2
Ion’s vibrational states
3
0  
0
0  
Laser probe frequency
• 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
Absorption
Resolved sideband cooling
0
1
2
Ion’s vibrational states
3
0  
0
0  
Laser probe frequency
• 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
Sideband cooling of Hg+ ion
• Doppler cooling on S → P
• Sideband cooling on S→ D
• Electron shelving to detect population of S1/2 state
F. Diedrich et al, PRL 62, 403 (1989)
• Lower sideband is suppressed • <nv> ≈ 0.05
• T ~ 10 μK
Trapping, cooling and measuring single electron
G. Gabrielse, Physics World, pp. 32‐36, February 2007