Cold Rydberg atoms
in Laboratoire Aimé Cotton
P. Cheinet, B. Pelle, R. Faoro, A. Zuliani and P. Pillet
Laboratoire Aimé Cotton, Orsay (France)
04/12/2013
Outline
• Introduction:
– Rydberg atoms and their properties
• Cold cesium experiment
• A new experiment on Ytterbium
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Cold Rydberg atoms in LAC
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Introduction: Rydberg atom
• Rydberg atom = highly excited atom
Failed screening at the core
imply quantum defects
eE=-1/2n2
|r>
Rydberg
levels
0,2
Potential
23p e Wavefunction
|e>
|f>
Cooling
levels
Energy or Amplitude
0,1
0,0
-0,1
Most weight
at large r!
-0,2
1
10
100
Radius (a.u.)
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Introduction: Rydberg atom
0,2
E-field perturbed potential
Unperturbed potential
e- Wavefunction
Energy or Amplitude
0,1
0,0
Ionization
-0,1
-0,2
1
10
100
Radius (a.u.)
Zimmerman et al. 1979
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Introduction: Rydberg atom
-270
24s
Energy (cm-1)
-280
23p3/2
-290
-300
Resonant energy transfer!
@ ≈ 80V/cm
23s
-310
0
50
2  23p3/ 2  23s  24s
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Cold Rydberg atoms in LAC
100
150
200
Field (V/cm)
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Introduction: Motivations
→ Possibility to tune interaction type and strength
over ORDERS OF MAGNITUDE
→ Selective Field Ionisation (SFI) TOF
→ Many studies:
→Dipole blocade
→Few and many-body physics
→Ultra-cold plasma
→2 electron systems
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Cs experiment
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Experimental setup
• Sequence=MOT,Rydberg,delay,ionisation
Ions extracted through
the 2 holes to the MCP
Up to 5kV ramp
applied between
the 2 central grids
MCP
Delay = 1.5μs (frozen!)
Then TOF recorded on MCP
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Cs exper./ 4-body interaction
• Two close Förster resonances:
→ 2  23p3/ 2  23s  24s @ ≈ 79.95V/cm
→ 2  24s  23p1/ 2  23d5/ 2 @ ≈ 80.4V/cm (quasi-forbidden!)
• A 4-body exchange
23p3/ 2  23d5 / 2
should be close…
-250
23d5/2
Energy (cm-1)
-260
-270
24s
-280
23p3/2
23p1/2
-290
-300
TOF!
d state is a
signature
of 4-body
energy transfer!
23s
-310
0
50
100
150
200
Field (V/cm)
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Cs exper./ 4-body interaction
• Two close Förster resonances:
→ 2  23p3/ 2  23s  24s @ ≈ 79.95V/cm
→ 2  24s  23p1/ 2  23d5/ 2 @ ≈ 80.4V/cm (quasi-forbidden!)
• A 4-body exchange
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23p3/ 2  23d5 / 2
Cold Rydberg atoms in LAC
should be close…
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Introduction / 1st 4-body scheme
• Two close Förster resonances:
→ 2  23p3/ 2  23s  24s @ ≈ 79.95V/cm
→ 2  24s  23p1/ 2  23d5/ 2 @ ≈ 80.4V/cm (quasi-forbidden!)
• A 4-body exchange
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23p3/ 2  23d5 / 2
Cold Rydberg atoms in LAC
should be close…
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Results / Resonances
• Observe the 2-body resonances:
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Results / Resonances
• Observe the 4-body resonance:
Observe d state :
4-body
energy transfer!
Shift
Observed
(79.99V/cm)
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Results / Density dependance
• Observe p → s → d transfer
No residual linear
cross-talk from s
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Results / Density dependance
• Observe p → s → d transfer
No residual linear
cross-talk from s
p → d transfer
governed by
4-body process
d   p4
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Conclusion on Cs Exper.
• Demonstration of a 4-body interaction
Too many
quasi-forbidden
Resonances in Cs
0,05
m5/2+m1/2
f7/2m5/2
f7/2m3/2
ns+(n+1)s
f5/2m1/2
ns+(n-3)f7/2m1/2
→ Spin mixture?
0,10
m3/2+m1/2
0,15
(n+1)p
ns
(n+1)s
m3/2+m3/2
→ RF to restore resonance?
Transfer from 32p3/2m3/2
• Other few-body schemes?
0,20
(n-2)d5/2m1/2+(n+1)p3/2m3/2
→ Observed 4-body resonant energy transfer
→ Studied density dependance
→ Many-body effect at MOT density for n=23
J. Gurian et al., PRL 108, 023005 (2012)
0,00
5
6
7
8
9
10
Electric field (V/cm)
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Towards a new experiment
On Ytterbium Rydberg atoms
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Ytterbium experiment
• Motivation for 2 electron atom:
eE=-1/2n2
|r>
|e>
|f>
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Rydberg
levels
Cooling
levels
ee-
Rydberg electron
no longer available
for optical manipulation
Second electron
is available for
cooling/trapping/imaging
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Yb experiment planning
• Yb cooling and trapping
6s6p 1P1
Yb
t = 5.5 ns 5d6s 3D
2
Zeeman
Slower
399nm
5d6s 3D1
398.8 nm
Efficient but
“hot” limit
6s6p 3P2
t = 875 ns
6s6p 3P1
6s6p 3P0
555.6 nm
6s2 1S0
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Weak but
“cold” limit
3D MOT
556nm
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Yb experiment planning
• Trapping practical issue:
– MOT capture velocity vc8m/s
– Large divergence of Zeeman slower… 2D MOT!
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Yb experiment planning
• Slowing and trapping simulation:
Longitudinal speed (m/s)
– Longitudinal speed Vs position
Position from Zeeman slower start (m)
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Yb experiment planning
• Slowing and trapping simulation:
Longitudinal speed (m/s)
– Longitudinal speed Vs position
Position from Zeeman slower start (m)
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Yb experiment planning
• Slowing and trapping simulation:
transverse position (m)
– Transverse position Vs longitudinal position
Position from Zeeman slower start (m)
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Yb experiment planning
• Electrodes and imaging
8 electrodes
forming 2 rings
Holding mechanics
letting all beams pass:
16 CF16 + 8 CF40 “in plane”
8 CF16 + 8 CF40 at 45°
2 CF63 at 90°
Possibility
to compensate
any field gradient
Under vacuum lens:
diffraction limited
imaging of 3µm
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Thank you
for your attention!
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Experimental setup
• Calibrate detection
→ Direct excitation of each relevant state:
Signal gates
Cross-talk
Compute the
inversion matrix
to retrieve signal:
 d   2.016  0.0645  0.082 d 
  
 
s


0
.
100
4
.
645

0
.
275
  
 s 
 p   0.083  3.147 4.149  p 
  
  gate
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(includes ionisation efficiency)
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Experimental sequence
•
•
•
•
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Fix electric field
Rydberg excitation + delay
Field ionization pulse + detection
Change electric field and repeat…
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Results / Resonances
• Minimal toy model:
→ 2 or 4 equidistant atoms at distance R
→ 2 or 4 state basis :
 p p p p 
 p p

 s  s'





 ss

 d  p'






 p  p  s  s'
 s  s  s ' s '

 d  p ' s ' s '







→ Compute Rabi oscillation to s or d for each field
• Average over distance R :
→ 2 atoms : Erlang nearest neighbour distribution
→ 4 atoms : Erlang distribution cubed
• Average over field inhomogeneity
→ ≈ 5V/cm/cm implies 0.1V/cm over sample
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Ytterbium autoinonisation
• Total internal energy > ionisation limit
– Autoionisation if nl too small:
ee-
• Adiabatic loading of large l states:
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