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Cooling of strontium from the broad to the
narrow transition
David Wilkowski
Strontium MOT
Institut Non Linéaire de Nice (INLN),
France http//www.inln.cnrs.fr/
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Cooling of strontium from the broad to the
narrow transition
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Outline of the talk
G2p32106 s-1
1P1
G 2p7.5103 s-1
3P1
461 nm
689 nm
1S0
Cooling on broad transition Extra heating due
to transverse intensity fluctuations and
narrow transition No gaussian
distributions Laser induced atomic external
states coherence
4
461 nm MOT set-up
M
O
T
b
e
a
m
s
d

-
1.5G
)
(
P

3
0
m
W

Magnetic Coils
Z
e
e
m
a
n
b
e
a
m
Z
e
e
m
a
n
O
v
e
n
(
T

5
0
0

C
)
s
l
o
w
e
r
)
d

-
8
G
(
P

3
0
m
W

Number of atoms 7.107 radiusRMS 0.7mm
density1010Atoms/cm3
Temperature 10mK, sv1m/s
Higher than the Doppler Prediction (TDop 0.5
mK)
Weiss et a.l., JOSA B 6, 2072 (1989), Xu et
a.l.,PRA 66, 011401(R) (2002)
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RMS Velocity of 1D molassa
RMS Velocity deduced by time of flight measurement
Experimental Data
Doppler Theory
I0.1Isat
Experimental Data
Doppler Theory
d-G/2
The measured rms velocities are still higher than
the Doppler predictions
Extra heating is due from transverse intensity
fluctuations
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transverse intensity fluctuations
Origins
Scattered light (speckle)
Laser
Mirror
Imperfections on optics, dusts, ...
Order of magnitude
The scattered field is coherently added to the
laser field
Locally IIlaserIscattered2ELaserEscatteredcos(
f)
If Iscattered0.01 Ilaser dI0.2 Ilaser
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1D Cooling in non-equilibrated intensities
Dynamic of the mean velocity
d
d
v0 F
Equilibrium at v¹0
I2¹I1
I1
Saturation term
With kvltltd,G
The damping time (I1, I2 ltlt Isat)
Steady state
veq dont depend on intensity if I1,I2ltltIsat
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1D Cooling with transverse intensity fluctuations
Definitions
Gaussian fluctuations of the transverse beam
intensities Mean value ltIgt
RMS value sI
I1 and I2 are two independent random variables
Order of magnitude
If each atom sees a fix intensity imbalance
With
(With sI ltlt ltIgt)
Inhomogeneous velocity broadening
With , svsDop (d-G/2, ltIgt ltlt
Isat)
Important effect !!!
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Cooling with transverse intensity
fluctuations The general case Moving atoms
Correlation time
v
Lc Correlation length of the transverse
fluctuation
Correlation time
v
Lc
tc gtgt tv limit case
Atom reaches this steady state before intensity
is decorrelated each atom sees a fix
intensity imbalance like previously
Inhomogeneous broadening
tc ltlt tv limit case
Intensities are randomly fluctuated in times
Flockker-Planck equation Homogeneous
broadening
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Comparison between tc ltlt tv and tc gtgt tv cases
ltIgt ltlt Isat d-G/2
tc ltlt tv leads to lowest temperature
Achieve if the intensity is low because
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Comparison with experiences Monté-Carlo
Simulations
Experimental Data
Doppler Theory
Experimental Data
Doppler Theory
I0.1Isat
d-G/2
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Cooling Dynamic in the tc gtgt tv case
Evolution of one atom
After integrating one has
With dI I1-I2 ltlt I1, I2
Here btvdIvf is the final velocity and v0 the
initial velocity
We average over the intensity fluctuation
Evolution of all the atoms
Where v0 and vf are independent random variables
no correlation between v0 and dI
At t ltlt tv, one has
Hence ltv2gt starts to decrease whatever ltvf2gt
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Cooling Dynamic Experiences
Time sequence
toff
tTOF
MOT Lasers
Time
ton
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Summary
Extra heating due to transverse intensity
fluctuations
Signature of intensity-velocity correlation
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Outline of the talk
G2p32106 s-1
1P1
G 2p7.5103 s-1
3P1
461 nm
689 nm
1S0
Cooling on broad transition Extra heating due
to transverse intensity fluctuations and
narrow transition No gaussian
distributions Laser induce atomic external
states coherence
16
Loading a 689 nm MOT
Velocity capture range
vc d/k G/k 1 cm/s
issue vc ltlt sv 1 m/s (_at_ 461 nm)
Broadening of the laser spectrum
Time sequence
Katori et a.l., PRL 82, 1116 (1999)
Loading efficiency 50
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Loading a 689 nm MOT
Velocity capture range
vc d/k G/k 1 cm/s
Problem vc ltlt sv 1 m/s (_at_ 461 nm)
Broadening of the laser spectrum
Loading movie
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MOT on narrow line and gravity
Cold cloud position
(G/2p7.5kHz)
Experimental data Resonance position
small radiation pressure acceleration lt 15g
Loftus et a.l., PRL 93, 073003 (2004)
The laser detuning d is compensated by the
Zeeman shift The detuning "see" by atoms is
fixed dr
d
Example of cooling with a constant force (the
gravity) and a fluctuating force (the laser)
Temperature independent on the laser detuning
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MOT Temperature
Temperature at recoil limit (0.5 µK) Gravity
plays an dominant role
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Horizontal 1D cooling
s0.2
-G/2
No gaussian distributions and red shift of the
rms minimum
Theory Castin and Dalibard, JOSA B 6 (1989)
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Broad transition velocity distribution
Broad transition wrltltG wr3.10-4G
for Sr
Monté-Carlo simulation wr10-2G
velocity
kvG/2
kv-G/2
position
Fµ-v and DCste Browian motion
Gaussian distribution
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Narrow transition velocity distribution
Narrow transition wrG wr0.6G for Sr
Monté-Carlo simulation wr0.6G
velocity
kv-5G
kv-5G
position
Fµ-v and DCste Browian motion
Gaussian distribution
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Narrow transition velocity distribution
Narrow transition wrG wr0.6G for Sr
Monté-Carlo simulation wr0.6G
velocity
kv-G
kv-G
position
F¹-v and D¹Cste No gaussian
distribution
Divergence of rms value
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Narrow transition velocity distribution
Narrow transition wrG wr0.6G for Sr
Monté-Carlo simulation wr0.6G
velocity
kvG/2
kv-G/2
position
F¹-v and D¹Cste No stationary solution

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Time evolution of velocity distribution
No stationary divergence of thr rms value
minimum of rms
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Horizontal 1D cooling
s0.2
-G/2
No gaussian distribution and red shift of the rms
velocity minimum
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Experimental velocity distribution
s0.2
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Increasing the saturation parameter
d-5.6 wr
d-5 wr
d-4.3 wr
E
E
S2
Laser
B
Laser
d-3.7 wr
d-3.1 wr
d-2.5 wr
S2
d-1.2 wr
d-0.6 wr
d-1.8 wr
S2
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Velocity distribution
s2
Two peaks at vr and -vr Velocity-selective
coherent population trapping with two-level atoms
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Original VSCPT
s-
s
J1
He experiment at ENS (Paris) Aspect et a.l. PRL
(1988)
J1
Laser
Laser
m1
m-1
NC(P)gt is not coupled to the excited state
NC(0)gt has no motional coupling Population is
accumulated in this state
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Quasi Dark state for narrow transition
Proposed by Doery et a.l. PRA 51, 4881 (1995)
First (non direct) observation on He (389nm)
With G2Gs(d-3wr)/2 and G0Gs(dwr)/2
GWC(0)G2
GC(0)2G0G2
The 'key' parameter wr/G not ltlt1
WC(0)gt not coupled to the e0gt state but
coupled to the off-resonant e 2hkgt state
WC(0)gt is a long living state
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VSCPT dependence on detuning
Dark state population
s2
W
Cgt
GC
NWCµGWC(d)/GC(d)
-hk
hk
WCgt
GWC
With WgtGCgtGWC
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VSCPT experimental results
s0.7
s2
s4
s0.2
W
p
-hk
hk
May expected NWCAGWC(d)/GC(d) Where A is the
feeding probability for the -hk or hk state A
should be proportional to the intensity
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VSCPT experimental results
s0.7
s2
s4
s0.2
s10
s20
s45
s200
Multi line at high intensity ? Issues motional
coupling off resonant coupling
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Summary
Red shift of the rms velocity minimum
No gaussian distributions
Evidence of VSCPT on two level system
Multi line at high saturation
s2
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People involved
R. Kaiser, T. Chanelière (PhD 2001-2004) J.L.
Meunier Monté-Carlo on intensity imbalance
problem Collaborations - A. Kastberg
(Umeå, Sueden) 1D cooling experiments - C.
Dion and M. Nylén (Umeå, Sueden) GOBE on VSCPT
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A cold Strontium MOT to study localization of
light
Multiple scattering
Strontium MOT
David Wilkowski
Copenhagen, September 2003 Cold Alkaline-Earth
Atoms workshop
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Cooling with transverse intensity fluctuations tc
ltlt tv limit case
Master equation for the velocity distribution
With
ltltv/tc
Small velocity change approximation
Expansion of P(v,t)
Flokker-Planck Equation
Abnormal diffusion
Friction term
Diffusion term
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Cooling with transverse intensity fluctuationstc
ltlt tv limit case
With
Steady state solution
Quasi Gaussian behavior G1 m/s a10