Light-induced instabilities in large magneto-optical traps G. Labeyrie, F. Michaud, G.L. Gattobigio,...
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Light-induced instabilities in largemagneto-optical traps
G. Labeyrie, F. Michaud, G.L. Gattobigio, R. KaiserInstitut Non Linéaire de Nice, Sophia Antipolis, France
T. PohlITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, USA
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Outline
1. Magneto-Optical Traps (MOTs) in the multiple scattering regime
2. New instability in large MOTs
3. Driven behavior
4. Conclusion
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Introductionmany body systems with long range interactions
interactions in MOTs : Dalibard, Opt. Commun. 68, 203 (1988)
compression force in optically-thick vapors
Walker et al., Phys. Rev. Lett. 64, 408 (1990)
long-range repulsive force MOT size
...
Vorozcovs et al., J. Opt. Soc. Am. B 22, 943 (2005)
temperature in the multiple scattering regime
plasmas & ultracold plasmasstars
...neutral cold atoms (light)
Wilkowski et al., Phys. Rev. Lett. 85, 1839 (2000)instabilities in retroreflected MOTs (shadow effect)
instabilities in MOTs :
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MOT basicsfew atoms (N < 104)
effective detuning :
I ,
x
B
0
I ,
at `
ekvBx
kv , Bx -3 -2 -1 0 1 2 3
0
vx
force : FFF
F
temperaturekBTD
size kBTx2
independent of N
2. New instability in large MOTs
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Long-range interactions in MOTs multiple scattering regimemany atoms (N >> 104)
restoring force -x
photon re-absorption multiple scattering force FR
repulsion LRd
L
R
dI ,
Coulomb-like interaction
q / e ~ 10-3 tunableeffective charge
I , I ,
x
laser attenuation absorption force FA
compression Lx
non local
2. New instability in large MOTs
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MOTs in the multiple scattering regime
FR FA ifrL
MOT size :R
Walker et al., Phys. Rev. Lett. 64, 408 (1990).
net repulsion density limit
inelastic scattering
x (
mm
)
1E8 1E9 1E10
10.29
N-15 -10 -5 0 5 10 15
0.0
0.2
0.4
0.6
0.8
1.0
fluo
resc
ence
(a.
u.)
x (mm)
2. New instability in large MOTs
uniform density
without spatial dependence of
with spatialdependence
of
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MOT Production and Characterization
vapor cell (Rb85) 6 independent trapping beams
N 1010
2R 6 mmT 40 K
photodiode
40 800 120 160time (ms)
dynamics ofMOT
photodiode
optical thickness
2. New instability in large MOTs
CCD
N, size, density
t
IL
B
trapping
imaging
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New instability in MOTs
spontaneous periodic oscillationsfor N > Nth (, B, IL , ...)
0 1 2 3 4 5 6 7 8 90
0 50 100 1501E-10
1E-8
1E-6
0 50 100 1501E-10
1E-8
1E-6
part
ial f
luor
esce
nce
MOT loading time (s)sp
ectr
um
(Hz)
(Hz)
unstable
Labeyrie et al., Phys. Rev. Lett. 96, 023003 (2006).
stable
2. New instability in large MOTs
0 50 100 150
2
3
4
5
6
fluo
resc
ence
@M
OT
cen
ter
(a. u
.)
time (ms)
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Simple 1-zone model threshold
±±kv±Bx
Fs{ } hk2
e-b
1+4() 1
1+4() RL
x Re-b
1+4()
x0 R
1 23
attenuatedtrapping beam 1
non-attenuatedtrapping beam 2
total repulsiveforce 3
x R :
negative friction Rth
R > Rth N
G/cm
Rth mm
2. New instability in large MOTs
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unstable
stable
0 5 10 15 20-2.0
-1.5
-1.0
-0.5
0.0 exp.
B (G/cm)
Investigation of threshold
0
1
2
3
4
5
6
0 5 10 15 200.0
0.5
1.0
0.0
0.5
1.0
size
(m
m)
tran
smis
sion
B (G/cm)
N (
a. u
.)
2. New instability in large MOTs
0 5 10 15 20-2.0
-1.5
-1.0
-0.5
0.0
model
B (G/cm)
N andR vary at threshold, but b 1 analytical model OK
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t < 0t > 0
2. New instability in large MOTs
Investigation of threshold
0 50 100 150ce
nter
-of-
mas
s po
siti
ontime (ms)
N
e-t sin(t)
below threshold
(
ms)
0 1 2 30
10
20
30
N
overdampedunderdamped
damping when N
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below threshold
above threshold
0 50 100 150
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
disp
lace
men
t (a.
u.)
time (ms)
2. New instability in large MOTs
t < 0t > 0
Investigation of threshold
20 40 60 80 100 120
40
60
80
100
120
2 4 6 8 10 12 140.0
0.5
1.0
1.5
2.0
B (G/cm)
crit
ical
par
amet
er
osc (
Hz)
0 (Hz)
0.6
MOT subcriticalat threshold
frequency continuousno hysteresis
supercritical Hopf
bifurcation
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Numerical modelN-zone model dynamics !
Pohl et al., Phys. Rev. A 74, 023409 (2006).
DopplerN < 106 test particlesdouble scatteringposition-dependent cross-sections
ingredients :
confirms analytical model for thresholdsupercritical Hopf bifurcationcomplex dynamics with external active motion zone
2. New instability in large MOTs
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Driven oscillations
10 20 30 40 50 60 70 80 90 100 110 120-50
-40
-30
-20
-10
no drive
2exc
exc
2osc
osc
pow
er (
dBm
)
frequency (Hz)
10 20 30 40 50 60 70 80 90 100 110 120-50
-40
-30
-20
-10
0
10
20
pow
er (
dBm
)
frequency (Hz)
below threshold
above threshold
3. Driven behavior
sint
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10 20 30 40 50 60 70 80
pow
er (
dB)
frequency (Hz)
exc (Hz)
Driven oscillations
sint
Hzexc osc
spontaneous oscillation suppressed harmonics of excitation
0 20 40 60 80-45
-40
-35
-30
-25
-20
pow
er @
2 ex
c (dB
)
exc
(Hz) 3. Driven behavior
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Driven oscillations
3. Driven behavior
exc osc
resonance at exc parametric resonance ?
0 20 40 60 80 100 120
-50
-45
-40
-35
-30
-25
-20
-15
pow
er @
exc /
2 (d
B)
exc
(Hz)
10 20 30 40 50 60 70 80po
wer
(dB
)frequency (Hz)
exc (Hz)
sint
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Driven oscillations
10 20 30 40 50 60 70 80 90 100 110 120-50
-40
-30
-20
-10
pow
er (
dBm
)
frequency (Hz)
3. Driven behavior
other resonances ...
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Conclusion
observation of a new instability in large MOTs competition between compressionand repulsive longe-range interaction (light)
mechanism predicted by simple analytical model and numerical simulations
perspectives :
better control of experiment new measurements (critical exponent, larger parameter space, ...)
numerical model quantitative comparison with experiment : dynamics, forced regime, ...