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

Outline

1. Magneto-Optical Traps (MOTs) in the multiple scattering regime

2. New instability in large MOTs

3. Driven behavior

4. Conclusion

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 :

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

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

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

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

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)

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

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

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

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

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

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

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

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

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 ...

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, ...