1. Light-induced instabilities in large magneto-optical traps G. Labeyrie, F. Michaud, G.L. Gattobigio, R. Kaiser Institut Non Linéaire de Nice, Sophia Antipolis, France T. Pohl ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, USA

2. Outline 1. Magneto-Optical Traps (MOTs) in the multiple scattering regime 2. New instability in large MOTs 3. Driven behavior 4. Conclusion

3. Introduction many 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 plasmas stars... neutral cold atoms (light)  Wilkowski et al., Phys. Rev. Lett. 85, 1839 (2000) instabilities in retroreflected MOTs (shadow effect) instabilities in MOTs :

4. MOT basics  few atoms  (N < 10 4 ) effective detuning : I,  x B 0  at ``   e   kv  Bx kv ,  Bx   v  x force : F   F  F FF temperature k B T   D  size k B T   x 2 independent of N 2. New instability in large MOTs

5. Long-range interactions in MOTs  multiple scattering regime  many atoms  (N >> 10 4 ) restoring force -  x  photon re-absorption  multiple scattering force F R repulsion  L  R  d   L   R  d I,  Coulomb-like interaction q / e ~ 10 -3 tunableeffective charge I,  x laser attenuation  absorption force F A  compression  L   x non local 2. New instability in large MOTs

6. MOTs in the multiple scattering regime F R  F A if   r    L  MOT size : R    Walker et al., Phys. Rev. Lett. 64, 408 (1990). net repulsion  density limit inelastic scattering  x (mm) N 2. New instability in large MOTs uniform density without spatial dependence of  with spatial dependence of 

7. MOT Production and Characterization  vapor cell (Rb 85 )  6 independent trapping beams N  10 10 2R  6 mm T  40  K photodiode 40800120160 time (ms)  dynamics of MOT photodiode  optical thickness 2. New instability in large MOTs CCD  N, size, density t ILIL BB trapping imaging 

8. New instability in MOTs spontaneous periodic oscillations for N > N th ( ,  B, I L,...) unstable  Labeyrie et al., Phys. Rev. Lett. 96, 023003 (2006). stable 2. New instability in large MOTs

9. Simple 1-zone model  threshold  ±   ±  kv  ±  Bx F   s  {   } hk  2 e -b 1+4(    )  1 1+4(    )   R   L  x R  e -b  1+4(    )  x 0 R 12 3 attenuated trapping beam 1 non-attenuated trapping beam 2 total repulsive force 3 x  R : negative friction  R th  R > R th  N    G/cm  R th  mm 2. New instability in large MOTs

10. unstable stable Investigation of threshold 2. New instability in large MOTs  N and  R vary at threshold, but b  1  analytical model  OK

11. t < 0t > 0 2. New instability in large MOTs Investigation of threshold N   e -t  sin(  t  ) below threshold  (ms)   N overdamped under damped damping when N

12. below threshold above threshold 2. New instability in large MOTs t < 0t > 0 Investigation of threshold   B (G/cm) critical parameter osc (Hz) 0 (Hz) 0.6  MOT subcritical at threshold  frequency continuous no hysteresis  supercritical Hopf bifurcation

13. Numerical model N-zone model  dynamics ! Pohl et al., Phys. Rev. A 74, 023409 (2006).   Doppler   N < 10 6 test particles   double scattering   position-dependent cross-sections ingredients :   confirms analytical model for threshold   supercritical Hopf bifurcation   complex dynamics with external active motion zone 2. New instability in large MOTs

14. Driven oscillations below threshold above threshold 3. Driven behavior     sin  t

15. exc (Hz)      Driven oscillations     sin  t  Hz  exc  osc spontaneous oscillation suppressed harmonics of excitation 3. Driven behavior

16. Driven oscillations 3. Driven behavior exc  osc resonance at exc  parametric resonance ? exc (Hz)          sin  t

17. Driven oscillations 3. Driven behavior other resonances...

18. Conclusion  observation of a new instability in large MOTs competition between compression and 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,...