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

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

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 :

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

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 ~ tunableeffective charge I,  x laser attenuation  absorption force F A  compression  L   x non local 2. New instability in large MOTs

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 

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

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

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

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

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

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

Numerical model N-zone model  dynamics ! Pohl et al., Phys. Rev. A 74, (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

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

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

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

Driven oscillations 3. Driven behavior other resonances...

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,...