1. Understanding Strong Field Closed Loop Learning Control Experiments PRACQSYS August 2006

2. Motivation and Outline Want to understand strong field learning control (closed loop) Single atom vs collective dynamics From atoms to molecules - controlling fragmentation + =

3. The ‘Coherent’ Control Toolbox Optical field control Feedback and learning algorithms Amplified ultrafast lasers Output:  = 3*10 -14 s Energy = 10 -3 J I control (10 18 W/m 2 ) >> I sun (6*10 7 W/m 2 ) Control E(  ) ~1000 ‘knobs’

4. Strong Field Population Inversion oo oo Stark shift: Coupling strength and energy shifts are of the same order of magnitude -> low efficiency Absorption -> Emission Without Stark shift With Stark shift Na energy levels |3s> |4s> |3p> 589 nm 1141 nm 777nm P |4s> R. R. Jones PRL 74, 1091 (1995)

5. Experimental Setup Pinhole PMT 589 nm Lens Na Sodium vapor T ~ 350 0 C Laser t = 30 fs 0 = 772 nm - 784 Pulse shaper G.A. PMT Cross correlation Na energy levels |3s> |4s> |3p> 589 nm 1141 nm 777 nm

6. Feeding back on Stimulated vs Spontaneous emission Spontaneous Emission Stimulated Emission Improvement over unshaped ~ 3Improvement over unshaped ~ 10 3

7. Understanding Single Atom Dynamics I 0 =784 nm 0 =772 nm 0 =777 nm I(t) and  (t) --- All solutions give substantial improvement over an unshaped pulse – but only for strong fields! C. Trallero-Herrero et al Phys. Rev. Lett. 96 063603 (2006)

8. Understanding Single Atom Dynamics II 22 Need to maximize: …but with constraints. P 4s (t),  (t) shaped P 4s (t),  (t) unshaped I(t)

9. Understanding Increase in Stimulated Emission Yield Solve coupled Schroedinger and Maxwell Equations Time and Frequency domain Measurements of Stimulated Emission D. Flickinger et. al. Applied Optics 45 6187 (2006)

10. Modeling Collective Behavior Na energy levels |3s> (Q 11 ) |4s> (Q 22 ) |3p> (Q 33 ) 589 nm =  2 1141 nm =  1 777 nm After laser field M. Spanner & P. Brumer PRA 70 023809 (2006)

11. Simulation Results Time [ps] Intensity [arb]

12. Measurement of the Stimulated Emission Experiment Theory

13. Superfluorescence (Yoked) Delayed pulse – not a parametric process  t<1(~0.5) – almost perfectly coherent - not ASE Cross correlation of Stimulated Emission M. S. Malcuit et. al. PRL 59 1189 (1987)

14. Stimulated Emission vs |  4s | 2 ExperimentTheory Note threshold at 2/3 Control is through optimizing single atom inversion to get over SF threshold Stimulated emission is superfluorescence – locking of dipole phases in ensemble

15. Molecular Experimental Apparatus

16. Control in Trifluoroacetone Unshaped Pulse Shaped Pulse CF 3 + CH 3 + R. J. Levis, G. M. Menkir, and H. Rabitz, Science 292, 709 (2001). D. Cardoza, M. Baertschy, T. Weinacht, J. Chem Phys. 123, 074315 (2005). Control goal = CF 3 + /CH 3 + CH 3 COCF 3

17. A B Optimal solution and Pump-Probe Measurement Time (fs) Intensity Phase (radians) τ τ =170 fs Laser cooperates with Molecular dynamics All other fragments flat CF 3 + yield vs pump-probe delay A~170 fs B~85 fs

18. Ab initio structure & wave packet calculations help reveal mechanism CH 3 COCF 3 + CF 3 + CH 3 CO +

19. Control Model 1 1.Ionization (launch) 2.Wave packet evolution 3.Enhanced ionization C-CF 3 bond length [Å] C-C-O angle [degrees] Energy[eV] J. Chem. Phys. 123 074315 (2005) Wave packet takes 145-175 fs to reach EI point. Pump- Probe peak is ~170 fs 1 2 3

20. Predictions for ‘Family Members’ CH 3 COCCl 3 CH 3 COCD 3 CH 3 COCF 3

21. Fragmentation of Family Members CH 3 COCD 3 CH 3 COCCl 3 CH 3 COCF 3

22. Results for CH 3 COCCl 3 and CH 3 COCD 3 ControlPulse Shape Pump-probe Chemical Physics Letters 411, 311 (2005)

23. General techniques for interpreting control: What are the right knobs?

24. Transforming from ‘bad’ to ‘good’ bases Can a given linear transformation, T 1, diagonalize entire search space? x1x1 x2x2 For linear transformations, PCA – J. Phys. B 37 L399 (2004)

25. Hessian Analysis Comparison

26. Physically Motivated Basis Transformation in CH 3 COCF 3 Journal of Chemical Physics, 122, 124306 (2005)

27. Hessian Analysis Shows Basis Change Works

28. Conclusions & Future Directions Demonstrated closed loop coherent control over strong field dynamics Both quantitative and qualitative understanding of both stimulated emission and single atom dynamics Understand control in a molecular family – ‘photonic reagents’

29. Acknowledgements David Cardoza Carlos Trallero Sarah Nichols Daniel Flickinger Brendan Keller Brett Pearson Jay Brown Collaborators: Mark Baertschy (CU Denver) Jayson Cohen (Focus, U Michigan) Michael Spanner (Toronto) Herschel Rabitz (Princeton) Funding: NSF, ACS-PRF, DURIP & Research Corp