1. Strong-field physics revealed through time-domain spectroscopy Grad student: Li Fang Funding : NSF-AMO May 20, 2009 DAMOP Charlottesville, VA George N. Gibson University of Connecticut Department of Physics

2. Pump-Probe Spectroscopy We started doing transient spectroscopy on dissociating molecules. We started doing transient spectroscopy on dissociating molecules. While this worked, we found a huge amount of vibrational structure. While this worked, we found a huge amount of vibrational structure. Pump Probe

3. I 2+ + I n+ dissociation channels

4. I 1+ + I n+ dissociation channels

9. Questions we can ask: What kinds of non-dissociating intermediate states can be populated by the strong laser field? What kinds of non-dissociating intermediate states can be populated by the strong laser field? How do these states couple to the final state? How do these states couple to the final state? Do we learn anything about the final state? Do we learn anything about the final state? Intensity dependence Intensity dependence Wavelength dependence Wavelength dependence Geometry or polarization dependence Geometry or polarization dependence

10. Neutral ground state vibrations in I 2 Oscillations in the data appear to come from the X state of neutral I 2. Oscillations in the data appear to come from the X state of neutral I 2. Measured the vibrational frequency and the revival time, to get the first derivative of frequency vs.. Measured the vibrational frequency and the revival time, to get the first derivative of frequency vs..

11. Revival structure Vibrational frequency Measured211.0  0.7 cm -1 Known215.1 cm -1 Finite temp210.3 cm -1 Vibrational frequency Measured211.0  0.7 cm -1 Known215.1 cm -1 Finite temp210.3 cm -1

12. Raman scattering/Bond softening Raman transitions are made possible through coupling to an excited electronic state. This coupling also gives rise to bond softening, which is well known to occur in H 2 +. Raman transitions are made possible through coupling to an excited electronic state. This coupling also gives rise to bond softening, which is well known to occur in H 2 +.

13. Lochfrass New mechanism for vibrational excitation: “Lochfrass” R-dependent ionization distorts the ground state wavefunction creating vibrational motion. New mechanism for vibrational excitation: “Lochfrass” R-dependent ionization distorts the ground state wavefunction creating vibrational motion. Seen by Ergler et al. PRL 97, 103004 (2006) in D 2 +. Seen by Ergler et al. PRL 97, 103004 (2006) in D 2 +.

14. Phase of the motion If I pump (R) and I probe (R) are the same, as they would be, to first order, the phase of the signal is  =  for S(  ) = S o cos(  +  ). If I pump (R) and I probe (R) are the same, as they would be, to first order, the phase of the signal is  =  for S(  ) = S o cos(  +  ).

15. Lochfrass vs. Bond softening Can distinguish these two effects through the phase of the signal. Can distinguish these two effects through the phase of the signal.  LF =   LF =   BS =  /2.  BS =  /2.

16. Iodine vs. Deuterium  S/S ave = 0.60  S/S ave = 0.60 Iodine better resolved: 23 fs pulse/155 fs period = 0.15 (iodine) 7 fs pulse/11 fs period = 0.64 (deuterium) Iodine better resolved: 23 fs pulse/155 fs period = 0.15 (iodine) 7 fs pulse/11 fs period = 0.64 (deuterium) Iodine signal huge: Iodine signal huge:  S/S ave = 0.10  S/S ave = 0.10

17. Variations in kinetic energy Amplitude of the motions is so large we can see variations in KER or. Amplitude of the motions is so large we can see variations in KER or.

18. Temperature effects Deuterium vibrationally cold at room temperature Iodine vibrationally hot at room temperature Deuterium vibrationally cold at room temperature Iodine vibrationally hot at room temperature Coherent control is supposed to get worse at high temperatures!!! But, we see a huge effect. Coherent control is supposed to get worse at high temperatures!!! But, we see a huge effect. Intensity dependence also unusual We fit =  Rcos(  t+  ) +R ave As intensity increases,  R increases, R ave decreases. We fit =  Rcos(  t+  ) +R ave As intensity increases,  R increases, R ave decreases.

19. Intensity dependence Also, for Lochfrass signal strength should decrease with increasing intensity, as is seen. Also, for Lochfrass signal strength should decrease with increasing intensity, as is seen.

20. But, R ave  temperature: But, R ave  temperature: T decreases while  R increases!!!

21. We have an incoherent sea of thermally populated vibrational states in which we ionize a coherent hole: So, we need a density matrix approach. So, we need a density matrix approach.

22. Density matrix for a 2-level model For a thermal system For a thermal system where p 1 (T) and p 2 (T) are the Boltzmann factors. This cannot be written as a superposition of state vectors.

23. Time evolution of  We can write: We can write: These we can evolve in time. These we can evolve in time.

24. Coherent interaction – use  pulse for maximum coherence Off diagonal terms have opposite phases. This means that as the temperature increases, p 1 and p 2 will tend to cancel out and the coherence will decrease. Off diagonal terms have opposite phases. This means that as the temperature increases, p 1 and p 2 will tend to cancel out and the coherence will decrease.

25. R-dependent ionization – assume only the right well ionizes.  f = (  g +  e )/2  f = (  g +  e )/2 Trace(  ) = ½ due to ionization Trace(  ) = ½ due to ionization What about excited state? NO TEMPERATURE DEPENDENCE!

26. Expectation value of R, Expectation value of R, The expectation values are  /2 out of phase for the two interactions as expected.

27. Comparison of two interactions Coherent interactions: Off diagonal terms are imaginary. Off diagonal terms are imaginary. Off diagonal terms of upper and lower states have opposite signs and tend to cancel out. Off diagonal terms of upper and lower states have opposite signs and tend to cancel out. R-dependent ionization Off-diagonal terms are real. No sign change, so population in the upper state not a problem. Motion produced by coherent interactions and Lochfrass are  /2 out of phase.

28. “Real” (many level) molecular system Include electronic coupling to excited state. Include electronic coupling to excited state. Use I(R) based on ADK rates. Probably not a good approximation but it gives R dependence. Use I(R) based on ADK rates. Probably not a good approximation but it gives R dependence. Include = 0 - 14 Include = 0 - 14

29. Generalize equations

30. Same conclusions For bond-softening Off-diagonal terms are imaginary and opposite in sign to next higher state.  12 (1)  -  12 (2) Off-diagonal terms are imaginary and opposite in sign to next higher state.  12 (1)  -  12 (2)  R decreases and increases with temperature.  R decreases and increases with temperature. For Lochfrass Off diagonal terms are real and have the same sign.  12 (1)   12 (2) Off diagonal terms are real and have the same sign.  12 (1)   12 (2)  R increases and decreases with temperature.  R increases and decreases with temperature.

31. Excitation from Lochfrass will always yield real off diagonal elements with the same sign for excitation and deexcitation [f(R) is the survival probablility]: Excitation from Lochfrass will always yield real off diagonal elements with the same sign for excitation and deexcitation [f(R) is the survival probablility]:

32.  R and  R and

33. Density matrix elements

34. Conclusions Coherent reversible interactions Off-diagonal elements are imaginary Off-diagonal elements are imaginary Excitation from one state to another is out-of-phase with the reverse process leading to a loss of coherence at high temperature Excitation from one state to another is out-of-phase with the reverse process leading to a loss of coherence at high temperature Cooling not possible Cooling not possible Irreversible dissipative interactions Off-diagonal elements are real Off-diagonal elements are real Excitation and de-excitation are in phase leading to enhanced coherence at high temperature Excitation and de-excitation are in phase leading to enhanced coherence at high temperature Cooling is possible Cooling is possible