1. Strong-field physics revealed through time-domain spectroscopy Grad student: Li Fang Funding : NSF-AMO May 30, 2009 XI Cross Border Workshop on Laser Science University of Ottawa, Ottawa, Canada George N. Gibson University of Connecticut Department of Physics

2. Motivation Vibrational motion in pump-probe experiments reveals the role of electronically excited intermediate states. Vibrational motion in pump-probe experiments reveals the role of electronically excited intermediate states. This raises questions about how the intermediate states are populated. Also, we can study how they couple to the final states that we detect. This raises questions about how the intermediate states are populated. Also, we can study how they couple to the final states that we detect. We observe inner-orbital ionization, which has important consequences for HHG and quantum tomography of molecular orbitals. We observe inner-orbital ionization, which has important consequences for HHG and quantum tomography of molecular orbitals.

3. Pump-probe experiment with fixed wavelengths. Pump Probe In these experiments we used a standard Ti:Sapphire laser: 800 nm 23 fs pulse duration 1 kHz rep. rate

4. Pump-probe spectroscopy on I 2 2+ Internuclear separation of dissociating molecule Enhanced Ionization at R c Enhanced Excitation

5. Lots of vibrational structure in pump-probe experiments

6. Vibrational structure Depends on: wavelength (400 to 800 nm). wavelength (400 to 800 nm). relative intensity of pump and probe. relative intensity of pump and probe. polarization of pump and probe. polarization of pump and probe. dissociation channel. dissociation channel. We learn something different from each signal. We learn something different from each signal. Will try to cover several examples of vibrational excitation. Will try to cover several examples of vibrational excitation.

7. I 2+ pump-probe data

8. (2,0) vibrational signal Amplitude of vibrations so large that we can measure changes in KER, besides the signal strength. Amplitude of vibrations so large that we can measure changes in KER, besides the signal strength. Know final state – want to identify intermediate state. Know final state – want to identify intermediate state.

9. I 2 potential energy curves

10. Simulation of A state

11. Simulation results From simulations: - Vibrational period - Wavepacket structure - (2,0) state

12. What about the dynamics? How is the A-state populated? How is the A-state populated? I 2  I 2 +  (I 2 + )* - resonant excitation? I 2  I 2 +  (I 2 + )* - resonant excitation? I 2  (I 2 + )* directly – innershell ionization? I 2  (I 2 + )* directly – innershell ionization? No resonant transition from X to A state in I 2 +. No resonant transition from X to A state in I 2 +.

13. From polarization studies The A state is only produced with the field perpendicular to the molecular axis. This is opposite to most other examples of strong field ionization in molecules. The A state is only produced with the field perpendicular to the molecular axis. This is opposite to most other examples of strong field ionization in molecules. The A state only ionizes to the (2,0) state!? Usually, there is a branching ratio between the (1,1) and (2,0) states, but what is the orbital structure of (2,0)? The A state only ionizes to the (2,0) state!? Usually, there is a branching ratio between the (1,1) and (2,0) states, but what is the orbital structure of (2,0)? Ionization of A to (2,0) stronger with parallel polarization. Ionization of A to (2,0) stronger with parallel polarization.

14. Implications for HHG and QT We can readily see ionization from orbitals besides the HOMO. We can readily see ionization from orbitals besides the HOMO. Admixture of HOMO-1 depends on angle. Admixture of HOMO-1 depends on angle. Could be a major problem for quantum tomography, although this could explain some anomalous results. Could be a major problem for quantum tomography, although this could explain some anomalous results.

15. (2,0) potential curve retrieval It appears that I 2 2+ has a truly bound potential well, as opposed to the quasi-bound ground state curves. This is an excimer-like system – bound in the excited state, dissociating in the ground state. Perhaps, we can form a UV laser out of this.

16. Wavelength-dependent pump probe scheme Change inner and outer turning points of the wave packet by tuning the coupling wavelength. Femtosecond laser pulses: Pump pulse: variable wavelength. (517 nm, 560 nm and 600 nm.) Probe pulse: 800 nm.

17. I 2+ spectrum: vibrations in signal strength and kinetic energy release (KER) for different pump pulse wavelength [517nm, 560 nm and 600 nm] Vibrational period (fs)‏ X-B coupling wavelength (nm)‏

18. Simulation: trapped population in the (2,0) potential well The (2,0) potential curve measured from the A state of I 2 + in our previous work: pump-probe delay=180 fs PRA 73, 023418 (2006)

19. I 2+ + I n+ dissociation channels

20. 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. Measured the vibrational frequency and the revival time.

21. 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

22. 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 +.

23. 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 +.

24. 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.

25. 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

26. 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.

27. 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.

28. 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.

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

30. 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.

31. 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.

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

33. 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.

34. 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!

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

36. 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.

37. “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

38. Generalize equations

39. 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.

40. 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]:

41.  R and  R and

42. Density matrix elements

43. 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

44. Conclusions Excitation of the A-state of I 2 + through inner-orbital ionization Excitation of the A-state of I 2 + through inner-orbital ionization Excitation of the B-state of I 2 to populate the bound region of (2,0) state of I 2 2+ Excitation of the B-state of I 2 to populate the bound region of (2,0) state of I 2 2+ Vibrational excitation through tunneling ionization. Vibrational excitation through tunneling ionization.

45. Laser System Ti:Sapphire 800 nm Oscillator Ti:Sapphire 800 nm Oscillator Multipass Amplifier Multipass Amplifier 750  J pulses @ 1 KHz 750  J pulses @ 1 KHz Transform Limited, 25 fs pulses Transform Limited, 25 fs pulses Can double to 400 nm Can double to 400 nm Have a pump-probe setup Have a pump-probe setup

46. Ion Time-of-Flight Spectrometer

47. Phase lag

48. Ionization geometry

50. I 2+ pump-probe data