Unveiling Strong-Field Physics Through Time-Domain Spectroscopy: Insights from Quantum Dynamics

1. Strong-field physics revealed through time-domain spectroscopy George N. Gibson University of Connecticut Department of Physics Grad student: Dr. Li Fang – now at LCLS Hui Chen, Vincent Tagliamonti Funding: NSF-AMO November 7, 2011 Stony Brook University Stony Brook, New York

2. What can strong-field physics offer chemistry? • Time resolution: femtosecond laser pulses can resolve nuclear motion, R • Can control both R and  • Can look at processes as a function of both • Ultimate goal: Quantum tomography as a function of R – united atom to separated atom Start with: End with:

3. 2-D 1-electron double-well gwavefunctions: Increasing internuclear separation:

4. Back to Basics:Tunneling ionization of a double-well potential(All strong field experiments on molecules start here!)Ionization is dominated by an effect called “R-critical ”

5. 10 5 0 5 10 U1 , j 0 Basic Tunneling Ionization: This separation is called “Rcritical” (Bandrauk, Seideman, Corkum, Ivanov)

6. Dynamics of 1 electron in field: Unified atom limit Dipole moment

7. Separated atom limit.

8. Intermediate case. Strongly driven gerade  ungerade transition creates large dipole moments, compared to atoms or even-charged ground state molecules.

9. Data and calculations for H2+: Better: Zuo and Bandrauk, PRA (1995), Data: Gibson et al., PRL (1997) End of story? This is from an ion. Also, not pump-probe, so a number of assumptions were made.

10. Simple 1-D 1-e- calculation:

11. Simple model for Rc • For H2+, Rc should be 3/(0.5) = 6, which is close. • Want to test in the neutral using pump-probe, since most experiments start in the neutral species. Find condition where the inner barrier just equals the energy of the ground state:

12. Resonant excitation provides a mechanism for studying the neutral Using pump-probe techniques, we can control R. Resonant excitation follows a cos()2 pattern, producing a well-aligned and well-defined sample. This gives: <cos()2> = 0.6at room temperature with one laser pulse. [For unaligned samples <cos()2> = 0.33]

13. Laser System • Ti:Sapphire 800 nm Oscillator with a Multipass Amplifier • 750 J pulses @ 1 KHz • Transform Limited, 30 fs pulses • TOPAS Optical Parametric Amplifer: 490nm – 2000nm

14. Ion Time-of-Flight Spectrometer

15. Nitrogen TOF Spectrum

16. Vibrational period (fs)‏ X-B coupling wavelength (nm)‏ Wavepacket motion in the B-state of I2 gives <R>(t)

17. Ionization vs. R • We know <R(t)> from the motion on the B state. • Can convert from time to R(t).

18. B-state wavepacket simulation

19. IpRc = 3.01 Wavelength check: Shorter wavelength: larger outer turning point longer vibrational period

20. Really want to study the ground state! • Can we return the wavepacket to the X-state? • Yes, with a pump-dump scheme:

22. Returning wavefunction in X-state (2,1) (2,0)

23. Single ionization: I2+

24. Diatomic molecules in strong fields:  N2+ + N0+ (15.1 eV)  N3+ + N1+ (17.8 eV)  N4+ + N2+ (30.1 eV) • N2  N21+ N22+ N1+ + N1+ N23+ N1+ + N2+N24+ N2+ + N2+N25+ N3+ + N2+N26+ N3+ + N3+ N27+ N4+ + N3+

26. Why is the observation of Charge-Asymmtric Dissociation so important? • It represents direction excitation of states with energies in the VUV spectral region. (Up to 30eV in N26+). • Excitation involves many photons. • Have seen everything up to I212+  I5+ + I7+. • Optimizing excitation process may lead to amplifiers in the VUV as inversions are likely occurring. • May be a new high-harmonic source. • CAD is a ubiquitous and robust process:There must be something generic about the structure of homonuclear diatomic molecules.

27. What is so special about (even) charged diatomic molecules? Ground state is a far off-resonant covalent state. Above this is a pair of strongly coupled ionic states. Only a weak coupling between them.

28. 3-Level Model System This system can be solved exactly for the n-photon Rabi frequency!

30. Three-level systems: “V”: “”: Now the “”:

31. Diatomic Dications • How are asymmetric states populated? Is it through multiphoton transitions in the -system? • (2,0) must have binding. In fact, it is an excimer-like system, bound in upper state, unbound in lower state. Can we trap population in this state? • Can we make a multiphoton pumped excimer laser? • We have evidence for bound population. • Evidence for 3- excitation – but is it due to the  structure???

32. Need spectroscopic information • Namely, there should be (2,0)g and (2,0)u. • TOF spectroscopy not sensitive enough to distinguish them. • However, coherent 12 fields provide an interesting spectroscopic tool.

33. What are 12 fields? If you add a fundamental laser frequency and its second harmonic, you can break spatial symmetry.

34. Molecular dissociation • Charge-asymmetric dissociation is generally spatially symmetric (with a single frequency pulse).I.e., for I2+ + I, the I2+ goes to the left as much as to the right. • However, with a spatially-asymmetric laser field can break the spatial symmetry of the dissociation.

35. Molecular dissociation,with a 12 field Phase = 0 Phase = /2

36. Eigenstates vs. Observables • Observable: I2+ + I  (2,0) or (0,2) (left or right) • Eigenstates: (2,0)g ~ (2,0) + (0,2) (2,0)u ~ (2,0) – (0,2) • Eigenstates must dissociate spatially symmetric.  Therefore, a spatial asymmetry requires a coherent superposition of g and u states, which is only possible in a spatially asymmetric field.

37. Simple tunneling model • g and u states strongly coupled – diagonalize in a dc field. • Assuming ionization into the lowest lying (down field) level. • Project back onto field-free states and calculate spatial asymmetry.

38. Spatial asymmetry as a function of R • We can measure the spatial asymmetry of the (2,0) dissociation channel by populating the B-state of I2.

39. What do we learn from 12 fields? • In strong-field ionization, it appears that the field induced states are populated directly through tunneling ionization. • It is not the case that ionization populates the ground state and the asymmetric states are then populated through the -system. (Very difficult to reproduce the spatial asymmetry dependence.) • Really must consider the field-induced molecular structure to understand strong-field ionization. • Also, raises interesting questions about decoherence and dephasing.

40. Conclusions • Strong fields offer unprecedented control over t, R, and . • We also have considerable control over nuclear wavepackets. • Can measure strong field processes as a function of these variables. • Can investigate the structure of unusual (highly ionized) molecules.