1. Intense LASER interactions with H2+ and D2+: A Computational Project
 Ted Cackowski

2. Project Description
Assisting the multiple-body-mechanics group at KSU with calculations of H2+/D2+ behavior under the influence of a short, yet intense laser pulse.

3. Motivation To explore the validity of the Axial Recoil Approximation
Exploring the quantum mechanics of H2+/D2+ in a time-varying electric field under various experimental conditions
Exploring the quantum dynamics there afterward

4. Modes of Operation Schrödinger's Equation
and the associated quantum mechanics
Fortran 90/95

5. Process Overview

6. Physical Situation

7. Scales of Physical Interest
Laser Intensity: ~1E14 watts/cm2
Pulse Length: ~7E -15 s (femtoseconds)
Frequency: 790E-9 m (nanometers)
H2/D2 Nuclear Separation:
~3E-10 m (angstroms)

8. Diatomic Hydrogen Two protons, two electrons
Born-Oppenheimer Approximation
First Electrons, then Nuclei

9. Figure 1

10. H2+ Molecule There are two separate pulses.
Ionizing pulse gives us our computational starting point
Franck-Condon Approximation

11. Figure 2

12. Note on Completeness The Overlap Integral
Where, |FCV|2 are bound/unbound probabilities
Unavoidable dissociation by ionization
Controlled dissociation

13. Mechanics The second pulse is the dissociating pulse.
We now have the Hamiltonian of interest
Dipole Approximation

14. Linear Methods We expand Yinitial onto an orthonormal basis
Overlap integral / Fourier’s trick
We then generate the matrix H as in
Propagate the vector through time using an arsenal of numerical techniques

15. Data Production
After producing a nuclear wave function associated with a particular dissociation channel, any physical observable can be predicted.
“Density Plots” are probability density plots (Ψ*Ψ)

16. Channels

17. Notable Observables Angular distribution of dissociation
as it depends on:
Pulse Duration
Pulse Intensity
Carrier Envelope Phase (CEP)

18. My Work Computational Oversight Two Fortran Programs
First: Calculate the evolution of the wave function when the Electric field is non-negligible
Second: Calculate the evolution of the wave function when the Electric field is negligible
Produce measurable numbers

19. Afore Mentioned Figure

24. Conclusions Rotational inertia plays an important role
Pulse intensity is critical
Further analysis will be required for pulse length and CEP

25. Future Work Simulate H2+ under various CEP initial conditions
Confidence Testing
Data Interpretation
Connect with JRM affiliates

26. Special Group Thanks Dr. Esry Fatima Anis Yujun Wang Jianjun Hua
Erin Lynch

27. Special REU Thanks
Dr. Weaver
Dr. Corwin
Participants
Jane Peterson

28. Bibliography
Figure 1 from Max Planck institute for Quantum Optics website
Figure 2 from Wikipedia, “Frank-Condon”