1. Ionization of the Hydrogen Molecular Ion by Ultrashort Intense Elliptically Polarized Laser Radiation Ryan DuToit Xiaoxu Guan (Mentor) Klaus Bartschat (Mentor)

2. Overview Motivation – Intense and ultrashort light pulses have opened up new avenues to trace and steer electronic motion in atomic and molecular systems (atomic- scale electron dynamics). – Generalize previous results to elliptical polarization

3. Overview Theoretical Formulation – Discretization of system using prolate spheroidal coordinates – Solve time dependent Schrödinger Equation (complicated partial differential equation)

4. Overview Results – Survival probability: orientation dependence – Angular distribution of photoelectron Outlook and Future Work

5. Introduction to Simulation Simulate short laser pulse acting on a H 2 + ion 10 18 attoseconds = 1 second More attoseconds in one second than there are seconds in the age of the universe! The electric field interacts with the electron, which is what we are interested in.

6. Prolate Spheroidal Coordinate System

7. Electric Field Linear Polarization Elliptical Polarization

9. Electric Field

10. Theoretical Foundation Need to solve the time dependent Schrödinger Equation for the electron: Using time propagation, solution is:

11. Theoretical Foundation Exponential of large matrix is a MASSIVE computational task Finite-Element Discrete-Variable Representation (FE-DVR) – Divide space into separate elements – Expand wavefunction into basis of Lagrange polynomials – Use Gaussian quadrature to approximate integrals Transform H into a smaller h matrix – Short iterative Lanczos algorithm

13. Solving Wavefunction After expanding into basis: Matrix h is orders of magnitude smaller than H – Rank of H ≈ 200,000 – Rank of h ≈ 15 Diagonalization goes like This is an approximation

14. Execution Code written in FORTRAN Use MPI for parallel programming Job runs on cluster here at Drake – 8 processors, 8 cores per processer = 64 threads Entire run takes 2-6 hours

15. Theoretical Foundation Once we have wave function of electron, we extract physical information via operators. Survival Probability Angular distribution of photoelectron

17. What is angular distribution? Probability of electron being ejected at a given angle Quantum effects easy to see

18. Parallel Electric Field 40 eV70 eV150 eV 200 eV 250 eV 300 eV

19. Perpendicular Electric Field 40 eV70 eV150 eV 200 eV 250 eV 300 eV

20. Circular Electric Field 40 eV 70 eV150 eV 200 eV250 eV300 eV

21. Conclusions Results confirm validity of our numerical implementation Orientation of polarization has significant impact on final result

22. Future Work Use longer wavelengths (infrared light) Include nuclear motion Address more complex molecular systems

23. Acknowledgements Mentors – Dr. Xiaoxu Guan – Dr. Klaus Bartschat Project support through NSF

24. Questions?