Ionization of the Hydrogen Molecular Ion by Ultrashort Intense Elliptically Polarized Laser

Radiation

Ryan DuToitXiaoxu Guan (Mentor)

Klaus Bartschat (Mentor)

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

Overview

• Theoretical Formulation– Discretization of system using prolate spheroidal

coordinates– Solve time dependent Schrödinger Equation

(complicated partial differential equation)

Overview

• Results– Survival probability: orientation dependence– Angular distribution of photoelectron

• Outlook and Future Work

Introduction to Simulation

• Simulate short laser pulse acting on a H2+ ion

• 1018 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.

Prolate Spheroidal Coordinate System

Electric Field

Linear Polarization Elliptical Polarization

Electric Field

Theoretical Foundation

• Need to solve the time dependent Schrödinger Equation for the electron:

• Using time propagation, solution is:

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

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

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

Theoretical Foundation

• Once we have wave function of electron, we extract physical information via operators.

• Survival Probability

• Angular distribution of photoelectron

What is angular distribution?

• Probability of electron being ejected at a given angle

• Quantum effects easy to see

Parallel Electric Field

40 eV 70 eV 150 eV

200 eV 250 eV 300 eV

Perpendicular Electric Field

40 eV 70 eV 150 eV

200 eV 250 eV 300 eV

Circular Electric Field

40 eV 70 eV 150 eV

200 eV 250 eV 300 eV

Conclusions

• Results confirm validity of our numerical implementation

• Orientation of polarization has significant impact on final result

Future Work

• Use longer wavelengths (infrared light)

• Include nuclear motion

• Address more complex molecular systems

Acknowledgements

• Mentors– Dr. Xiaoxu Guan – Dr. Klaus Bartschat

• Project support through NSF

Questions?