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

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Dec 1, 2013 (3 years and 6 months ago)

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Ionization of the Hydrogen
Molecular Ion by Ultrashort
Intense Elliptically Polarized
Laser Radiation
Ryan DuToit
Xiaoxu 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?