Transcript Powerpoint from Oral presentation (4.034Mb)

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 (atomicscale 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?