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

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.

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

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

Process Overview

Physical Situation

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)

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

Figure 1

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

Figure 2

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

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

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

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)

Channels

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

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

Afore Mentioned Figure

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

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

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

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

Bibliography Figure 1 from Max Planck institute for Quantum Optics website Figure 2 from Wikipedia, “Frank-Condon” http://images.google.com/imgres?imgurl=http://www.mpq.mpg.de/~haensch/grafik/3DdistributionD.gif&imgrefurl=http://www.mpq.mpg.de/~haensch/htm/Research.htm&h=290&w=420&sz=24&hl=en&start=0&um=1&tbnid=rOBflIUYzSm7xM:&tbnh=86&tbnw=125&prev=/images%3Fq%3DH2%252B%26svnum%3D10%26um%3D1%26hl%3Den%26sa%3DN