intense laser interactions with h 2 and d 2 a computational project
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Intense LASER interactions with H 2 + and D 2 + : A Computational Project.  Ted Cackowski. Project Description. Assisting the multiple-body-mechanics group at KSU with calculations of H 2 + /D 2 + behavior under the influence of a short, yet intense laser pulse. Motivation.

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project description
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
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
Modes of Operation
  • Schrödinger\'s Equation

and the associated quantum mechanics

  • Fortran 90/95
scales of physical interest
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
Diatomic Hydrogen
  • Two protons, two electrons
  • Born-Oppenheimer Approximation
    • First Electrons, then Nuclei
h 2 molecule
H2+ Molecule
  • There are two separate pulses.
  • Ionizing pulse gives us our computational starting point
  • Franck-Condon Approximation
note on completeness
Note on Completeness
  • The Overlap Integral
    • Where, |FCV|2 are bound/unbound probabilities
  • Unavoidable dissociation by ionization
  • Controlled dissociation
mechanics
Mechanics
  • The second pulse is the dissociating pulse.
  • We now have the Hamiltonian of interest
  • Dipole Approximation
linear methods
Linear Methods
  • We expand Yinitialonto 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
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)
notable observables
Notable Observables
  • Angular distribution of dissociation

as it depends on:

    • Pulse Duration
    • Pulse Intensity
    • Carrier Envelope Phase (CEP)
my work
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
conclusions
Conclusions
  • Rotational inertia plays an important role
  • Pulse intensity is critical
  • Further analysis will be required for pulse length and CEP
future work
Future Work
  • Simulate H2+ under various CEP initial conditions
  • Confidence Testing
  • Data Interpretation
  • Connect with JRM affiliates
special group thanks
Special Group Thanks
  • Dr. Esry
  • Fatima Anis
  • Yujun Wang
  • Jianjun Hua
  • Erin Lynch
special reu thanks
Special REU Thanks
  • Dr. Weaver
  • Dr. Corwin
  • Participants
  • Jane Peterson
bibliography
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

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