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Intense LASER interactions with H 2 + and D 2 + : A Computational Project

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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Intense LASER interactions with H 2 + and D 2 + : A Computational Project

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

  2. 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.

  3. 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

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

  5. Process Overview

  6. Physical Situation

  7. 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)

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

  9. Figure 1

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

  11. Figure 2

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

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

  14. 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

  15. 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)

  16. Channels

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

  18. 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

  19. Afore Mentioned Figure

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

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

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

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

  24. 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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