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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)

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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

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Overview Theoretical Formulation – Discretization of system using prolate spheroidal coordinates – Solve time dependent Schrödinger Equation (complicated partial differential equation)

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Overview Results – Survival probability: orientation dependence – Angular distribution of photoelectron Outlook and Future Work

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Introduction to Simulation Simulate short laser pulse acting on a H 2 + ion 10 18 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.

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Prolate Spheroidal Coordinate System

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Electric Field Linear Polarization Elliptical Polarization

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Electric Field

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Theoretical Foundation Need to solve the time dependent Schrödinger Equation for the electron: Using time propagation, solution is:

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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

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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

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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

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Theoretical Foundation Once we have wave function of electron, we extract physical information via operators. Survival Probability Angular distribution of photoelectron

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What is angular distribution? Probability of electron being ejected at a given angle Quantum effects easy to see

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Parallel Electric Field 40 eV70 eV150 eV 200 eV 250 eV 300 eV

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Perpendicular Electric Field 40 eV70 eV150 eV 200 eV 250 eV 300 eV

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Circular Electric Field 40 eV 70 eV150 eV 200 eV250 eV300 eV

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Conclusions Results confirm validity of our numerical implementation Orientation of polarization has significant impact on final result

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Future Work Use longer wavelengths (infrared light) Include nuclear motion Address more complex molecular systems

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Acknowledgements Mentors – Dr. Xiaoxu Guan – Dr. Klaus Bartschat Project support through NSF

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