Nonlinear Spectroscopy and Bilinear Control Theory Using light to - PowerPoint PPT Presentation

Sep 04, 2023 •406 likes •502 views

Nonlinear Spectroscopy and Bilinear Control Theory Using light to estimate stuff NE 155, Spring 2016 Kunal Marwaha Huh? Research project! Prof. Birgitta Whaley (quantum information) On-and-off since Spring 2015 Computational science: theory

Nonlinear Spectroscopy and Bilinear Control Theory Using light to estimate stuff NE 155, Spring 2016 Kunal Marwaha
Huh? Research project! Prof. Birgitta Whaley (quantum information) On-and-off since Spring 2015 Computational science: theory + simulations
Goal Find physical parameters of molecular system Using spectroscopy! How? http://cdn.phys.org/newman/gfx/news/hires/2013/schrodingerequation1.jpg https://www.mbi-berlin.de/de/research/projects/3.1/topics/history/Subproject5/p3_experiment.jpg
Idea Let’s find a space where equations are linear. Then, we invert! http://i.stack.imgur.com/hx8PR.png We can recursively expand perturbations:
Control Theory Model systems from input-output measurements. http://1.bp.blogspot.com/_U3umjVzCXTA/TJ2qDnhANMI/AAAAAAAAAPk/AHIC2YGuO1U/s1600/I-O-block+diagram.gif https://users.ece.cmu.edu/~koopman/des_s99/control_theory/stateq.gif Hamiltonian is time-dependent!
Pulses Experiments use “ultrafast pulses” (femto-sec) Approximated as Or as rectangular pulse Dirac delta http://idav.ucdavis.edu/~okreylos/PhDStudies/Winter2000/BoxFilter.gif https://upload.wikimedia.org/wikibooks/en/thumb/c/c2/NM16_10.gif/380px-NM16_10.gif
Things simplify! Now we’re linear! To simulate the forward direction, we input A and x(0) to get x(t).
Remember the goal... Find physical parameters: ● transition dipole ● energy splitting ● energy coupling http://sebastianraschka.com/images/faq/visual-backpropagation/nonconvex-cost.png It’s harder than expected, but some iterative methods might work.
Code Part 1: Forward direction http://thumbs.dreamstime.com/z/binary-code-abstract-background- animation-digits-falling-downwards-against-black-42622233.jpg → Does the simulated data match experiment? Part 2: Inversion direction → Can we get physical parameters from data?

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