Principles for determining mechanistic pathways from observable quantum control data

Richard Sharp, Abhra Mitra, Herschel Albert Rabitz

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Hamiltonian encoding (HE) methods have been used to understand mechanism in computational studies of laser controlled quantum systems. This work studies the principles for extending such methods to extract control mechanisms from laboratory data. In an experimental setting, observables replace the utilization of wavefunctions in computational HE. With laboratory data, HE gives rise to a set of quadratic equations for the interfering transition amplitudes, and the solution to the equations reveals the mechanistic pathways. The extraction of the mechanism from the system of quadratic equations raises questions of uniqueness and solvability, even in the ideal case without noise. Symmetries are shown to exist in the quadratic system of equations, which is generally overdetermined. Therefore, the mechanism is likely to be unique up to these symmetries. Numerical simulations demonstrate the concepts on simple model systems.

Original languageEnglish (US)
Pages (from-to)142-171
Number of pages30
JournalJournal of Mathematical Chemistry
Volume44
Issue number1
DOIs
StatePublished - Jul 1 2008

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Applied Mathematics

Keywords

  • Control mechanism
  • Hamiltonian Encoding
  • Quantum control
  • Quantum theory
  • Schrödinger equation

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