Principles for determining mechanistic pathways from observable quantum control data
type: Item
instance of: scholarly article
title: Principles for determining mechanistic pathways from observable quantum control data
zbMATH Open document ID: 1180.81073
author: Richard Sharp
author: Abhra Mitra
author: Herschel Rabitz
publication date: 2008-08-15T00:00:00Z
review text: The paper discusses fundamental issues related to the mechanism extraction from observable quantum control data. In the introductory section the authors present the origin and goals of Hamiltonian encoding (HE). In section 2 the HE is summarily discussed from the standpoint of field modulation. For that a dipole coupling between the quantum system and a shaped laser pulse is introduced and the corresponding matrix elements of the time evolution operator \(U(t)\) is written in a series expansion form a la Dyson. At this point the control field is decomposed using some basis functions \(\varepsilon_n(t)\). In this way each term in the Dyson expansion can be interpreted as the complex amplitude of a transition pathway. Next, encoding each component of the control field, the transition matrix elements \(U_{ba}(s)\) can be written as a sum over all pathway amplitudes of all orders. The authors are pointing out that precisely this is the strength of the HE method, since otherwise resorting to laboratory data the direct access to the Hamiltonian and the wavefunction would not be possible. Section 3 debates the representation of the control field within three distinct schemes: amplitude modulation, phase modulation and simultaneous modulation of the control amplitudes and phases. The corresponding modulated equations and their solutions are disccussed in sect. 4 and 5 along with the pathways extractions from observable data. It is stressed out that in general the number of equations obtained via the process of encoding is much larger than the number of variables to be extracted and therefore multiple solutions are unlikely to occur except those related to each other by simple symmetries. Sections 6 and 7 illustrate by means of a simple analytical model how does HE method work.
reviewed by: Serban Misicu
Mathematics Subject Classification ID: 81Q93
Mathematics Subject Classification ID: 81P45
Mathematics Subject Classification ID: 81P70
Mathematics Subject Classification ID: 94A14
zbMATH DE Number: 5312665
zbMATH Keywords: quantum control
zbMATH Keywords: Hamiltonian encoding
zbMATH Keywords: Dyson series
MaRDI profile type: Publication
full work available at URL: s10910-007-9298-7
OpenAlex ID: W1987021225
cites work: Coherent Control of Quantum Dynamics: The Dream Is Alive
cites work: On the inversion of quantum mechanical systems: Determining the amount and type of data for a unique solution
cites work: Q4394946
DOI: 10.1007/S10910-007-9298-7
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 5312665