Principles for determining mechanistic pathways from observable quantum control data
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.
scientific article; zbMATH DE number 5312665