Quantum Hamiltonian and dipole moment identification in presence of large control perturbations

¹ UniversitéParis-Dauphine, PSL Research University, CNRS, Ceremade, 75016 Paris, France.
fu@ceremade.dauphine.fr
² Institut Universitaire de France, 1 Rue Descartes, 75231 Paris cedex 05, France.
Gabriel.Turinici@dauphine.fr

Received: 26 September 2014
Revised: 20 January 2016
Accepted: 17 May 2016

Abstract

The problem of recovering the Hamiltonian and dipole moment is considered in a bilinear quantum control framework. The process uses as inputs some measurable quantities (observables) for each admissible control. If the implementation of the control is noisy the data available is only in the form of probability laws of the measured observable. Nevertheless it is proved that the inversion process still has unique solutions (up to phase factors). Both additive and multiplicative noises are considered. Numerical illustrations support the theoretical results.