0000000000724335
AUTHOR
Quentin Ansel
Optimal control of inhomogeneous spin ensembles : applications in NMR and quantum optics
The goal of this thesis is to apply optimal control theory to the dynamics ofinhomogeneous spin ensembles. The first part focuses on the control of a spin ensemble coupled to a cavity. The theory is introduced in detail, and a general method to efficiently control spins ispresented. Several pulses are derived in the bad/good cavity regimes using numerical optimal control techniques. Additionally, non-linear generalized functions are used in order to derivesimple approximated solutions. In a second step, the problem of spin echo Signal to Noise Ratio maximization is investigated, and maximization conditions are derived. It is shown that new pulses are superior to state-of-the-art square puls…
Calculus of Variation and Path-Integrals with Non-Linear Generalized Functions
The calculus of variation and the construction of path integrals is revisited within the framework of non-linear generalized functions. This allows us to make a rigorous analysis of the variation of an action that takes into account the boundary effects, even when the approach with distributions has pathological defects. A specific analysis is provided for optimal control actions, and we show how such kinds of actions can be used to model physical systems. Several examples are studied: the harmonic oscillator, the scalar field, and the gravitational field. For the first two cases, we demonstrate how the boundary cost function can be used to assimilate the optimal control adjoint state to th…