Control of an ensemble of half-spin systems replacing Rabi pulses by adiabatic following.

• Ano de defesa: 2021
• Autor(a) principal: Maciel Neto, Ulisses Alves
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Bloch equations; Control of partial differential equations; Controle de equações diferenciais parciais; Equações de Bloch; Espaços de Sobolev; Estabilização de Lyapunov; Lyapunov stabilization; Nonlinear systems; Quantum systems; Sistema quântico; Sistemas não lineares
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/3/3139/tde-08112021-112808/

One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M(t, ·) belongs to the Sobolev space H1((?*, ?*), S2) where the parameter ? ? (?*, ?*) is the Larmor frequency. Previous works have constructed a Lyapunov based stabilizing feedback in a convenient H1- norm that assures local L?-convergence of the initial state M0(?) to -e3, solving locally the approximate steering problem from M0 close enough to -e3 to a final condition -e3. However, its control law contains a comb of periodic ?-Rabi pulses (Dirac impulses), which represents an unbounded control. The present work shows the existence of a bounded control law for this local steering problem, where the Rabi pulses are replaced by adiabatic pulses (adiabatic following technique). Furthermore, simulations have shown that this new strategy produces faster convergence, even for initial conditions \"relatively far\" from the target state