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Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control

Ulisses Alves Maciel Neto 1 Paulo Sergio Pereira da Silva 2 Pierre Rouchon 3, 4
4 QUANTIC - QUANTum Information Circuits
MINES ParisTech - École nationale supérieure des mines de Paris, ENS Paris - École normale supérieure - Paris, SU - Sorbonne Université, Inria de Paris
Abstract : 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 H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works have constructed a Lyapunov based stabilizing feedback in a convenient H 1-norm that assures local L ∞convergence of the initial state M0(ω) to the south pole, solving locally the approximate steering problem from M0 towards the south pole. However, the corresponding control law contains a comb of periodic π-Rabi pulses (Dirac impulses), corresponding to strongly unbounded control. The present work propose smooth uniformly bounded time-varying controls for this local steering problem, where the Rabi pulses are replaced by adiabatic following smooth pulses. Furthermore, simulations show that this new strategy produces faster convergence, even for initial conditions "relatively far" from the south pole.
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Preprints, Working Papers, ...
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https://hal-mines-paristech.archives-ouvertes.fr/hal-03325203
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Submitted on : Tuesday, August 24, 2021 - 2:41:04 PM
Last modification on : Tuesday, January 11, 2022 - 11:16:07 AM
Long-term archiving on: : Friday, November 26, 2021 - 9:24:16 AM

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  • HAL Id : hal-03325203, version 1

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Ulisses Alves Maciel Neto, Paulo Sergio Pereira da Silva, Pierre Rouchon. Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control. 2021. ⟨hal-03325203⟩

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