Singular extremals for the time-optimal control of dissipative spin 1/2 particles

TL;DR

This paper investigates the role of singular extremals in the time-optimal control of a dissipative spin 1/2 particle, providing explicit control laws and the first experimental demonstration using NMR techniques.

Contribution

It introduces the first experimental demonstration of singular extremals in quantum control with bounded amplitudes and explicitly determines the control law for a simple case.

Findings

Explicit control law for the simple case analyzed.

First experimental demonstration of singular extremals in quantum systems.

Validation of control strategies using nuclear magnetic resonance.

Abstract

We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.