Reverse engineering protocols for controlling spin dynamics

Qi Zhang,D Guéry-Odelin,Xi Chen

doi:10.1038/s41598-017-16146-2

Abstract

We put forward reverse engineering protocols to shape in time the components of the magnetic field to manipulate a single spin, two independent spins with different gyromagnetic factors, and two interacting spins in short amount of times. We also use these techniques to setup protocols robust against the exact knowledge of the gyromagnetic factors for the one spin problem, or to generate entangled states for two or more spins coupled by dipole-dipole interactions.

Highlights

We put forward reverse engineering protocols to shape in time the components of the magnetic field to manipulate a single spin, two independent spins with different gyromagnetic factors, and two interacting spins in short amount of times
We propose to work out such an inversion with three different formulations of a spin 1/2 in a time-dependent magnetic field: (i) the direct reversing of the time evolution operator, (ii) the inversion of Madelung representation formulation of the problem and (iii) the inversion of the precession equations
We have proposed a reverse engineering approach to shape a time-dependent magnetic field to manipulate a single spin, two spins with different gyromagnetic factors, and two or more interacting spins in short amount of times

Summary

OPEN Reverse engineering protocols for controlling spin dynamics

We put forward reverse engineering protocols to shape in time the components of the magnetic field to manipulate a single spin, two independent spins with different gyromagnetic factors, and two interacting spins in short amount of times. Reverse engineering protocols can be worked out analytically, see refs[29,30], Its performance when combined with a given constraint has been compared with optimal control in ref.[27] They provide an efficient way to drive spin-1/2 system[31,32], or, equivalently, a generic two-level system with cold atoms[33,34,35]. We setup (i) a few general procedures for reverse engineering, (ii) an algorithm to build up the smooth variations in time of the magnetic field components that one should apply to spin flip a spin 1/2 (or connect two points on the Bloch sphere) in an arbitrary short amount of time, (iii) expand the parameter space of those solutions to fulfill extra requirements such as the robustness of the operation or the application of the transformation to two spins with different coupling strength to the magnetic field. We discuss how those protocols shall be modified to take into account interactions between spins, and generate in an optimal amount of time entangled states of two or more spins

Results

Discussion

Additional Information