Elliptic functions and efficient control of Ising spin chains with unequal couplings

TL;DR

This paper develops a method for optimal control of three-spin chains with unequal Ising couplings, using elliptic functions to derive time-efficient pulse sequences for creating multiple quantum coherences.

Contribution

It introduces a novel approach employing elliptic functions and geodesic calculations to achieve time-optimal control in complex spin systems with unequal couplings.

Findings

Derived explicit time-optimal pulse sequences for three-spin chains.

Connected geodesic solutions to elliptic integrals for control optimization.

Achieved efficient creation of multiple spin coherences in experimental settings.

Abstract

In this article, we study optimal control of dynamics in a linear chain of three spin 1/2, weakly coupled with unequal Ising couplings. We address the problem of time-optimal synthesis of multiple spin quantum coherences. We derive time-optimal pulse sequence for creating a desired spin order by computing geodesics on a sphere under a special metric. The solution to the geodesic equation is related to the nonlinear oscillator equation and the minimum time to create multiple spin order can be expressed in terms of an elliptic integral. These techniques are used for efficient creation of multiple spin coherences in Ising spin-chains with unequal couplings.