The quantum brachistochrone problem for an arbitrary spin in a magnetic field

TL;DR

This paper investigates the quantum brachistochrone problem for arbitrary spin systems on rotational manifolds, deriving conditions for optimal evolution based on the geometry of these manifolds.

Contribution

It extends the quantum brachistochrone problem to arbitrary spin systems and characterizes the geometry of their evolution manifolds.

Findings

Derived Fubini-Study metrics for spin-$s$ rotational manifolds

Established conditions for optimal quantum evolution on these manifolds

Analyzed the geometric structure of spin system evolutions

Abstract

We consider quantum brachistochrone evolution for a spin-$s$ system on rotational manifolds. Such manifolds are determined by the rotation of the eigenstates of the operator of projection of spin-$s$ on some direction. The Fubini-Study metrics of these manifolds are those of spheres with radii dependent on the value of the spin and on the value of the spin projection. The conditions for optimal evolution of the spin-$s$ system on rotational manifolds are obtained.