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

•The Fubini–Study metrics of rotational manifolds of spin-s system are considered.•It is shown that they are spheres.•The brachistochrone problem for a spin-s system on rotational manifolds is examined.

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.