Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits

Abstract

In this paper, we investigate the quantum dynamics of two spin-1 systems, Ŝ1and Ŝ2, adopting a generalised (Ŝ1+ Ŝ2) 2-nonconserving Heisenberg model. We show that due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two subdynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result, consisting of the fact that in the four-dimensional dynamically invariant subspace, the two qutrit quantum dynamics, with no approximations, is equivalent to that of two noninteracting spin-1/2s. The interpretative advantages stemming from such a remarkable and nonintuitive nesting are systematically exploited, and various intriguing features that consequently emerge in the dynamics of the two qutrits are deeply scrutinised. The possibility of exploiting the dynamical reduction brought to light in this paper for exactly treating the time-dependent versions of our Hamiltonian model is briefly discussed as well.