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, S 1 and S 2 , adopting a generalized ( S 1 + S 2 ) 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 sub-dynamics living in two orthogonal four-and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The interpretative advantages stemming from such a remarkable and non-intuitive nesting are systematically exploited and various intriguing features consequently emerging 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 as well time-dependent versions of our Hamiltonian model is briefly discussed.

Landau-Majorana-Stückelberg-Zener dynamics driven by coupling for two interacting qutrit systems

“…III C, exhibits a constant maximum level of entanglement (1/2) during the evolution. Such a peculiar feature is independent of the specific time-dependence of the field and it may be understood at the light of the analysis reported in 53 . There the authors analyse the same two-qutrit model but with time-independent fields.…”

“…In Ref. 53 it was shown that two dynamically invariant Hilbert subspaces exist: one of dimension four spanned by {|10 , |01 , |0 − 1 , |−10 } and the other one of dimension five spanned by {|11 , |1 − 1 , |00 , |−11 , |−1 − 1 }. They are related to the two eigenvalues (±1) of the constant of mo-tionK = cos(πΣ z tot ),…”

“…It is easy to see that, considering the time-independent case, such states result to be the eigenstates of the Hamiltonian 53 . So, this model, in this specific case, presents a peculiar characteristic consisting in maintaining its steady states also when the Hamiltonian parameters are time-dependent.…”

“…Secondly, we show how such an effect may be exploited for two relevant applications: the estimation of the strength of the coupling parameters and the possibility of generating asymptotically entangled states of the two qutrits by appropriately setting the slope of the ramp. Our symmetry-based analysis of the Hamiltonian model, usefully used in several problems [52][53][54][55] , allows us to consider also effects stemming from the presence of a noisy field component.…”

An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

“…[42], which, besides having been already applied to treat timedependent spin Hamiltonian models beyond the relatively simpler s = 1/2 case [46,48,49], has even the merit of offering tools to solve a wide class of special DREs not considered in the specialized literature so far.…”