Abstract
It has been theoretically demonstrated that two spins (qubits or qutrits), coupled by exchange interaction only, undergo a coupling-based joint Landau-Majorana-St\"uckelberg-Zener (LMSZ) transition when a linear ramp acts upon one of the two spins. Such a transition, under appropriate conditions on the parameters, drives the two-spin system toward a maximally entangled state. In this paper, effects on the quantum dynamics of the two qudits, stemming from the Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, are investigated qualitatively and quantitatively. The enriched Hamiltonian model of the two spins, shares with the previous microscopic one the same C2-symmetry which once more brings about an exact treatment of the new quantum dynamical problem. This paper transparently reveals that the DM and d-d interactions generate independent, enhancing or hindering, modifications in the dynamical behaviour predicted for the two spins coupled exclusively by the exchange interaction. It is worthy noticing that, on the basis of the theory here developed, the measurement of the time evolution of the magnetization in a controlled LMSZ scenario, can furnish information on the relative weights of the three kinds of couplings describing the spin system. This possibility is very important since it allows in principle to legitimate the choice of the microscopic model to be adopted in a given physical scenario.
Highlights
The anisotropic interaction term known as DzyaloshinskiiMoriya (DM) interaction or antisymmetric exchange interaction was first phenomenologically introduced by I
This paper transparently reveals that the DM and d-d interactions generate independent, enhancing or hindering, modifications in the dynamical behavior predicted for the two spins coupled exclusively by the exchange interaction
In this work we study the effects of the DM and d-d interactions in a system of two interacting three-level systems, too, where the occurrence of coupling-based LMSZ transitions has been analytically demonstrated [39]
Summary
The anisotropic interaction term known as DzyaloshinskiiMoriya (DM) interaction or antisymmetric exchange interaction was first phenomenologically introduced by I. Moriya furnished a theoretical derivation of such an interaction term grounded on a robust general theory of the superexchange interaction including the spin-orbit coupling [2] This anisotropic interaction term arises when antiferromagnetic systems present low symmetry and strongly depends on the geometry of the system as shown by T. Different sources of incoherences in the experimental framework, can influence the system dynamics [35,36,37,38], like relaxation processes (e.g., spontaneous emission) or interaction with a surrounding environment (e.g., nuclear spin bath) Such an aspect has been taken into account in the previous paper [25] and is analyzed here, too, in the presence of the DM interaction.
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