EPR And Quantum Spin Dynamics In The Supermolecule-Dimer

The theoretical and experimental studies on the quantum effects of molecule-magnet systems are not only of fundamental importance in modern physics, but also lead to the potential applications in information storage, quantum computing and quantum information process. Especially, the supermolecule-dimer is an excellent candidate in designing the quantum computing devices. This paper is devoted to three aspects of the theoretical investigations on the quantum effects of the magnetic molecule-dimer. After a brief indtroduction of the theoretical and experimental studies in the literature we , firstly, study the multi-high-frequency electron paramagnetic resonance(EPR) transitions in the supermolecule-dimer [Mn₄]₂ employing the high-order perturbation method and obtain the high-order corrections of level splitting. The EPR-peak positions are calculated in terms of the eigenstates at various frequencies. From the best fit of theoretical level splittings with the measured values we obtain the anisotropy constant and exchange coupling which are in agreement with the corresponding values of experimental observation. Our theoretical studies shine more light on the prediction of Hill et al that the two Mn₄ units within the dimer are coupled quantum mechanically by the antiferromagnetic exchange interaction and the supermolecule-dimer behaviors in analogy with artificially fabricated quantum dots. Next, we study the entanglement in the supermolecule-dimer [Mn₄]₂ with respect to energy eigenvectors. The conventional von Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M=M₁+M₂=-9 to 0. It is shown that the von Neumann entropy is not a monotonic function of the coupling strength. We also present the time-evolution of entanglement from various initial states. Finally, we investigate quantum dynamics and geometric phase of the spin dimer. An exact solution of time-dependent Schrodinger equation for two coupled spins of arbitrary values in a rotating magnetic field is obtained by means of a time-dependent gauge transformation technique. The AA phase and time-evolution operator are obtained explicitly. We also explain how the Berryphase comes out from the exact solution as a consequence of slow rotation of the driving field.