We give a further step in the quantum mechanical description of engineered atomic spin structures by deriving a master equation of the Redfield type that governs the dynamics of the atomic spin density matrix. By generalizing this approach to charge specific density matrices, we are able to describe magnetic transport quantities, such as the average inelastic current and the shot noise, accessible by tunneling spectroscopy. Our method suitably describes moderate lead-atom coupling regimes where quantum coherence effects cannot be disregarded. We contrast our approach with the existing descriptions in terms of rate equations and show examples where coherence effects are crucial to understand the physics of spin-polarized tunnel current through spin structures.
We show how the spin-transfer torque generated by an ac voltage may be used to excite a paramagnetic resonance of an atomic spin deposited on a metallic surface. This mechanism is independent of the environment of the atom and may explain the ubiquity of the paramagnetic resonance reported by Baumann et al. [Science 350, 417 (2015)]. The current and spin dynamics are modeled by a time-dependent Redfield master equation generalized to account for the periodic driven voltage. Our approach shows that the resonance effect is a consequence of the nonlinearity of the coupling between the magnetic moment and the spin-polarized current which generates a large second-harmonic amplitude that can be measured in the current signal.
The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of T1 and T2 characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.
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