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arXiv:1704.06466 · Physical review. B./Physical review. B

Distribution of eigenstate populations and dissipative beating dynamics in uniaxial single-spin magnets

Takuya Hatomura, B. Barbara, Seiji Miyashita

Published Oct 18, 2017• 1 citation
arXivHTMLPDF

Abstract

Numerical simulations of magnetization reversal of a quantum uniaxial magnet under a swept magnetic field [Hatomura et al., Phys. Rev. Lett. 116, 037203 (2016)] are extended. In particular, how the ``wave packet'' describing the time evolution of the system is scattered in the successive avoided level crossings is investigated from the viewpoint of the distribution of the eigenstate populations. It is found that the peak of the distribution as a function of the magnetic field does not depend on spin-size $S$, which indicates that the delay of magnetization reversal due to the finite sweeping rate is the same in both the quantum and classical cases. The peculiar synchronized oscillations of all the spin components result in the beating of the spin length. Here, dissipative effects on this beating are studied by making use of the generalized Lindblad-type master equation. The corresponding experimental situations are also discussed in order to find conditions for experimental observations.

DOI
10.1103/physrevb.96.134309

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Numerical simulations of magnetization reversal of a quantum uniaxial magnet under a swept magnetic field [Hatomura et al., Phys. Rev. Lett. 116, 037203 (2016)] are extended. In particular, how the ``wave packet'' describing the time evolution of the system is scattered in the successive avoided level crossings is investigated from the viewpoint of the distribution of the eigenstate populations. It is found that the peak of the distribution as a function of the magnetic field does not depend on spin-size SSS, which indicates that the delay of magnetization reversal due to the finite sweeping rate is the same in both the quantum and classical cases. The peculiar synchronized oscillations of all the spin components result in the beating of the spin length. Here, dissipative effects on this beating are studied by making use of the generalized Lindblad-type master equation. The corresponding experimental situations are also discussed in order to find conditions for experimental observations.
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We study the time evolution of wave packets on coupled energy levels including the irreversible effect of spontaneous emission. As a test case we choose a simple two-state level-crossing problem of the Landau-Zener type. The numerical treatment of this situation is demanding, and we explore two approaches based on different views of the quantum-mechanical dynamics. First, we solve the time evolution of the wave packet using the traditional master equation giving directly the ensemble averages. Second, we use the recently developed Monte Carlo simulation method, which gives the individual members of an ensemble of quantum states undergoing spontaneous quantum jumps. The results are compared and found to agree when large enough ensembles are used. We discuss the computational requirements for the two methods and we find both quite demanding but qualitatively different.
It has been shown that the irreversible dynamics of a system in a dissipative environment can be described by an effective one-particle Hamiltonian (in the classical case) or an effective one-particle Schrödinger equation (in the quantum mechanical case) without taking into account the environmental degrees of freedom explicitly. In the quantum mechanical case, the description can be achieved either by a nonlinear modification of the Schrödinger equation or an explicitly time-dependent Hamiltonian operator — where both forms are connected via a non-unitary transformation, corresponding to a non-canonical transformation on the classical level. Taking into account an external magnetic field, in both formalisms, an additional unphysical gauge-dependent term occurs in the equations of motion. This shortcoming can be eliminated if the Lagrangian and Hamiltonian that provide Maxwell’s equations of electrodynamics undergo, in the dissipative case, the same kind of transformation as the mechanical degrees of freedom of the system. As a result, a consistent description in terms of exact analytical wave packet-solutions for the dissipative motion in a magnetic field can be obtained that will be discussed in detail.
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