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Progress of Theoretical Physics Supplement

Noise Effect on the Nonadiabatic Transition in the System of Fe8

Masamichi Nishino, Keiji Saito, Seiji Miyashita

Published Jan 1, 2002• 0 citations
Publisher

Abstract

We study the effect of noise on the tunnel splitting in the system of Fe8. The tunnel gap between the lowest two states is estimated making use of the Landau-Zener-Stückelberg (LZS) formula. We consider how the estimated gap deviates from the true tunneling gap. We also study the difference of the effect of noise between the systems of S=1/2 and S=10 and discuss the relation to the experimental results.

DOI
10.1143/ptps.145.399

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We study the effect of noise on the tunnel splitting in the system of Fe8. The tunnel gap between the lowest two states is estimated making use of the Landau-Zener-Stückelberg (LZS) formula. We consider how the estimated gap deviates from the true tunneling gap. We also study the difference of the effect of noise between the systems of S=1/2 and S=10 and discuss the relation to the experimental results.
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We analyze the influence of a two-state autocorrelated noise on the decoherence and on the tunneling Landau-Zener (LZ) transitions during a two-level crossing of a central electron spin (CES) coupled to a one dimensional anisotropic-antiferomagnetic spin, driven by a time-dependent global external magnetic field. The energy splitting of the coupled spin system is found through an approach that computes the noise-averaged frequency. At low magnetic field intensity, the decoherence (or entangled state) of a coupled spin system is dominated by the noise intensity. The effects of the magnetic field pulse and the spin gap antiferromagnetic material used suggest to us that they may be used as tools for the direct observation of the tunneling splitting through the LZ transitions in the sudden limit. We found that the dynamical frequencies display basin-like behavior decay with time, with the birth of entanglement, while the LZ transition probability shows Gaussian shape.
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To determine the possibility of single-electron operation in electronic devices, we investigated the Landau-Zener (LZ) tunneling process with dissipation. This work presents an analytical formula and detailed numerical results for dynamical tunneling phenomena with an Ohmic reservoir and a noise source. First, we calculated the transient and final density matrices of a single-electron system coupled to a reservoir at zero temperature, and then noted the rigid tunneling process and a noticeable decoherence of the tunneling. The rigidity of the LZ tunneling suggests that we can suppress errors in single-electron operations. However, our analytical and numerical results clarified the fact that noise strongly affects the tunneling process. When half of the noise spectrum bandwidth ${\ensuremath{\omega}}_{\mathrm{max}}$ is larger than the gap of the adiabatic potential, thermal excitation by the noise source considerably increases the tunneling probability. On the other hand, our numerical results found that the noise effect is proportional to ${\ensuremath{\omega}}_{\mathrm{max}}^{3}$ when ${\ensuremath{\omega}}_{\mathrm{max}}$ is smaller than the gap. Then we can accurately operate single electrons if the noise source has a sufficiently narrow band.
We investigate the Landau-Zener transition in two- and three-level systems subject to a classical Gaussian noise. Two complementary limits of the noise being fast and slow compared to characteristic Landau-Zener tunnel times are discussed. The analytical solution of a density matrix (Bloch) equation is given for a long-time asymptotic of transition probability. It is demonstrated that the transition probability induced or assisted by the fast noise can be obtained through a procedure of Bloch's equation averaging with further reducing it to a master equation. In contrast to the case of fast noise, the transition probability for LZ transition induced, or assisted, by the slow classical noise can be obtained by averaging the solution of Bloch's equation over the noise realization. As a result, the transition probability is described by the activation Arrhenius law. The approximate solution of the Bloch's equation at finite times is written in terms of Fresnel's integrals and interpreted in terms of interference pattern. We discuss consequences of a local isomorphism between SU(2) and SO(3) groups and connections between Schr\"odinger and Bloch descriptions of spin dynamics. Based on this isomorphism, we establish the relations between S=1/2S=1/2S=1/2 and 1 transition probabilities influenced by the noise. A possibility to use the slow noise as a probe for tunnel time is discussed.