The quantum dynamics of nano-scale molecular magnets is studied from a viewpoint of adiabatic transition in a time dependent external field. The effect of noise is studied by the quantum Langevin equation and the quantum master equation, and how the pure quantum dynamics is disturbed by the noise is investigated. The origin of the quantum fluctuation is studied for Heisenberg antiferromagnets with half-odd-integer spins on a ring. Novel use of quantum dynamical effects is also discussed.
The quantum dynamics of nano-scale molecular magnets is studied from a viewpoint of adiabatic transition in a time dependent external field. The effect of noise is studied by the quantum Langevin equation and the quantum master equation, and how the pure quantum dynamics is disturbed by the noise is investigated. The origin of the quantum fluctuation is studied for Heisenberg antiferromagnets with half-odd-integer spins on a ring. Novel use of quantum dynamical effects is also discussed.
Abstract. Recently, explicit real time dynamics has been studied in various systems. These quantum mechanical dynamics could provide new recipes in information processing. We study quantum dynamics under time dependent external fields, and explore how to control the quantum state, and also how to bring the state into a target state. Here, we investigate a pure quantum mechanical dynamics, dynamics in quantum Monte Carlo simulation and also in quantum master equation. For the control magnetic states, operators which do not commute with magnetization are important. We study case of the transverse Ising model, in which we compare natures of thermal and quantum fluctuations. We also study the cases of the Dzyaloshinsky-Moriya interaction, where we find a peculiar energy level structure. Moreover we study the case of itinerant magnetic state, where we study the change from the Mott insulator to the Nagaoka ferromagnetic state. Effects of dissipation are also discussed. 1.
We have constructed an algorithm to treat quantum mechanical dynamics, such as the nonadiabatic transitions in a dissipative environment, by making use of the formula of reduced density matrix, i.e., Quantum Master Equation (QME). We applied the method to investigate dynamics of magnetization of nanoscale magnets, such as Mn12 and Fe8, in a time dependent field. Due to the discreteness of the energy levels in small systems the resonating tunneling phenomena play an important role. At relatively high temperatures the excited levels contribute to the transition and the transition rate depends significantly on the temperature. On the other hand, at very low temperatures the magnetization process does not depend on the temperature. Even at such a low temperature, the effect of environments is still relevant. We demonstrate such a process with the method of QME. We also analyze temperature dependent phenomena of hysteresis of the nanoscale magnets.
Recently, explicit real time dynamics has been studied in various systems. These quantum mechanical dynamics could provide new recipes in information processing. We study quantum dynamics under time dependent external fields, and explore how to control the quantum state, and also how to bring the state into a target state. Here, we investigate a pure quantum mechanical dynamics, dynamics in quantum Monte Carlo simulation and also in quantum master equation. For the control magnetic states, operators which do not commute with magnetization are important. We study case of the transverse Ising model, in which we compare natures of thermal and quantum fluctuations. We also study the cases of the Dzyaloshinsky-Moriya interaction, where we find a peculiar energy level structure. Moreover we study the case of itinerant magnetic state, where we study the change from the Mott insulator to the Nagaoka ferromagnetic state. Effects of dissipation are also discussed.
When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin equation, for mapping the noise to the dynamical degrees of freedom. When the spin dynamics is discretized in time, a general fluctuation-dissipation theorem, valid for non-Markovian noise, can be established, even when zero modes are present. We discuss the subtleties that arise, when Gilbert damping is present and the mapping between noise and spin degrees of freedom is non--linear.
We will discuss on the quantum dynamics on the following three cases. (1) First, we will study structure of adiabatic energy levels for a triangle magnetic cluster with the Dzyaloshinsky-Moriya (DM) interaction. Generally, in single molecular magnets, the magnetic energy levels are discrete and we can find various interesting magnetic behavior when we sweep the external magnetic field. For the dynamics, the adiabatic energy level structure, in particular, avoided level structures at the energy level crossings, plays an important role. The mechanism to open the gap is attributed to some interactions which do not commute with the magnetization. We will discuss dependence of the dynamical magnetization process under the field cycling on the angle between the DM interaction vector and the external magnetic fields.[1,2] We also discuss a hidden conserved quantity due to the chiral symmetry.[3] The dynamical DM effect will be also discussed. (2) We will study the quantum dynamics of one-dimensional transverse Ising model which exhibits a quantum phase transition at zero temperature. There, we find a metastable state and a kind of spinodal decomposition phenomena in the sense of the quantum dynamics. We also refer to the cases of very fast sweep where some size independent collective motions are observed.[4] (3) Finally, we will also study an itinerant electron system in which the Mott insulator-Nagaoka ferromagnetism transition. There, we study the adiabatic change from the Mott insulator to the Nagaoka ferromagnetic state under removal of an electron from the lattice. We also study the magnetization process as a function of the magnetic field.
We extend our theory of Bloch oscillations of cold atoms inside an optical cavity [Venkatesh et al., Phys. Rev. A 80, 063834 (2009)] to include the effects of quantum noise arising from coupling to external modes. The noise acts as a form of quantum measurement backaction by perturbing the coupled dynamics of the atoms and the light. We take it into account by solving the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical mean fields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio, as well as heating effects. One of the hurdles we overcome in this paper is the proper treatment of fluctuations about time-dependent mean fields in the context of cold-atom cavity QED.