A standard relaxation theory known as the BPP theory is of common use in magnetic resonance spectroscopy. A typical phenomenon that can be briefly elucidated by the theory is a broadening of peaks in Fourier spectra due to a transverse relaxation of a spin magnetization. There are, however, drawbacks: this theory is a classical phenomenological theory and often claimed to be insufficient to describe small relaxation time. In addition, it cannot describe a motional narrowing without introducing a phenomenological approach. We introduce a simple model in which a system spin ଵ ଶ is coupled with an environmental system localized around the system. The environmental system probabilistically dissipates into a thermal bath and a thermal environmental system migrates into the place instead. We show analytically that this model can describe a transverse relaxation and a motional narrowing simultaneously. We also show numerical simulations of decoherence in a spin system coupled with on-resonance bosonic modes. Our model will hopefully contribute to easier understanding of motional narrowing for a pedagogical purpose.
A standard relaxation theory known as the BPP theory is of common use in magnetic resonance spectroscopy. A typical phenomenon that can be briefly elucidated by the theory is a broadening of peaks in Fourier spectra due to a transverse relaxation of a spin magnetization. There are, however, drawbacks: this theory is a classical phenomenological theory and often claimed to be insufficient to describe small relaxation time. In addition, it cannot describe a motional narrowing without introducing a phenomenological approach. We introduce a simple model in which a system spin ଵ ଶ is coupled with an environmental system localized around the system. The environmental system probabilistically dissipates into a thermal bath and a thermal environmental system migrates into the place instead. We show analytically that this model can describe a transverse relaxation and a motional narrowing simultaneously. We also show numerical simulations of decoherence in a spin system coupled with on-resonance bosonic modes. Our model will hopefully contribute to easier understanding of motional narrowing for a pedagogical purpose.
An open quantum system is a system coupled to an environment that can describe time-irreversible dynamics through which the system evolves toward the thermal equilibrium state.We present a quantum mechanically rigorous theory in order to help the analysis of spectra obtained from the advanced nuclear magnetic resonance (NMR) and muon spin rotation, relaxation or resonance (μSR) techniques.Our approach is based on the numerically "Exact" hierarchical equations of motion (HEOM) approach, which allows us to study the reduced system dynamics for non-perturbative and non-Markovian system-bath interactions at finite temperature even under strong time-dependent perturbations.We demonstrate the present theory to analyze μSR and low-field NMR spectra, as an extension of the Kubo-Toyabe theory focusing on the effects of temperature and anisotropy of a local magnetic field on spectra, to help further the development of these experimental means.
The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many `environmental' modes. At low T these environmental effects are dominated by localized modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a `spin bath' model. This contrasts with `oscillator bath' models (originated by Feynman and Vernon) which describe delocalized environmental modes such as electrons, phonons, photons, magnons, etc. The couplings to N spin bath modes are independent of N (rather than the ~O(1/( N ) 1/2 ) dependence typical of oscillator baths), and often strong. One cannot in general map a spin bath to an oscillator bath (or vice versa); they constitute distinct `universality classes' of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We then focus on the `central spin' model, which couples a central two-level system to a background spin bath. It is the spin bath analogue of the famous `spin-boson' oscillator model, and describes, e.g., the tunnelling dynamics of nanoscopic and mesoscopic magnets and superconductors. We show how to average over (or `integrate out') spin bath modes, using an operator instanton technique, to find the central spin dynamics. The formal manouevres involve four separate averages - each average corresponds physically to a different `decoherence' mechanism acting on the central spin dynamics. Each environmental spin has its own topological `spin phase', which by interacting with the phase of the central system, decoheres it - this can happen even without dissipation. We give analytic results for the central spin correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems. Particular attention is given to recent work on tunnelling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunnelling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs. Finally, we discuss decoherence mechanisms and coherence experiments in superconductors and magnets. We show that a spin bath environment causes decoherence even in the T 0 limit. Control of this decoherence will be essential in the effort to construct `qubits' for quantum computers.
A general procedure is given for finding the equation of motion of the density matrix of a system in contact with a thermal bath, as for example a nuclear spin system weakly coupled to a crystal lattice. The thermal bath is treated both classically and quantum mechanically, and the theory is similar to, and a generalization of, conventional theories of time proportional transition probabilities. Relaxation of the system by the thermal bath is expressed by a linear matrix operator, and it is stressed that elements of this operator can be regarded as secular or nonsecular perturbations on the equation of motion and can be treated accordingly. When the motion of the system is slow compared to that of the thermal bath, the equation of motion can be expressed in an operator form which is independent of representation. If the system has a time-dependent Hamiltonian which varies slowly compared to the motion of the thermal bath, the same equation of motion is obeyed and the system is relaxed by the bath toward a Boltzmann distribution with respect to its instantaneous Hamiltonian. If the time variation of the Hamiltonian is more rapid, higher order corrections to the equation of motion must be applied. The theory is applied to spin-lattice relaxation of a coupled nuclear spin system in a metal, for arbitrary externally applied fixed magnetic field.
Driving an open spin system by two strong, nearly degenerate fields enables addressing populations of individual spin states, characterisation of their interaction with thermal bath, and measurements of their relaxation/decoherence rates. With such addressing we observe nested magnetic resonances having nontrivial dependence on microwave field intensity: while the width of one of the resonances undergoes a strong power broadening, the other one exhibits a peculiar field-induced stabilization. We also observe light-induced narrowing of such composite resonances. The observations are explained by the dynamics of bright and dark superposition states and their interaction with reservoir.
We apply our recently developed resonance perturbation theory to describe the dynamics of magnetization in paramagnetic spin systems interacting simultaneously with local and collective bosonic environments. We derive explicit expressions for the evolution of the reduced density matrix elements. This allows us to calculate explicitly the dynamics of the macroscopic magnetization, including characteristic relaxation and dephasing timescales. We demonstrate that collective effects (i) do not influence the character of the relaxation processes but merely renormalize the relaxation times and (ii) significantly modify the dephasing times, leading in some cases to a complicated (time inhomogeneous) dynamics of the transverse magnetization, governed by an effective time-dependent magnetic field.
The authors study the dynamics of an impurity spin coupled to a spin-boson dissipative system. They calculate the transverse correlation function of the impurity spin and compare the result with that obtained from an equivalent stochastic model. A phenomenological rate parameter in the stochastic model is represented in terms of microscopically obtained quantities. The authors also calculate the NMR lineshapes for various temperatures which are relevant in the context of a particular physical realization of the model. Motional narrowing of lines is observed at high temperatures.