Two-level Subsystems Research Articles

Non-Arrhenius relaxation effects in collections of two-level subsystems

We present numerical simulations of relaxation isotherms for an ensemble of thermally activated, two-level subsystems, with double-well free energy profiles, and with a distribution of dissipation barriers and level splittings. The field history imitates a typical experimental viscosity protocol, and consists of saturation in a large positive field, followed by recoil to a negative holding field, and then by the thermally driven decay of the moment towards equilibrium at fixed temperature and fixed field. The numerical simulations show that systems whose relaxation dynamics are governed explicitly by the Arrhenius law of thermal activation, can exhibit relaxation effects which are apparently ``non-Arrhenius'' in origin. In particular, the maximum value of the relaxation rate $S\ensuremath{\equiv}\ensuremath{-}\ensuremath{\partial}M(t)∕\ensuremath{\partial}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}t$ extracted from model viscosity isotherms over a typical experimental time window $100\phantom{\rule{0.3em}{0ex}}\mathrm{s}\ensuremath{\leqslant}t\ensuremath{\leqslant}{10}^{4}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, and the thermal viscosity field ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{\mathrm{f}}(T)$ extracted, over the same time window, from the field dependence of the logarithm of the time at which the moment reverses direction as it relaxes towards equilibrium, both exhibit variations with temperature which are highly nonlinear, and which are characterized by coincident maxima, very similar to those observed experimentally in a variety of particulate systems.

Ageing and memory in the relaxation dynamics of collections of two-level subsystems

The relaxation dynamics of collections of interacting, thermally activated, two-levelsubsystems are shown to be characterized by nonequilibrium ageing and memory effectswhich are analogous to those observed in magnetic systems where randomness andfrustration yield a collectively frozen magnetic state with spin-glass-like correlations.Numerical simulations of these nonequilibrium relaxation effects are presented andcompared with measurements performed on assemblies of nanodimensional magneticparticles, and their physical origins, as well as their relationship to genuinely collectivenonequilibrium relaxation phenomena, are discussed within a theoretical framework basedon the Preisach model of hysteresis.

Effect of phonon decay processes on the formation of a phonon nonequilibrium signal in crystals with two two-level subsystems

The effect of phonon decay on the characteristic propagation time and shape of a phonon nonequilibrium signal in disordered crystals, including crystals containing inelastic phonon scattering centers, is studied theoretically. Attention is focused on slow processes, which are typical of yttrium-aluminum garnet solid solutions and erbium-doped aluminates. It is shown that the temperature dependence of the arrival time of a phonon nonequilibrium signal in these systems can be governed, to a considerable extent, by phonon-phonon interactions. The results of the theoretical studies are compared with experimental data on the propagation of weakly nonequilibrium thermal phonons in solid solutions of rare-earth yttrium-aluminum garnets and aluminates.

Simple quantum systems as a source of coherent information

A set of very important simple quantum systems is analyzed from the standpoint of the amount of coherent information that is accessible when information channels corresponding to the systems are used. It is shown that for simple quantum models the coherent information can be calculated and used for estimating the potential possibilities of the corresponding quantum channel as a source of physical information in experiments associated with the effects of the coherence of quantum states. The following physical models are studied: a two-level atom in a laser radiation field, an aggregate of two two-level subsystems in a multilevel atom (hydrogen), a system of two two-level atoms in the process of joint quantum-deterministic evolution and under the action of transformations of quantum measurement and quantum duplication, as well as one and two two-level atoms in the process of emission.

Decoherence and relevant universality in quantum algorithms via a dynamic theory for quantum measurement

It is well known that environment may decohere a quantum bit (qubit) system immersed in it, making a quantum computation invalid. But the quantitative features of the decoherence seem to depend on both the constitution of the environment and the details of its coupling with the qubit system. In this paper, based on the dynamic approach for quantum measurement developed from the Hepp-Coleman model [K. Hepp, Helv. Phys. Acta 45, 237 (1972)], we generally model the environment as a collection of a large number of subsystems and then consider to what extent and in which way the environment and its coupling with the qubit system may affect a quantum computation process. In the weak-coupling limit, we find that as far as decoherence time is concerned, there is no essential difference between an environment of two-level subsystems and an environment of harmonic oscillators. This implies that there exists some universality independent of specific constitutions of environments. However, it is also shown that this is not true at finite temperature or in the case of strong coupling. So only if the coupling is weak and the temperature low does there exist the possibility of developing a universal scheme of controlling a qubit system such that the decoherence is avoided. The possible effect of environment on the efficiency of a quantum algorithm is also explicitly illustrated through the example of Shor's prime factorization algorithm.

A Preisach model with a temperature and time-dependent remanence maximum

We present a simple physical model which is capable of generating a maximum in the field dependence of both the isothermal remanent magnetization and the thermoremanent magnetization, with temperature and time-dependent systematics which are identical to those observed experimentally in spin glasses. The model uses an output dependent (moving) Preisach formalism to calculate the response to an applied field of a collection of interacting two-level subsystems with intrinsic anisotropy barriers, which are allowed to relax to equilibrium by thermal over-barrier activation. The maxima occur when the distribution of subsystem anisotropies has an output dependence which reduces the mean activation barrier in proportion to the magnetization induced in the system, so that the thermal relaxation processes become progressively more effective as the system approaches saturation.

Preisach model for spin-glass remanences

We present numerical calculations, based on a finite temperature Preisach model of hysteresis for a collection of thermally activated two-level subsystems, which yield peaks in the field dependence of the remanence, with identical systematics to those observed experimentally in spin glasses and some fine particle suspensions. The model allows thermally activated switching events over all energy barriers W\ensuremath{\equiv}kT ln(t/${\mathrm{\ensuremath{\tau}}}_{0}$ ), where T is the temperature, t is the observation time, and ${\mathrm{\ensuremath{\tau}}}_{0}$ is a microscopic time, in addition to those induced by an applied field ${\mathrm{h}}_{\mathrm{a}}$ . The Preisach distribution is a product of a Gaussian distribution of interaction fields ${\mathrm{h}}_{\mathrm{s}}$ , with zero mean, and a Gaussian distribution of coercive fields ${\mathrm{h}}_{\mathrm{c}}$ . The remanence peaks are generated by allowing the mean coercive field h-${\mathrm{bar}}_{\mathrm{c}}$ to decrease in proportion to the magnetization m impressed on the system, as h-${\mathrm{bar}}_{\mathrm{c}}$ =h-${\mathrm{bar}}_{\mathrm{c}0}$ -\ensuremath{\gamma}m, where h-${\mathrm{bar}}_{\mathrm{c}0}$ and \ensuremath{\gamma} are positive constants. The isothermal remanent magnetization (IRM), obtained by assuming the same value for the cutoff parameter W for both the magnetizing and remanence processes, exhibits a peak which becomes sharper and shifts towards lower applied fields as W increases. The thermoremanent magnetization, obtained by assuming an 'infinite' value for W for the magnetizing process and a finite value for the remanence process, exhibits a peak which is larger and occurs at lower fields than the peak in the corresponding IRM.

Nonlinear magnetic and optical coherence in coupled two-level systems

The question is raised whether nonlinear coherence can be created in coupled systems whose subsystems interact with distinct radiation fields. The simplest coupled system consisting of two two-level subsystems is treated in interaction with two electromagnetic fields, each close to resonance of one of the subsystems. The problem is treated within the SU(4) symmetries. The generators of SU(4) are defined and their properties under transformations deduced. The Hamiltonian and the density operator of the coupled system are expressed in terms of the generators of SU(4) and the Liouville equation is then used to find the time evolution of the density operator. When the frequencies of the radiation fields are equal to the resonant frequencies of the uncoupled subsystems, one obtains two two-photon nutation processes, provided that the interactions of the subsystems with the radiation fields are weaker than the mutual interaction of the two subsystems. The nutation frequency is proportional to the product of the field strengths and inversely proportional to the coupling parameter which in this case represents the resonance offset of the intermediate levels. Alternatively, the frequencies of the radiation fields can be arranged so that only one two-photon transition is on resonance. The amplitude of the nutation then depends on the strengths of the radiation fields, and acquires maximum value for ${\ensuremath{\omega}}_{1}={\ensuremath{\omega}}_{2}$. The nutation frequency increases when one approaches the resonance with the intermediate level. With a two-photon $\ensuremath{\pi}$ pulse one transfers the population difference from the levels of one subsystem to those of the other. This procedure can be used to polarize rare spins in the case of strong spin-spin coupling with the abundant spins when the method of thermodynamic contact is inapplicable. Both magnetic and optical coupled systems can be described with the same equations.

Separated subsystems in four-level atom

We study a four-level system with two lasers. We show that under certain conditions it is possible to group our four-level system into two completely separated two-level subsystems and this separation holds when the detunings and the Rabi frequencies in our system are time-dependent.