Irreducible components of the density matrix. Application to optical pumping

On the base of the stochastic model of M. Blume for time-dependent hyperfine interactions the perturbation factors of the angular correlation function are evaluated. The results of numerical calculations for some special configurations of stochastic fluctuating field gradients as well as magnetic fields are presented. In the medium range where the fluctuation rates are comparable with the nuclear precession frequencies, interesting features are worked out for the spinrotation spectra. For the limiting case of very fast fluctuations it is proved that the well-known exponential decay of anisotropy as predicted by the theory of Abragam and Pound appears.

γγ-angular correlations perturbed by stochastic fluctuating fields

In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n twolevel quantum systems is considered as an element of 4 n -dimensional operator Hilbert space (Liouville space). It allows us to use a quantum computer model with four-valued logic. The gates of this model are general superoperators which act on n-ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n-qubit open system are considered as four-valued logic gates acting on n-ququats. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates.

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Quantum computer with mixed states and four-valued logic

Time-dependent hyperfine interactions constitute a useful nuclear tool for probing interactions in condensed matter. The hyperfine coupling between, say, a nucleus and its surrounding electrons in an atom, is rendered time dependent when the atom becomes a component of a many-body system. The time dependence can arise from a variety of effects, e.g., interaction of the electronic shell of the nucleus with phonons, magnons, other electrons, etc., or modulation of the electronic environment of the nucleus owing to defect kinetics, etc. The experimental methods usually employed for studying hyperfine interactions consist of the perturbed angular correlation (PAC) of γ-rays, the Mossbauer effect, nuclear magnetic resonance (NMR), or muon spin rotation (μSR). The aim of this review is to provide a common theoretical basis for analyzing time-dependent hyperfine spectra by the above-mentioned techniques. This is achieved by expressing the experimentally measured quantity in each case in terms of an object termed the perturbation factor. With a view to calculating the latter, the time-dependent hyperfine interaction is modelled in terms of a stochastic hamiltonian. Two distinct kinds of stochastic models are considered, and their applications illustrated within a random-phase-like approximation. Various physical examples are then investigated. These include fluctuating electric quadrupolar and magnetic dipolar interactions. Comparison of the computed plots of the perturbation factor brings out the similarities and dissimilarities between the PAC, Mossbauer, μSR and NMR techniques.

Study of time-dependent hyperfine interactions by PAC, Mössbauer effect, μSR and NMR: A review of stochastic models

Using Liouville space and superoperator formalism we consider pure stationary states of open and dissipative quantum systems We discuss stationary states of open quantum systems, which coincide with stationary states of closed quantum systems Open quantum systems with pure stationary states of linear oscillator are suggested We consider stationary states for the Lindblad equation We discuss bifurcations of pure stationary states for open quantum systems which are quantum analogs of classical dynamical bifurcations

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Pure stationary states of open quantum systems

The effect of electronic relaxation processes on the angular correlation and on the angular distribution of radiation from oriented nuclei is investigated. The influence of the environment on the radioactive nuclei is taken into account by reducing the density operator for the total system (nucleus and surroundings mutually interacting) to a density operator for the nucleus alone. Elimination of the unobserved bath variables is performed with the help of Zwanzig's projection-operator technique. The Liouville formalism is used throughout. The (initially unspecified) properties of the environment enter the theory via second-order correlation functions, which are defined in terms of equilibrium ensemble averages of certain bath operators, like, e.g., the hyperfine-field operator. The matrix elements of the nuclear-evolution operator (which is a superoperator in Liouville space) with respect to a complete orthonormal set of multipole operators are just the usual perturbation factors ${{G}_{k{k}^{\ensuremath{'}}}}^{q{q}^{\ensuremath{'}}}$ of perturbed-angular-correlations theory. The consequent use of the multipole representation yields immediately the final formulas needed in the expression for both the angular distribution of radiation from oriented nuclei and the angular correlation function. The general theory includes relaxation processes due to magnetic and quadrupole interactions. The important case of purely magnetic interactions is discussed in more detail. Specialization to relaxation caused by randomly fluctuating fields yields a formula which contains both the Abragam-Pound result for time-fluctuating quadrupole interaction and Micha's extension to randomly time-varying magnetic fields in multidomain ferromagnets. Exact high-temperature solutions are presented for single crystals in a static magnetic field and with magnetic-type relaxation processes (axially symmetric case). For nuclei with spin $I=1$, the extension to arbitrary temperatures has been considered. The application of the present theory to the problem of multipole relaxation (which arises, e.g., in spin-lattice relaxation measurements with NMR/ON technique) is discussed.

Theory of the Influence of Environment on the Angular Distribution of Nuclear Radiation

The effect of a radio-frequency field on M\"ossbauer spectra is reconsidered. Both the ground and the excited state of the source nuclei are simultaneously exposed to the rf magnetic field. As an example, the effect of the rf field on $^{57}\mathrm{Fe}$ nuclei in a source with magnetic splitting (detected by a single-line absorber) is discussed in detail for two experimental geometries. M\"ossbauer spectra taken at a constant velocity, but with varying radio frequency, show that the main features can be understood in terms of two-quantum processes (rf-induced transitions between the magnetic sublevels preceding or subsequent to the emission of a $\ensuremath{\gamma}$ quantum), as long as the rf amplitude is small compared to the static magnetic field at the nucleus.

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Helmut Gabriel

Papers

Theory of the Influence of Environment on the Angular Distribution of Nuclear Radiation

Effect of Radio-Frequency Fields on Mössbauer Spectra