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- Fachbereich Physik (76) (remove)

Abstract: We present experimental and theoretical results of a detailed study of laser-induced continuum structures (LICS) in the photoionization continuum of helium out of the metastable state 2s^1 S_0. The continuum dressing with a 1064 nm laser, couples the same region of the continuum to the 4s^1 S_0 state. The experimental data, presented for a range of intensities, show pronounced ionization suppression (by asmuch as 70% with respect to the far-from-resonance value) as well as enhancement, in a Beutler-Fano resonance profile. This ionization suppression is a clear indication of population trapping mediated by coupling to a contiuum. We present experimental results demonstrating the effect of pulse delay upon the LICS, and for the behavior of LICS for both weak and strong probe pulses. Simulations based upon numerical solution of the Schrödinger equation model the experimental results. The atomic parameters (Rabi frequencies and Stark shifts) are calculated using a simple model-potential method for the computation of the needed wavefunctions. The simulations of the LICS profiles are in excellent agreement with experiment. We also present an analytic formulation of pulsed LICS. We show that in the case of a probe pulse shorter than the dressing one the LICS profile is the convolution of the power spectra of the probe pulse with the usual Fano profile of stationary LICS. We discuss some consequences of deviation from steady-state theory.

Hexagonal BN films have been deposited by rf-magnetron sputtering with simultaneous ion plating. The elastic properties of the films grown on silicon substrates under identical coating conditions have been de-termined by Brillouin light scattering from thermally excited surface phonons. Four of the five independent elastic constants of the deposited material are found to be c11 = 65 GPa, c13 = 7 GPa, c33 = 92 GPa and c44 = 53 GPa exhibiting an elastic anisotropy c11/c33 of 0.7. The Young's modulus determined with load indenta-tion is distinctly larger than the corresponding value taken from Brillouin light scattering. This discrepancy is attributed to the specific morphology of the material with nanocrystallites embedded in an amorphous matrix.

We present detailed studies of the enhanced coercivity of exchange-bias bilayer Fe/MnPd, both experimentally and theoretically. We have demonstrated that the existence of large higher-order anisotropies due to exchange coupling between different Fe and MnPd layers can account for the large increase of coercivity in Fe/MnPd system. The linear dependence of coercivity on inverse Fe thickness are well explained by a phenomenological model by introducing higher-order anisotropy terms into the total free energy of the system.

High frequency switching of single domain, uniaxial magnetic particles is discussed in terms of transition rates controlled by a small transverse bias field. It is shown that fast switching times can be achieved using bias fields an order of magnitude smaller than the effective anisotropy field. Analytical expressions for the switching time are derived in special cases and general configurations of practical interest are examined using numerical simulations.

Abstract: We utilize the generation of large atomic coherence to enhance the resonant nonlinear magneto-optic effect by several orders of magnitude, thereby eliminating power broadening and improving the fundamental signal-to-noise ratio. A proof-of-principle experiment is carried out in a dense vapor of Rb atoms. Detailed numerical calculations are in good agreement with the experimental results. Applications such as optical magnetometry or the search for violations of parity and time reversal symmetry are feasible.

Epitaxial growth of metastable Pd(001) at high deposition temperatures up to a critical thickness of 6 monolayers on bcc-Fe(001) is reported, the critical thickness being depending dramatically on the deposition temperature. For larger thicknesses the Pd film undergoes a roughening transition with strain relaxation by forming a top polycrystalline layer. These results allow to make a correlation between previ-ously reported unusual magnetic properties of Fe/Pd double layers and the crystallographic structure of the Pd overlayer.

Wall energy and wall thickness of exchange-coupled rare-earth transition-metal triple layer stacks
(1999)

The room-temperature wall energy sw 54.0310 23 J/m 2 of an exchange-coupled Tb 19.6 Fe 74.7 Co 5.7 /Dy 28.5 Fe 43.2 Co 28.3 double layer stack can be reduced by introducing a soft magnetic intermediate layer in between both layers exhibiting a significantly smaller anisotropy compared to Tb+- FeCo and Dy+- FeCo. sw will decrease linearly with increasing intermediate layer thickness, d IL , until the wall is completely located within the intermediate layer for d IL d w , where d w denotes the wall thickness. Thus, d w can be obtained from the plot sw versus d IL .We determined sw and d w on Gd+- FeCo intermediate layers with different anisotropy behavior ~perpendicular and in-plane easy axis! and compared the results with data obtained from Brillouin light-scattering measurements, where exchange stiffness, A, and uniaxial anisotropy, K u , could be determined. With the knowledge of A and K u , wall energy and thickness were calculated and showed an excellent agreement with the magnetic measurements. A ten times smaller perpendicular anisotropy of Gd 28.1 Fe 71.9 in comparison to Tb+- FeCo and Dy+- FeCo resulted in a much smaller sw 51.1310 23 J/m 2 and d w 524 nm at 300 K. A Gd 34.1 Fe 61.4 Co 4.5 with in-plane anisotropy at room temperature showed a further reduced sw 50.3310 23 J/m 2 and d w 517 nm. The smaller wall energy was a result of a different wall structure compared to perpendicular layers.

Abstract: We aim to establish a link between path-integral formulations of quantum and classical field theories via diagram expansions. This link should result in an independent constructive characterisation of the measure in Feynman path integrals in terms of a stochastic differential equation (SDE) and also in the possibility of applying methods of quantum field theory to classical stochastic problems. As a first step we derive in the present paper a formal solution to an arbitrary c-number SDE in a form which coincides with that of Wick's theorem for interacting bosonic quantum fields. We show that the choice of stochastic calculus in the SDE may be regarded as a result of regularisation, which in turn removes ultraviolet divergences from the corresponding diagram series.

We show that the solution to an arbitrary c-number stochastic differential equation (SDE) can be represented as a diagram series. Both the diagram rules and the properties of the graphical elements reflect causality properties of the SDE and this series is therefore called a causal diagram series. We also discuss the converse problem, i.e. how to construct an SDE of which a formal solution is a given causal diagram series. This then allows for a nonperturbative summation of the diagram series by solving this SDE, numerically or analytically.

Starting from the Hamiltonian operator of the noncompensated two-sublattice model of a small antiferromagnetic particle, we derive the e effective Lagrangian of a biaxial antiferromagnetic particle in an external magnetic field with the help of spin-coherent-state path integrals. Two unequal level-shifts induced by tunneling through two types of barriers are obtained using the instanton method. The energy spectrum is found from Bloch theory regarding the periodic potential as a superlattice. The external magnetic field indeed removes Kramers' degeneracy, however a new quenching of the energy splitting depending on the applied magnetic field is observed for both integer and half-integer spins due to the quantum interference between transitions through two types of barriers.

We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.

In this paper we present a renormalizability proof for spontaneously broken SU (2) gauge theory. It is based on Flow Equations, i.e. on the Wilson renormalization group adapted to perturbation theory. The power counting part of the proof, which is conceptually and technically simple, follows the same lines as that for any other renormalizable theory. The main difficulty stems from the fact that the regularization violates gauge invariance. We prove that there exists a class of renormalization conditions such that the renormalized Green functions satisfy the Slavnov-Taylor identities of SU (2) Yang-Mills theory on which the gauge invariance of the renormalized theory is based.

Abstract: In this paper we present a renormalizability proof for spontaneously broken SU (2) gauge theory. It is based on Flow Equations, i.e. on the Wilson renormalization group adapted to perturbation theory. The power counting part of the proof, which is conceptually and technically simple, follows the same lines as that for any other renormalizable theory. The main difficulty stems from the fact that the regularization violates gauge invariance. We prove that there exists a class of renormalization conditions such that the renormalized Green functions satisfy the Slavnov-Taylor identities of SU (2) Yang-Mills theory on which the gauge invariance of the renormalized theory is based.

A new method for calculating Stark resonances is presented and applied for illustration to the simple case of a one-particle, one-dimensional model Hamiltonian. The method is applicable for weak and strong dc fields. The only need, also for the case of many particles in multi-dimensional space, are either the short time evolution matrix elements or the eigenvalues and Fourier components of the eigenfunctions of the field-free Hamiltonian.

We present an entropy concept measuring quantum localization in dynamical systems based on time averaged probability densities. The suggested entropy concept is a generalization of a recently introduced [PRL 75, 326 (1995)] phase-space entropy to any representation chosen according to the system and the physical question under consideration. In this paper we inspect the main characteristics of the entropy and the relation to other measures of localization. In particular the classical correspondence is discussed and the statistical properties are evaluated within the framework of random vector theory. In this way we show that the suggested entropy is a suitable method to detect quantum localization phenomena in dynamical systems.

It is shown, that recently constructed PST Lagrangians for chiral supergravities follow directly from earlier Kavalov-Mkrtchyan Lagrangians by an Ansatz for the ' tensor by expressing this in terms of the PST scalar. The susy algebra which included earlier ff-symmetry in the commutator of supersymmetry transformations, is now shown to include both PST symmetries, which arise from the single ff-symmetry term. The Lagrangian for the 5-brane is not described by this correspondence, and probably can be obtained from more general Lagrangians, posessing ff-symmetry.

Abstract: We describe a general technique that allows for an ideal transfer of quantum correlations between light fields and metastable states of matter. The technique is based on trapping quantum states of photons in coherently driven atomic media, in which the group velocity is adiabatically reduced to zero. We discuss possible applications such as quantum state memories, generation of squeezed atomic states, preparation of entangled atomic ensembles and quantum information processing.

Abstract: The periodic bounce configurations responsible for quantum tunneling are obtained explicitly and are extended to the finite energy case for minisuperspace models of the Universe. As a common feature of the tunneling models at finite energy considered here we observe that the period of the bounce increases with energy monotonically. The periodic bounces do not have bifurcations and make no contribution to the nucleation rate except the one with zero energy. The sharp first order phase transition from quantum tunneling to thermal activation is verified with the general criterions.

Continuous and discrete superselection rules induced by the interaction with the environment are investigated for a class of exactly soluble Hamiltonian models. The environment is given by a Boson field. Stable superselection sectors can only emerge if the low frequences dominate and the ground state of the Boson field disappears due to infrared divergence. The models allow uniform estimates of all transition matrix elements between different superselection sectors.

Quantum Chaos
(1999)

The study of dynamical quantum systems, which are classically chaotic, and the search for quantum manifestations of classical chaos, require large scale numerical computations. Special numerical techniques developed and applied in such studies are discussed: The numerical solution of the time-dependent Schr-odinger equation, the construction of quantum phase space densities, quantum dynamics in phase space, the use of phase space entropies for characterizing localization phenomena, etc. As an illustration, the dynamics of a driven one-dimensional anharmonic oscillator is studied, both classically and quantum mechanically. In addition, spectral properties and chaotic tunneling are addressed.

The global dynamical properties of a quantum system can be conveniently visualized in phase space by means of a quantum phase space entropy in analogy to a Poincare section in classical dynamics for two-dimensional time independent systems. Numerical results for the Pullen Edmonds systems demonstrate the properties of the method for systems with mixed chaotic and regular dynamics.

Die Untersuchung von semiklassischen Näherungen des Zeitentwicklungsoperators in der Quantenmechanik ist sowohl von fundamentalem als auch von didaktischem Interesse. Das fundamentale Interesse ist in der Beschreibung des Zusammenhangs zwischen klassischer Mechanik und Quantenmechanik begründet, das didaktische erklärt sich aus dem anschaulichen Zugang, den die Beschreibung von quantenmechanischen Prozessen durch klassische Größen liefert. Besonders klar wird dieser Zusammenhang, wenn eine Phasenraumdarstellung der Quantenmechanik betrachtet wird. Eine erste semiklassische Näherung für den Propagator im Phasenraum, den sogenannten "coherent state"-Propagator, wurde von Klauder vorgestellt. Weissman motivierte diese Näherung durch die Erweiterung der semiklassischen Korrespondenzrelationen auf den Begriff der kohärenten Variablen. In späteren Veröffentlichungen wird auf eine rigorose Herleitung mittels Pfadintegralmethoden verwiesen, die aber bis zum heutigen Tage nicht verwirklicht wurde. Ein zentraler Punkt dieser Arbeit wird es sein, zum ersten Mal diese alternative Herleitung vollständig zu präsentieren. Die Eigenschaften der semiklassischen Näherung des Phasenraumpropagators wurden für eine Reihe fundamentaler Quantenprozesse untersucht. Ausgehend von der semiklassischen Näherung des Phasenraumpropagators ergibt sich durch eine Ortsraumdarstellung desselben der Herman-Kluk-Propagator. Dieser gehört zur Klasse der Anfangswertdarstellungen ("initial value representations", IVRs), die die sonst bei semiklassischen Näherungen auftretenden Schwierigkeiten wie Kaustiken, Singularitäten und beidseitige Randbedingungen für die zugrundeliegenden klassischen Bahnen umgehen. Dies erlaubt ihre Anwendung auch auf Quantensysteme, deren klassisches Äquivalent chaotische Phasenraumbereiche enthält. Erste Untersuchungen hierzu wurden in unserer Arbeitsgruppe Ende 1997 durchgeführt. Die Frage nach der Klärung grundsätzlicher Eigenschaften des verwendeten Propagators und der verwendeten Methode sowie die Beleuchtung des theoretischen Hintegrunds lieferten die Anregung für diese Arbeit. Zu dieser Arbeit: In dieser Arbeit wird die semiklassische Näherung für den Phasenraumpropagator und hierauf aufbauend der Herman-Kluk-Propagator hergeleitet und ihre Eigenschaften untersucht. Im einzelnen gliedert sich die Arbeit folgendermaßen: In einem ersten, einführenden Kapitel werden kurz die grundlegenden Begriffe aus den drei Gebieten der klassischen Mechanik, der Quantenmechanik und der Semiklassik erläutert. Das zweite Kapitel gibt einen Überblick über die semiklassische Theorie nach Miller und Weissman. Der zentrale Begriff ist hierbei der der Korrespondenzrelation, der einen direkten Zusammenhang zwischen klassischen Größen (erzeugenden Funtionen) und unitären Transformationen in der Quantenmechanik liefert. Ein Spezialfall dieser Korrespondenz ist der Zusammenhang zwischen der Zeitentwicklung eines quantenmechanischen kohärenten Zustands und der Evolution klassischer Bahnen. Im zentralen dritten Abschnitt wird erstmalig eine vollständige Herleitung des Phasenraumpropagators mittels Pfadintegralmethoden gegeben. Aus dieser Herleitung wird klar, daß eines der Probleme der Semiklassik in der Frage liegt, welche Hamiltonfunktion einem gegebenen Hamiltonoperator zuzuordnen ist. Auch der durch die semiklassischen Näherung eingeführte Fehler wird diskutiert. Anschließend wird aus dem "coherent state"-Propagator der Herman-Kluk-Propagator hergeleitet und dessen Eigenschaften besprochen. Das vierte Kapitel beschreibt in Vorgriff auf den letzten Abschnitt die numerische Implementierung des Herman-Kluk-Propagators und verschiedene Methoden zur Gewinnung von Energieeigenwerten eines Quantensystems. Hierzu wird eine phasenraumsensitive Integrationsroutine vorgestellt. Abschließend werden die Ergebnisse der numerischen Anwendung des Propagators auf verschiedene, charakteristische Quantensysteme vorgestellt und sowohl mit der exakten Quantenmechanik, als auch mit anderen semiklassischen Methoden verglichen. Dabei werden sowohl die Stärken, als auch die Schwächen dieser Methode deutlich werden.

An experimental study of spin wave quantization in arrays of micron size magnetic Ni80Fe20 islands (dots and wires) by means of Brillouin light scattering spectroscopy is reported. Dipolar-dominated spin wave modes laterally quantized in a single island with quantized wavevector values determined by the size of the island are studied. In the case of wires the frequencies of the modes and the transferred wavevector interval, where each mode is observed, are calculated. The results of the calculations are in a good agreement with the experimental data. In the case of circular dots the frequencies of the lowest observed modes decrease with increasing distance between the dots, thus indicating an essential dynamic magnetic dipole interaction between the dots with small interdot distances.

We report on the observation of spin wave quantization in tangentially magnetized Ni80Fe20 discs by means of Brillouin light scattering spectroscopy. For a large wave vector interval several discrete, dispersionless modes with a frequency splitting up to 2.5 GHz were observed. The modes are identified as being magne-tostatic surface spin wave modes quantized by their lateral confinement in the disc. For the lowest modes dynamic magnetic dipolar coupling between the discs is found for a disc spacing of 0.1microm.

Annual Report 1998
(1999)

We report on the observation of spin wave quantization in square arrays of micron size circular magnetic Ni80Fe20 dots by means of Brillouin light scattering spectroscopy. For a large wavevector interval several discrete, dispersionless modes with a frequency splitting of up to 2.5 GHz were observed. The modes are identified as magnetostatic surface spin waves laterally quantized due to in- plane confinement in each single dot. The frequencies of the lowest observed modes decrease with increasing distance between the dots, thus indicating an essential dynamic magnetic dipole interaction between the dots with small interdot distances.

The static and spin wave properties of regular square lattices of magnetic dots of 0.5-2 microm dot diameter and 1-4 microm periodicity patterned in permalloy films have been investigated by Brillouin light scattering. The samples have been structured using x-ray lithography and ion beam etching. The Brillouin light scattering spectra reveal both surface and bulk spin wave modes. The spin wave frequencies can be well described taking into account the demagnetization factor of each single dot. For the samples with smallest dot separation of 0.1 microm a fourfold in-plane magnetic anisotropy with the easy axis directed along the pattern diagonal is observed, indicating anisotropic coupling between the dots.

A computer control for a Sandercock-type multipath tandem Fabry-Perot interferometer is described, which offers many advantages over conventionally used analog control: The range of stability is increased due to active control of the laser light intensity and the mirror dither amplitude. The alignment is fully automated enabling start of a measurement within a minute after start of align, including optionally finding the optimum focus on the sample. The software control enables a programmable series of measurements with control of, e.g., the position and rotation of the sample, the angle of light incidence, the sample temperature, or the strength and direction of an applied magnetic field. Built-in fitting routines allow for a precise determination of frequency positions of excitation peaks combined with increased frequency accuracy due to a correction of a residual nonlinearity of the mirror stage drive.

We investigate the temperature dependence of the magnetization reversal process and of spinwaves in epi-taxially grown (001)-oriented [Fem/Aun]30 multilayers (m = 1, 2; n = 1- 6). Both polar magneto-optic Kerrr effect and Brillouin light scattering measurements reveal that all investigated multilayers, apart from the [Fe2/Au1]30-sample, are magnetized perpendicular to the film plane. The out-of-plane anisotropy constants are obtained. At high temperature, the magnetization curves are well described by an alternating stripe domain structure with free mobile domain walls, and at low temperature by a thermal activation model for the domain wall motion.

An experimental study of spin wave quantization in arrays of micron size magnetic Ni80Fe20 wires by means of Brillouin light scattering spectroscopy is reported. Dipolar-dominated Damon-Eshbach spin wave modes laterally quantized in a single wire with quantized wavevector values determined by the width of the wire are studied. The frequency splitting between quantized modes, which decreases with increasing mode number, depends on the wire sizes and is up to 1.5 GHz. The transferred wavevector interval, where each mode is observed, is calculated using a light scattering theory for confined geometries. The frequen-cies of the modes are calculated, taking into account finite size effects. The results of the calculations are in a good agreement with the experimental data.

Collisions of Spin Wave Envelope Solitons and Self-Focused Spin Wave Packets in Magnetic Films
(1999)

Head-on collisions between two-dimensional self-focused spin wave packets and between quasi-one-dimensional spin wave envelope solitons have been directly observed for the first time in yttrium-iron garnet (YIG) films by means of a space- and time-resolved Brillouin light scattering technique. We show that quasi-one-dimensional envelope solitons formed in narrow film strips ("waveguides") retain their shapes after collision, while the two-dimensional self-focused spin wave packets formed in wide YIG films are destroyed in collision.

Static and dynamic properties of patterned magnetic permalloy films are investigated. In square lattices of circular shaped permalloy dots an anisotropic coupling mechanism has been found, which is identified as being due to intrinsically unsaturated parts of the dots caused by spatial variations of demagnetizing field. In arrays of magnetic wires a quantization of the surface spin wave mode in several dispersionless modes is observed and quantitatively described. For large wavevectors the frequency separation between the modes becomes smaller and the frequencies converge to the dispersion of the dipole-exchange surface mode of a continuous film.

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The invariants of the basis can be used as coordinates in any cell of the coroot space and lead to an exactly solvable model of Sutherland type. We apply this construction to the \(F_4\) case.

The Hamiltonian of the \(N\)-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For \(N = 3\) and \(N = 4\) such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all \(N\).

The Filter-Diagonalization Method is applied to time periodic Hamiltonians and used to find selectively the regular and chaotic quasienergies of a driven 2D rotor. The use of N cross-correlation probability amplitudes enables a selective calculation of the quasienergies from short time propagation to the time T (N). Compared to the propagation time T (1) which is required for resolving the quasienergy spectrum with the same accuracy from auto-correlation calculations, the cross-correlation time T (N) is shorter by the factor N , that is T (1) = N T (N).