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The coordination of multiple external representations is important for learning, but yet a difficult task for students, requiring instructional support. The subject in this study covers a typical relation in physics between abstract mathematical equations (definitions of divergence and curl) and a visual representation (vector field plot). To support the connection across both representations, two instructions with written explanations, equations, and visual representations (differing only in the presence of visual cues) were designed and their impact on students’ performance was tested. We captured students’ eye movements while they processed the written instruction and solved subsequent coordination tasks. The results show that students instructed with visual cues (VC students) performed better, responded with higher confidence, experienced less mental effort, and rated the instructional quality better than students instructed without cues. Advanced eye-tracking data analysis methods reveal that cognitive integration processes appear in both groups at the same point in time but they are significantly more pronounced for VC students, reflecting a greater attempt to construct a coherent mental representation during the learning process. Furthermore, visual cues increase the fixation count and total fixation duration on relevant information. During problem solving, the saccadic eye movement pattern of VC students is similar to experts in this domain. The outcomes imply that visual cues can be beneficial in coordination tasks, even for students with high domain knowledge. The study strongly confirms an important multimedia design principle in instruction, that is, that highlighting conceptually relevant information shifts attention to relevant information and thus promotes learning and problem solving. Even more, visual cues can positively influence students’ perception of course materials.

Initiated by a task in tunable microoptics, but not limited to this application, a microfluidic droplet array in an upright standing module with 3 × 3 subcells and droplet actuation via electrowetting is presented. Each subcell is filled with a single (of course transparent) water droplet, serving as a movable iris, surrounded by opaque blackened decane. Each subcell measures 1 × 1 mm ² and incorporates 2 × 2 quadratically arranged positions for the droplet. All 3 × 3 droplets are actuated synchronously by electrowetting on dielectric (EWOD). The droplet speed is up to 12 mm/s at 130 V (Vrms) with response times of about 40 ms. Minimum operating voltage is 30 V. Horizontal and vertical movement of the droplets is demonstrated. Furthermore, a minor modification of the subcells allows us to exploit the flattening of each droplet. Hence, the opaque decane fluid sample can cover each water droplet and render each subcell opaque, resulting in switchable irises of constant opening diameter. The concept does not require any mechanically moving parts or external pumps.

Topological insulators (TI) are a fascinating new state of matter. Like usual insulators, their band structure possesses a band gap, such that they cannot conduct current in their bulk. However, they are able to conduct current along their edges and surfaces, due to edge states that cross the band gap. What makes TIs so interesting and potentially useful are these robust unidirectional edge currents. They are immune to significant defects and disorder, which means that they provide scattering-free transport.
In photonics, using topological protection has a huge potential for applications, e.g. for robust optical data transfer [1-3] – even on the quantum level [4, 5] – or to make devices more stable and robust [6, 7]. Therefore, the field of topological insulators has spread to optics to create the new and active research field of topological photonics [8-10].
Well-defined and controllable model systems can help to provide deeper insight into the mechanisms of topologically protected transport. These model systems provide a vast control over parameters. For example, arbitrary lattice types without defects can be examined, and single lattice sites can be manipulated. Furthermore, they allow for the observation of effects that usually happen at extremely short time-scales in solids. Model systems based on photonic waveguides are ideal candidates for this.
They consist of optical waveguides arranged on a lattice. Due to evanescent coupling, light that is inserted into one waveguide spreads along the lattice. This coupling of light between waveguides can be seen as an analogue to electrons hopping/tunneling between atomic lattice sites in a solid.
The theoretical basis for this analogy is given by the mathematical equivalence between Schrödinger and paraxial Helmholtz equation. This means that in these waveguide systems, the role of time is assigned to a spatial axis. The field evolution along the waveguides' propagation axis z thus models the temporal evolution of an electron's wave-function in solid states. Electric and magnetic fields acting on electrons in solids need to be incorporated into the photonic platform by introducing artificial fields. These artificial gauge fields need to act on photons in the same way that their electro-magnetic counterparts act on electrons. E.g., to create a photonic analogue of a topological insulator the waveguides are bent helically along their propagation axis to model the effect of a magnetic field [3]. This means that the fabrication of these waveguide arrays needs to be done in 3D.
In this thesis, a new method to 3D micro-print waveguides is introduced. The inverse structure is fabricated via direct laser writing, and subsequently infiltrated with a material with higher refractive index contrast. We will use these model systems of evanescently coupled waveguides to look at different effects in topological systems, in particular at Floquet topological systems.
We will start with a topologically trivial system, consisting of two waveguide arrays with different artificial gauge fields. There, we observe that an interface between these trivial gauge fields has a profound impact on the wave vector of the light traveling across it. We deduce an analog to Snell's law and verify it experimentally.
Then we will move on to Floquet topological systems, consisting of helical waveguides. At the interface between two Floquet topological insulators with opposite helicity of the waveguides, we find additional trivial interface modes that trap the light. This allows to investigate the interaction between trivial and topological modes in the lattice.
Furthermore, we address the question if topological edge states are robust under the influence of time-dependent defects. In a one-dimensional topological model (the Su-Schrieffer-Heeger model [11]) we apply periodic temporal modulations to an edge wave-guide. We find Floquet copies of the edge state, that couple to the bulk in a certain frequency window and thus depopulate the edge state.
In the two-dimensional Floquet topological insulator, we introduce single defects at the edge. When these defects share the temporal periodicity of the helical bulk waveguides, they have no influence on a topological edge mode. Then, the light moves around/through the defect without being scattered into the bulk. Defects with different periodicity, however, can – likewise to the defects in the SSH model – induce scattering of the edge state into the bulk.
In the end we will briefly highlight a newly emerging method for the fabrication of waveguides with low refractive index contrast. Moreover, we will introduce new ways to create artificial gauge fields by the use of orbital angular momentum states in waveguides.

We report the design, fabrication and experimental investigation of a spectrally wide-band terahertz spatial light modulator (THz-SLM) based on an array of 768 actuatable mirrors with each having a length of 220 μm and a width of 100 μm. A mirror length of several hundred micrometers is required to reduce diffraction from individual mirrors at terahertz frequencies and to increase the pixel-to-pixel modulation contrast of the THz-SLM. By means of spatially selective actuation, we used the mirror array as reconfigurable grating to spatially modulate terahertz waves in a frequency range from 0.97 THz to 2.28 THz. Over the entire frequency band, the modulation contrast was higher than 50% with a peak modulation contrast of 87% at 1.38 THz. For spatial light modulation, almost arbitrary spatial pixel sizes can be realized by grouping of mirrors that are collectively switched as a pixel. For fabrication of the actuatable mirrors, we exploited the intrinsic residual stress in chrome-copper-chrome multi-layers that forces the mirrors into an upstanding position at an inclination angle of 35°. By applying a bias voltage of 37 V, the mirrors were pulled down to the substrate. By hysteretic switching, we were able to spatially modulate terahertz radiation at arbitrary pixel modulation patterns.

A measurement technique, i.e. reflectance anisotropy/difference spectroscopy (RAS/RDS), which had originally been developed for in-situ
epitaxial growth control, is employed here for in-situ real-time etch-depth control during reactive ion etching (RIE) of cubic crystalline III/V
semiconductor samples. Temporal optical Fabry-Perot oscillations of the genuine RAS signal (or of the average reflectivity) during etching due
to the ever shrinking layer thicknesses are used to monitor the current etch depth. This way the achievable in-situ etch-depth resolution has
been around 15 nm. To improve etch-depth control even further, i.e. down to below 5 nm, we now use the optical equivalent of a mechanical
vernier scale– by employing Fabry-Perot oscillations at two different wavelengths or photon energies of the RAS measurement light – 5%
apart, which gives a vernier scale resolution of 5%. For the AlGaAs(Sb) material system a 5 nm resolution is an improvement by a factor of 3
and amounts to a precision in in-situ etch-depth control of around 8 lattice constants.

Previously in this journal we have reported on fundamental transversemode selection (TMS#0) of broad area semiconductor lasers
(BALs) with integrated twice-retracted 4f set-up and film-waveguide lens as the Fourier-transform element. Now we choose and
report on a simpler approach for BAL-TMS#0, i.e., the use of a stable confocal longitudinal BAL resonator of length L with a
transverse constriction.The absolute value of the radius R of curvature of both mirror-facets convex in one dimension (1D) is R = L
= 2f with focal length f.The round trip length 2L = 4f againmakes up for a Fourier-optical 4f set-up and the constriction resulting
in a resonator-internal beam waist stands for a Fourier-optical low-pass spatial frequency filter. Good TMS#0 is achieved, as long
as the constriction is tight enough, but filamentation is not completely suppressed.
1. Introduction
Broad area (semiconductor diode) lasers (BALs) are intended
to emit high optical output powers (where “high” is relative
and depending on the material system). As compared to
conventional narrow stripe lasers, the higher power is distributed
over a larger transverse cross-section, thus avoiding
catastrophic optical mirror damage (COMD). Typical BALs
have emitter widths of around 100 ????m.
Thedrawback is the distribution of the high output power
over a large number of transverse modes (in cases without
countermeasures) limiting the portion of the light power in
the fundamental transverse mode (mode #0), which ought to
be maximized for the sake of good light focusability.
Thus techniques have to be used to support, prefer, or
select the fundamental transverse mode (transverse mode
selection TMS#0) by suppression of higher order modes
already upon build-up of the laser oscillation.
In many cases reported in the literature, either a BAL
facet, the

We report on generation of pulsed broadband terahertz radiation utilizing the inverse spin hall effect in Fe/Pt bilayers on MgO and sapphire substrates. The emitter was optimized with respect to layer thickness, growth parameters, substrates and geometrical arrangement. The experimentally determined optimum layer thicknesses were in qualitative agreement with simulations of the spin current induced in the ferromagnetic layer. Our model takes into account generation of spin polarization, spin diffusion and accumulation in Fe and Pt and electrical as well as optical properties of the bilayer samples. Using the device in a counterintuitive orientation a Si lens was attached to increase the collection efficiency of the emitter. The optimized emitter provided a bandwidth of up to 8 THz which was mainly limited by the low-temperature-grown GaAs (LT-GaAS) photoconductive antenna used as detector and the pulse length of the pump laser. The THz pulse length was as short as 220 fs for a sub 100 fs pulse length of the 800 nm pump laser. Average pump powers as low as 25 mW (at a repetition rate of 75 MHz) have been used for terahertz generation. This and the general performance make the spintronic terahertz emitter compatible with established emitters based on optical rectification in nonlinear crystals.

The scales of white beetles strongly scatter light within a thin disordered network of
chitin filaments. There is no comparable artificial material achieving such a high scat-
tering strength within a thin layer of low refractive index material. Several analyses
investigated the scattering but could not explain the underlying concept. Here a model
system is described, which has the same optical properties as the white beetles’ scales
in the visible wavelength range. With some modification, it also explains the behavior
of the structures in the near infrared range. The comparison of the original structure and
the model system is done by finite-difference time-domain calculations. The calcula-
tions show excellent agreement with the beetles’ scales with respect to the reflectance,
the time-of-flight, and the intensity distribution in the far-field.

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N = 41 physics majors. We found that students’ performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88% correct). This finding supports the idea of introducing multiple representations of a physical concept to foster student understanding.Relevant eye-tracking measures demonstrate that both strategies imply different visual processing of the vector field plots, therefore reflecting conceptual differences between the strategies. Advanced analysis methods further reveal significant differences in eye movements between the best and worst performing students. For instance, the best students performed predominantly horizontal and vertical saccades, indicating correct interpretation of partial derivatives. They also focused on smaller regions when they balanced positive and negative flux. This mixed method research leads to new insights into student visual processing of vector field representations, highlights the advantages and limitations of eye-tracking methodologies in this context, and discusses implications for teaching and for future research. The introduction of saccadic direction analysis expands traditional methods, and shows the potential to discover new insights into student understanding and learning difficulties.

III/V semiconductor quantum dots (QD) are in the focus of optoelectronics research for about 25 years now. Most of the work
has been done on InAs QD on GaAs substrate. But, e.g., Ga(As)Sb (antimonide) QD on GaAs substrate/buffer have also gained
attention for the last 12 years.There is a scientific dispute on whether there is a wetting layer before antimonide QD formation, as
commonly expected for Stransky-Krastanov growth, or not. Usually ex situ photoluminescence (PL) and atomic force microscope
(AFM) measurements are performed to resolve similar issues. In this contribution, we show that reflectance anisotropy/difference
spectroscopy (RAS/RDS) can be used for the same purpose as an in situ, real-time monitoring technique. It can be employed not
only to identify QD growth via a distinct RAS spectrum, but also to get information on the existence of a wetting layer and its
thickness. The data suggest that for antimonide QD growth the wetting layer has a thickness of 1 ML (one monolayer) only.

Indentation into a metastable austenite may induce the phase transformation to the bcc phase. We study this process using
atomistic simulation. At temperatures low compared to the equilibrium transformation temperature, the indentation triggers the
transformation of the entire crystallite: after starting the transformation, it rapidly proceeds throughout the simulation crystallite.
The microstructure of the transformed sample is characterized by twinned grains. At higher temperatures, around the equilibrium
transformation temperature, the crystal transforms only locally, in the vicinity of the indent pit. In addition, the indenter
produces dislocation plasticity in the remaining austenite. At intermediate temperatures, the crystal continuously transforms
throughout the indentation process.

Influence of the Crystal Surface on the Austenitic and Martensitic Phase Transition in Pure Iron
(2018)

Using classical molecular dynamics simulations, we studied the influence that free
surfaces exert on the austenitic and martensitic phase transition in iron. For several single-indexed
surfaces—such as (100)bcc and (110)bcc as well as (100)fcc and (110)fcc surfaces—appropriate
pathways exist that allow for the transformation of the surface structure. These are the Bain,
Mao, Pitsch, and Kurdjumov–Sachs pathways, respectively. Tilted surfaces follow the pathway
of the neighboring single-indexed plane. The austenitic transformation temperature follows the
dependence of the specific surface energy of the native bcc phase; here, the new phase nucleates at
the surface. In contrast, the martensitic transformation temperature steadily decreases when tilting
the surface from the (100)fcc to the (110)fcc orientation. This dependence is caused by the strong
out-of-plane deformation that (110)fcc facets experience under the transformation; here, the new
phase also nucleates in the bulk rather than at the surface.

Based on the Lindblad master equation approach we obtain a detailed microscopic model of photons in a dye-filled cavity, which features condensation of light. To this end we generalise a recent non-equilibrium approach of Kirton and Keeling such that the dye-mediated contribution to the photon-photon interaction in the light condensate is accessible due to an interplay of coherent and dissipative dynamics. We describe the steady-state properties of the system by analysing the resulting equations of motion of both photonic and matter degrees of freedom. In particular, we discuss the existence of two limiting cases for steady states: photon Bose-Einstein condensate and laser-like. In the former case, we determine the corresponding dimensionless photon-photon interaction strength by relying on realistic experimental data and find a good agreement with previous theoretical estimates. Furthermore, we investigate how the dimensionless interaction strength depends on the respective system parameters.

Annual Report 2017
(2017)

Bulk-boundary correspondence in non-equilibrium dynamics of one-dimensional topological insulators
(2017)

Dynamical phase transitions (DPT) are receiving a rising interest. They are known to behave analogously to
equilibrium phase transitions (EPT) to a large extend. However, it is easy to see that DPT can occur in finite
systems, while EPT are only possible in the thermodynamic limit. So far it is not clear how far the analogy of
DPT and EPT goes. It was suggested, that there is a relation between topological phase transitions (TPT)
and DPT, but many open questions remain.
Typically, to study DPT, the Loschmidt echo (LE) after a quench is investigated, where DPT are visible as
singularities. For one-dimensional systems, each singularity is connected to a certain critical time scale, which
is given by the dispersion in the chain.
In topological free-fermion models with winding numbers 0 or 1, only the LE in periodic boundary conditions
(PBC) has been investigated. In open boundary conditions (OBC), these models are characterized by symmetry
protected edge modes in the topologically non-trivial phase. It is completely unclear how these modes affect
DPT. We investigate systems with PBC governed by multiple time scales with a Z topological invariant. In
OBC, we provide numerical evidence for the presence of bulk-boundary correspondence in DPT in quenches
across a TPT.

Annual Report 2016
(2017)

Combining ultracold atomic gases with the peculiar properties of Rydberg excited atoms gained a lot of theoretical and experimental attention in recent years. Embedded in the ultracold gas, an interaction between the Rydberg atom and the surrounding ground state atoms arises through the scattering of the Rydberg electron from an intruding perturber atom. This peculiar interaction gives rise to a plenitude of previously unobserved effects. Within the framework of the present thesis, this interaction is studied in detail for Rydberg \(P\)-states in rubidium.
Due to their long lifetime, atoms in Rydberg states are subject to scattering with the surrounding ground state atoms in the ultracold cloud. By measuring their lifetime as a function of the ground state atom flux, we are able to obtain the total inelastic scattering cross section as well as the partial cross section for associative ionisation. The fact that the latter is three orders of magnitude larger than the size of the formed molecular
ion indicates the presence of an efficient mass transport mechanism that is mediated by the Rydberg–ground state interaction. The immense acceleration of the collisional process shows a close analogy to a catalytic process. The increase of the scattering cross section renders associative ionisation an important process that has to be considered for experiments in dense ultracold systems.
The interaction of the Rydberg atom with a ground state perturber gives rise to a highly oscillatory potential that supports molecular bound states. These so-called ultralong-range Rydberg molecules are studied with high resolution time-of-flight spectroscopy, where we are able to determine the binding energies and lifetimes of the molecular states between the two fine structure split \(25P\)-states. Inside an electric field, we observe a broadening of the
molecular lines that indicates the presence of a permanent electric dipole moment, induced by the mixing with high angular momentum states. Due to the mixing of the ground state atom’s hyperfine states by the molecular interaction, we are able to observe a spin-flip of the perturber upon creation of a Rydberg molecule. Furthermore, an incidental near-degeneracy in the underlying level scheme of the \(25P\)-state gives rise to highly entangled states between the Rydberg fine structure state and the perturber’s hyperfine structure. These mechanisms can be used to manipulate the quantum state of a remote particle over distances that exceed by far the typical contact interaction range.
Apart from the ultralong-range Rydberg molecules that predominantly consist of only one low angular momentum state, a class of Rydberg molecules is predicted to exist that strongly mixes the high angular momentum states of the degenerate hydrogenic manifolds. These states, the so-called trilobite- and butterfly Rydberg molecules, show very peculiar properties that cannot be observed for conventional molecules. Here we present the first experimental observation of butterfly Rydberg molecules. In addition to an extensive spectroscopy that reveals the binding energy, we are also able to observe the rotational structure of these exotic molecules. The arising pendular states inside an electric field allow us, in comparison to the model of a dipolar rotor, to extract the precise bond
length and dipole moment of the molecule. With the information obtained in the present study, it is possible to photoassociate butterfly molecules with a selectable bond length, vibrational state, rotational state, and orientation inside an electric field.
By shedding light on various previously unrevealed aspects, the experiments presented in this thesis significantly deepen our knowledge on the Rydberg–ground state interaction and the peculiar effects arising from it. The obtained spectroscopic information on Rydberg molecules and the changed reaction dynamics for molecular ion creation will surely provide valuable data for quantum chemical simulations and provide necessary data to plan future experiments. Beyond that, our study reveals that the hyperfine interaction in Rydberg molecules and the peculiar properties of butterfly states provide very promising new ways to alter the short- and long-range interactions in ultracold many-body systems. In this sense the investigated Rydberg–ground state interaction not only lies right at
the interface between quantum chemistry, quantum many-body systems, and Rydberg physics, but also creates many new and fascinating possibilities by combining these fields.

Annual Report 2015
(2016)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2014
(2015)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2013
(2014)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2012
(2013)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2011
(2012)

Annual Report, Jahrbuch AG Magnetismus

The present dissertation contains the theoretical studies performed on the topic of a high energy deposition in matter. The work focuses on electronic excitation and relaxation processes on ultrafast timescales. Energy deposition by means of intense ultrashort (femtosecond) laser pulses or by means of swift heavy ions irradiation have a certain similarities: the final observable material modifications result from a number of processes on different timescales. First, the electronic excitation by photoabsorption or by ion impact takes place on subfemtosecond timescales. Then these excited electrons propagate and redistribute their energy interacting among themselves and exciting secondary generations of electrons. This typically takes place on femtosecond timescales. On the order of tens to hundreds femtoseconds the excited electrons are usually thermalized. The energy exchange with the lattice atoms lasts up to tens of picoseconds. The lattice temperature can reach melting point; then the material cools down and recrystalizes, forming the final modified nanostructures, which are observed experimentally. The processes on each previous step form the initial conditions for the following step. Thus, to describe the final phase transition and formation of nanostructures, one has to start from the very beginning and follow through all the steps.
The present work focuses on the early stages of the energy dissipation after its deposition, taking place in the electronic subsystems of excited materials. Different models applicable for different excitation mechanisms will be presented: in the thesis I will start from the description of high energy excitation (electron energies of \(\sim\) keV), then I shall focus on excitations to intermediate energies of electrons (\(\sim\) 100 eV), and finally coming down to a few eV electron excitations (visible light). The results will be compared with experimental observations.
For the high energy material excitation assumed to be caused by irradiation with swift heavy ions, the classical Asymptotical Trajectory Monte-Carlo (ATMC) is applied to describe the excitation of electrons by the impact of the projectile, the initial kinetics of electrons, secondary electron creation and Auger-redistribution of holes. I first simulate the early stage (first tens of fs) of kinetics of the electronic subsystem (in silica target, SiO\(_2\)) in tracks of ions decelerated in the electronic stopping regime. It will be shown that the well pronounced front of excitation in the electronic and ionic subsystems is formed due to the propagation of electrons, which cannot be described by models based on diffusion mechanisms (e.g. parabolic equations of heat diffusion). On later timescales, the thermalization time of electrons can be estimated as a time when the particle- and the energy propagation turns from the ballistic to the diffusive one. As soon as the electrons are thermalized, one can apply the Two Temperature Model. It will be demonstrated how to combine the MC output with the two temperature model. The results of this combination demonstrate that secondary ionizations play a very important role for the track formation process, leading to energy stored in the hole subsystem. This energy storage causes a significant delay of heating and prolongs the timescales of lattice modifications up to tens of picoseconds.
For intermediate energies of excitation (XUV-VUV laser pulse excitation of materials) I applied the Monte-Carlo simulation, modified where necessary and extended in order to take into account the electronic band structure and Pauli's principle for electrons within the conduction band. I apply the new method for semiconductors and for metals on examples of solid silicon and aluminum, respectively.
It will be demonstrated that for the case of semiconductors the final kinetic energy of free electrons is much less than the total energy provided by the laser pulse, due to the energy spent to overcome ionization potentials. It was found that the final total number of electrons excited by a single photon is significantly less than \(\hbar \omega / E_{gap}\). The concept of an 'effective energy gap' is introduced for collective electronic excitation, which can be applied to estimate the free electron density after high-intensity VUV laser pulse irradiation.
For metals, experimentally observed spectra of emitted photons from irradiated aluminum can be explained well with our results. At the characteristic time of a photon emission due to radiative decay of \(L-\)shell hole (\(t < 60\) fs), the distribution function of the electrons is not yet fully thermalized. This distribution consists of two main branches: low energy distribution as a distorted Fermi-distribution, and a long high energy tail. Therefore, the experimentally observed spectra demonstrate two different branches of results: the one observed with \(L-\)shell radiation emission reflects the low energy distribution, the Bremsstrahlung spectra reflects high energy (nonthermalized) tail. The comparison with experiments demonstrated a good agreement of the calculated spectra with the experimentally observed ones.
For the irradiation of semiconductor with low energy photons (visible light), a statistical model named the "extended multiple rate equation" is proposed. Based on the earlier developed multiple rate equation, the model additionally includes the interaction of electrons with the phononic subsystem of the lattice and allows for the direct determination of the conditions for crystal damage. Our model effectively describes the dynamics of the electronic subsystem, dynamical changes in the optical properties, and lattice heating, and the results are in very good agreement with experimental measurements on the transient reflectivity and the fluence damage threshold of silicon irradiated with a femtosecond laser pulse.

Annual Report 2010
(2011)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2009
(2010)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2008
(2009)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2007
(2008)

Annual Report, Jahrbuch AG Magnetismus

Ion energy spectra of a laser-produced Ta plasma have been investigated as a function of the flight distance from the focus. The laser (Nd:YAG, 20 ns, 210 mJ) is incident obliquely (45°) and focused to an intensity of about 10^11 W cm-2. The changes in the ion distributions have been analysed for the Ta+ to Ta6+ ions in an expansion range 64 - 220 cm. With increasing distance from the target, a weak but monotonic decrease is observed for the total number of ions, which is essentially due to the decrease in the number of the more highly charged species. For the Ta+ and Ta2+ ions the net changes approximately cancel. A more sophisticated picture of the recombination dynamics is obtained, however, if the changes within individual groups of ions expanding with different velocities are compared. Here, in the same spectrum, both increasing and decreasing ion numbers can be observed. This can be interpreted as direct evidence of recombination and its dependence on temperature, density and charge.

The particle flux produced by an obliquely incident Nd Q-switched pulse (20 ns) on a Ta target has been analysed with regard to its angular distribution resolved for both its neutral and ion components. The laser intensity has been varied in the range between about 10^10 - 10^11 W cm-2, which is appropriate for many low-irradiance applications. It is observed that, at all emission angles and for the whole range of laser intensities, the number of neutral species clearly dominates the composition of the particles. At 1.3 x 10^10 W cm-2 the total number of emitted particles is 4 x 10^14, scaling as E_L^¾ with the laser energy. While for relatively low laser energies the angular distribution shows the usual smooth cos-behaviour, an additional strong directive emission cone, superimposed upon the cos-distribution, develops if the laser energy is enhanced. Both the strength and the width strongly depend on the laser intensity. While at lower intensities a fit by a cos^n function with n ~ 10 seems appropriate, n increases to 26 at an intensity of 10^11 W cm-2 . It can be assumed that secondary energy transfer processes that are not yet fully understood are responsible for this anomalous emission.

The conversion efficiency of laser energy into kinetic ion energy in a laser-produced plasma has been investigated for two quite different targets: graphite and tantalum. The laser energy (intensity) varied from several mJ to 200 mJ (1O^9 to 7 x 10^10 W cm-2) which is appropriate to many applications of a laser produced ion source. The conversion efficiency as a function of the laser energy was directly determined by differential measurements of the charge, kinetic energy and angular emission distribution of the plasma ions in absolute units. Whilst for the Ta target a nearly constant efficiency of about 30% was observed, the graphite result shows an unexpectedly strong enhancement of the transfer efficiency of up to 80% in the laser intensity range around 1.5 x l0^10 W cm-2. It is assumed that the results are related to the difference in the surface roughness of the targets.

thesis deals with the investigation of the dynamics of optically excited (hot) electrons in thin and ultra-thin layers. The main interests concern about the time behaviour of the dissipation of energy and momentum of the excited electrons. The relevant relaxation times occur in the femtosecond time region. The two-photon photoemission is known to be an adequate tool in order to analyse such dynamical processes in real-time. This work expands the knowledge in the fields of electron relaxation in ultra-thin silver layers on different substrates, as well as in adsorbate states in a bandgap of a semiconductor. It contributes facts to the comprehension of spin transport through an interface between a metal and a semiconductor. The primary goal was to prove the predicted theory by reducing the observed crystal in at least one direction. One expects a change of the electron relaxation behaviour while altering the crystal’s shape from a 3d bulk to a 2d (ultra-thin) layer. This is due to the fact that below a determined layer thickness, the electron gas transfers to a two-dimensional one. This behaviour could be proven in this work. In an about 3nm thin silver layer on graphite, the hot electrons show a jump to longer relaxation time all over the whole accessible energy range. It is the first time that the temporal evolution of the relaxation of excited electrons could be observed during the transition from a 3d to a 2d system. In order to reduce or even eliminate the influence coming from the substrate, the system of silver on the semiconductor GaAs, which has a bandgap of 1.5eV at the Gamma-point, was investigated. The observations of the relaxation behaviour of hot electron in different ultra-thin silver layers on this semiconductor could show, that at metal-insulator-junctions, plasmons in the silver and in the interface, as well as cascading electrons from higher lying energies, have a huge influence to the dissipation of momentum and energy. This comes mainly from the band bending of the semiconductor, and from the electrons, which are excited in GaAs. The limitation of the silver layer on GaAs in one direction led to the expected generation of quantum well states (QWS) in the bandgap. Those adsorbate states have quantised energy- and momentum values, which are directly connected to the layer thickness and the standing electron wave therein. With the experiments of this work, published values could not only be completed and proved, but it could also be determined the time evolution of such a QWS. It came out that this QWS might only be filled by electrons, which are moving from the lower edge of the conduction band of the semiconductor to the silver and suffer cascading steps there. By means of the system silver on GaAs, and of the known fact that an excitation of electrons in GaAs with circularly polarised light of the energy 1.5eV does produce spin polarised electrons in the conduction band, it became possible to bring a contribution to the hot topic of spin injection. The main target of spin injection is the transfer of spin polarised electrons out of a ferromagnet into a semiconductor, in order to develop spin dependent switches and memories. It could be demonstrated here that spin polarised electrons from GaAs can move through the interface into silver, could be photoemitted from there and their spin was still being detectable. As a third investigation system, ultra-thin silver layers were deposited on the insulator MgO, which has a bandgap of 7.8eV. Also in this system, one could recognize a change in the relaxation time while reducing the dimension of the silver layer from thick to ultra-thin. Additionally, it came out an extreme large relaxation time at a layer thickness of 0.6 – 1.2nm. This time is an order of magnitude longer than at thick films, and this is a consequence of two factors: first, the reduction of the phase space due to the confined electron gas in the z-direction, and second, the slowlier thermalisation of the electron gas due to less accessible scattering partners.

Annual Report 2006
(2007)

Annual Report, Jahrbuch AG Magnetismus

Matter-wave Optics of Dark-state Polaritons: Applications to Interferometry and Quantum Information
(2006)

The present work "Materwave Optics with Dark-state Polaritons: Applications to Interferometry and Quantum Information" deals in a broad sense with the subject of dark-states and in particular with the so-called dark-state polaritons introduced by M. Fleischhauer and M. D. Lukin. The dark-state polaritons can be regarded as a combined excitation of electromagnetic fields and spin/matter-waves. Within the framework of this thesis the special optical properties of the combined excitation are studied. On one hand a new procedure to spatially manipulate and to increase the excitation density of stored photons is described and on the other hand the properties are used to construct a new type of Sagnac Hybrid interferometer. The thesis is devided into four parts. In the introduction all notions necessary to understand the work are described, e.g.: electromagnetically induced transparency (EIT), dark-state polaritons and the Sagnac effect. The second chapter considers the method developed by A. Andre and M. D. Lukin to create stationary light pulses in specially dressed EIT-media. In a first step a set of field equations is derived and simplified by introducing a new set of normal modes. The absorption of one of the normal modes leads to the phenomenon of pulse-matching for the other mode and thereby to a diffusive spreading of its field envelope. All these considerations are based on a homogeneous field setup of the EIT preparation laser. If this restriction is dismissed one finds that a drift motion is superimposed to the diffusive spreading. By choosing a special laser configuration the drift motion can be tailored such that an effective force is created that counteracts the spreading. Moreover, the force can not only be strong enough to compensate the diffusive spreading but also to exceed this dynamics and hence to compress the field envelope of the excitation. The compression can be discribed using a Fokker-Planck equation of the Ornstein-Uhlenbeck type. The investigations show that the compression leads to an excitation of higher-order modes which decay very fast. In the last section of the chapter this exciation will be discussed in more detail and conditions will be given how the excitation of higher-order modes can be avoided or even suppressed. All results given in the chapter are supported by numerical simulatons. In the third chapter the matterwave optical properties of the dark-state polaritons will be studied. They will be used to construct a light-matterwave hybrid Sagnac interferometer. First the principle setup of such an interferometer will be sketched and the relevant equations of motion of light-matter interaction in a rotating frame will be derived. These form the basis of the following considerations of the dark-state polariton dynamics with and without the influence of external trapping potentials on the matterwave part of the polariton. It will be shown that a sensitivity enhancement compared to a passive laser gyroscope can be anticipated if the gaseous medium is initially in a superfluid quantum state in a ring-trap configuration. To achieve this enhancement a simultaneous coherence and momentum transfer is furthermore necessary. In the last part of the chapter the quantum sensitivity limit of the hybrid interferometer is derived using the one-particle density matrix equations incorporating the motion of the particles. To this end the Maxwell-Bloch equations are considered perturbatively in the rotation rate of the noninertial frame of reference and the susceptibility of the considered 3-level \(\Lambda\)-type system is derived in arbitrary order of the probe-field. This is done to determine the optimum operation point. With its help the anticipated quantum sensitivity of the light-matterwave hybrid Sagnac interferometer is calculated at the shot-noise limit and the results are compared to state-of-the-art laser and matterwave Sagnac interferometers. The last chapter of the thesis originates from a joint theoretical and experimental project with the AG Bergmann. This chapter does no longer consider the dark-state polaritons of the last two chapters but deals with the more general concept of dark states and in particular with the transient velocity selective dark states as introduced by E. Arimondo et al. In the experiment we could for the first time measure these states. The chapter starts with an introduction into the concept of velocity selective dark states as they occur in a \(\Lambda\)-configuration. Then we introduce the transient velocity selective dark-states as they occur in an particular extension of the \(\Lambda\)-system. For later use in the simulations the relevant equations of motion are derived in detail. The simulations are based on the solution of the generalized optical Bloch equations. Finally the experimental setup and procedure are explained and the theoretical and experimental results are compared.

Annual Report 2005
(2006)

Annual Report, Jahrbuch AG Magnetismus

The symplectic group of homogeneous canonical transformations is represented in the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states. The intertwining relations between this representation and the algebra of Weyl operators are derived. They confirm the identification of this representation with Bogoliubov transformations.

Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial state (reference state) of the Boson field is either a normal state or a KMS state. The superselection sectors emerge if and only if the Boson field is infrared divergent, i. e. the bare photon number diverges and the ground state of the Boson field disappears in the continuum. The time scale of the decoherence depends on the strength of the infrared contributions of the interaction and on properties of the initial state of the Boson system. These results are first derived for a Hamiltonian with conservation laws. But in the most general case the Hamiltonian includes an additional scattering potential, and the only conserved quantity is the energy of the total system. The superselection sectors remain stable against the perturbation by the scattering processes.

Annual Report 2004
(2005)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2003
(2004)

Annual Report, Jahrbuch AG Magnetismus

Annual Report 2002
(2003)

Microsystem technology has been a fast evolving field over the last few years. Its ability to handle volumes in the sub-microliter range makes it very interesting for potential application in fields such as biology, medicine and pharmaceutical research. However, the use of micro-fabricated devices for the analysis of liquid biological samples still has to prove its applicability for many particular demands of basic research. This is particularly true for samples consisting of complex protein mixtures. The presented study therefore aimed at evaluating if a commonly used glass-coating technique from the field of micro-fluidic technology can be used to fabricate an analysis system for molecular biology. It was ultimately motivated by the demand to develop a technique that allows the analysis of biological samples at the single-cell level. Gene expression at the transcription level is initiated and regulated by DNA-binding proteins. To fully understand these regulatory processes, it is necessary to monitor the interaction of specific transcription factors with other elements - proteins as well as DNA sites - in living cells. One well-established method to perform such analysis is the Chromatin Immunoprecipitation (CHIP) assay. To map protein-DNA interactions, living cells are treated with formaldehyde in vivo to cross-link DNA-binding proteins to their resident sites. The chromatin is then broken into small fragments, and specific antibodies against the protein of interest are used to immunopurify the chromatin fragments to which those factors are bound. After purification, the associated DNA can be detected and analyzed using Polymerase Chain Reaction (PCR). Current CHIP technology is limited as it needs a relatively large number of cells while there is increasing interest in monitoring DNA-protein interactions in very few, if not single cells. Most notably this is the case in research on early organism development (embryogenesis). To investigate if microsystem technology can be used to analyze DNA-protein complexes from samples containing chromatin from only few cells, a new setup for fluid transport in glass capillaries of 75 µm inner diameter has been developed, forming an array of micro-columns for parallel affinity chromatography. The inner capillary walls were antibody-coated using a silane-based protocol. The remaining surface was made chemically inert by saturating free binding sites with suitable biomolecules. Variations of this protocol have been tested. Furthermore, the sensitivity of the PCR method to detect immunoprecipitated protein-DNA complexes was improved, resulting in the reliable detection of about 100 DNA fragments from chromatin. The aim of the study was to successively decrease the amount of analyzed chromatin in order to investigate the lower limits of this technology in regard to sensitivity and specificity of detection. The Drosophila GAGA transcription factor was used as an established model system. The protein has already been analyzed in several large-scale CHIP experiments and antibodies of excellent specificity are available. The results of the study revealed that this approach is not easily applicable to "real-world" biological samples in regard to volume reduction and specificity. Particularly, material that non-specifically adsorbed to capillary surfaces outweighed the specific antibody-antigen interaction, the system was designed for. It became clear that complex biological structures, such as chromatin-protein compositions, are not as easily accessible by techniques based on chemically modified glass surfaces as pre-purified samples. In the case of the investigated system, it became evident that there is a need for more research that goes beyond the scope of this work. It is necessary to develop novel coatings and materials to prevent non-specific adsorption. In addition to improving existing techniques, fundamentally new concepts, such as microstructures in biocompatible polymers or liquid transport on hydrophobic stripes on planar substrates to minimize surface contact, may also help to advance the miniaturization of biological experiments.

Annual Report 2000
(2001)

Annual Report 2001
(2002)

Abstract: This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras included) with respect to which the multiplication is continuous. 2) Such norms cannot be chosen to be submultiplicative and equal to one on the unit of the algebra.

Abstract: Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and SU_(2) lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.

Beyond the Thouless energy
(1999)

Abstract: The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy E_= 1 / sqrt (V), where V is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly 1/V < E < 1/sqrt (V), where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important totake into account only those symmetries which are exactly realized on the lattice.

Abstract: Recently, the chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that the deviations of lattice results from random matrix theory starting around the so-called Thouless energy can be understood in terms of chiral perturbation theory as well. Comparison of lattice data with chiral perturbation theory formulae allows us to compute the pion decay constant. We present results from a calculation for quenched SU(2) with Kogut-Susskind fermions at ß = 2.0 and 2.2.

Abstract: Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).

Abstract: Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. We focus on the bulk of the spectrum. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three-point correlation functions.

Abstract: We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body centered cubic solid on solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperature K_R = 0.40754(5) is almost by two orders of magnitude more accurate than the estimate of Mon, Landau and Stauffer [9].

Abstract: Local field effects on the rate of spontaneous emission and Lamb shift in a dense gas of atoms are discussed taking into account correlations of atomic center-of-mass coordinates. For this the exact retarded propagator in the medium is calculated in independent scattering approximation and employing a virtual-cavity model. The resulting changes of the atomic polarizability lead to modi cations of the medium response which can be of the same order of magnitude but of opposite sign than those due to local field corrections of the dielectric function derived by Morice, Castin, and Dalibard [Phys.Rev.A 51, 3896 (1995)].

Abstract: We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in Electromagnetically Induced Transparency. The properties of the dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.

Abstract: We analyze systematic (classical) and fundamental (quantum) limitations of the sensitivity of optical magnetometers resulting from ac-Stark shifts. We show that incontrast to absorption-based techniques, the signal reduction associated with classical broadening can be compensated in magnetometers based on phase measurements using electromagnetically induced transparency (EIT). However due to ac-Stark associated quantum noise the signal-to-noise ratio of EIT-based magnetometers attains a maximum value at a certain laser intensity. This value is independent on the quantum statistics of the light and defines a standard quantum limit of sensitivity. We demonstrate that an EIT-based optical magnetometer in Faraday configuration is the best candidate to achieve the highest sensitivity of magnetic field detection and give a detailed analysis of such a device.

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: We show that it is possible to "store" quantum states of single-photon fields by mapping them onto collective meta-stable states of an optically dense, coherently driven medium inside an optical resonator. An adiabatic technique is suggested which allows to transfer non-classical correlations from traveling-wave single-photon wave-packets into atomic states and vise versa with nearly 100% efficiency. In contrast to previous approaches involving single atoms, the present technique does not require the strong coupling regime corresponding to high-Q micro-cavities. Instead, intracavity Electromagnetically Induced Transparency is used to achieve a strong coupling between the cavity mode and the atoms.

Mirrorless oscillation based on resonantly enhanced 4-wave mixing: All-order analytic solutions
(1999)

Abstract: The phase transition to mirrorless oscillation in resonantly enhanced four-wave mixing in double-A systems are studied analytically for the ideal case of infinite lifetimes of ground-state coherences. The stationary susceptibilities are obtained in all orders of the generated fields and analytic solutions of the coupled nonlinear differential equations for the field amplitudes are derived and discussed.

Abstract: We analyze the above-threshold behavior of a mirrorless parametric oscillator based on resonantly enhanced four wave mixing in a coherently driven dense atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of pump photons is sufficient to reach the oscillator threshold. We demonstrate that due to the large group velocity delays associated with coherent media, an extremely narrow oscillator linewidth is possible, making a narrow-band source of non-classical radiation feasible.

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.

Abstract: Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are discussed. A Green's-function approach is used based on the multipolar interaction Hamiltonian of a collection of atomic dipoles with the quantised radiation field. The rate of decay and level shifts are determined by the retarded Green's-function of the interacting electric displacement field, which is calculated from a Dyson equation describing multiple scattering. The positions of the atomic dipoles forming the dielectrics are assumed to be uncorrelated and a continuum approximation is used. The associated unphysical interactions between different atoms at the same location is eliminated by removing the point-interaction term from the free-space Green's-function (local field correction). For the case of an atom in a purely dispersive medium the spontaneous emission rate is altered by the well-known Lorentz local-field factor. In the presence of absorption a result different from previously suggested expressions is found and nearest-neighbour interactions are shown to be important.

Abstract: We investigate the quantum properties of fields generated by resonantly enhanced wave mixing based on atomic coherence in Raman systems. We show that such a process can be used for generation of pairs of Stokes and anti-Stokes fields with nearly perfect quantum correlations, yielding almost complete (i.e. 100%) squeezing without the use of a cavity. We discuss the extension of the wave mixing interactions into the domain of a few interacting light quanta.

Abstract: Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.

Abstract: We show that the physical mechanism of population transfer in a 3-level system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive toolto design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which give maximum population transfer also under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses) there exists a higher-order trapping state, which is an exact constant of motion and analytic solutions for the atomic dynamics can be derived.

Abstract: We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum uctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.

Abstract: Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account non-cooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and level shifts due to multiple scattering or reabsorption of spontaneously emitted photons. In the Markov limit a non-linear and nonlocal single-atom density matrix equation is derived. To illustrate the effects of the quantum corrections we discuss amplified spontaneous emission and radiation trapping in a dense ensemble of initially inverted two-level atoms and the effects of radiative interactions on intrinsic optical bistability in coherently driven systems.

Abstract: We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response.

Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations
(1998)

Abstract: Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus static force. Originally this problem was formulated for a crystalline electron subject to the static electric field and is known nowadays as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and, in this sense, solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems like optical or semiconductor superlattices.

Abstract: We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, Quantum Noise (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic di erence equations in discretised time.

Abstract: We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as non-classical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.

Abstract: The recently proposed idea to generate entanglement between photon states via exchange interactions in an ensemble of atoms (J. D. Franson and T. B. Pitman, Phys. Rev. A 60 , 917 (1999) and J. D. Franson et al., (quant- ph/9912121)) is discussed using an S -matix approach. It is shown that if the nonlinear response of the atoms is negligible and no additional atom-atom interactions are present, exchange interactions cannot produce entanglement between photons states in a process that returns the atoms to their initial state. Entanglement generation requires the presence of a nonlinear atomic response or atom-atom interactions.

We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman - Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

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.

Abstract: The effect of intracavity Electromagnetically Induced Transparency on the properties of optical resonators and active laser devices is discussed theoretically. A pronounced frequency pulling and cavity linewidth narrowing are predicted. The effect can be used to substantially reduce classical and quantum phase noise of the beat-note of optical oscillators. Fundamental limits of this stabilization mechanism are discussed as well as its potential application to high-resolution spectroscopy.

Introduction: Recent developments in quantum communication and computing [1-3] stimulated an intensive search for physical systems that can be used for coherent processing of quantum information. It is generally believed that quantum entanglement of distinguishable quantum bits (qubits) is at the heart of quantum information processing. Significant efforts have been directed towards the design of elementary logic gates, which perform certain unitary processes on pairs of qubits. These gates must be capable of generating specific, in general entangled, superpositions of the two qubits and thus require a strong qubit-qubit interaction. Using a sequence of single and two-bit operations, an arbitrary quantum computation can be performed [2]. Over the past few years many systems have been identified for potential implementations of logic gates and several interesting experiments have been performed. Proposals for strong qubit-qubit interaction involve e.g. the vibrational coupling of cooled trapped ions [4], near dipole-dipole or spin-spin interactions such as in nuclear magnetic resonance [5], collisional interactions of confined cooled atoms [6] or radiative interactions between atoms in cavity QED [7]. The possibility of simple preparation and measurement of qubit states as well as their relative insensitivity to a thermal environment makes the latter schemes particularly interesting for quantum information processing. Most theoretical proposals on cavity-QED systems focus on fundamental systems involving a small number of atoms and few photons. These systems are sufficiently simple to allow for a first-principle description. Their experimental implementation is however quite challenging. For example, extremely high-Q micro-cavities are needed to preserve coherence during all atom-photon interactions. Furthermore, single atoms have to be confined inside the cavities for a sufficiently long time. This requires developments of novel cooling and trapping techniques, which is in itself a fascinating direction of current research. Despite these technical obstacles, a remarkable progress has been made in this area: quantum processors consisting of several coupled qubits now appear to be feasible.

Abstract: We propose a simple method for measuring the populations and the relative phase in a coherent superposition of two atomic states. The method is based on coupling the two states to a third common (excited) state by means of two laser pulses, and measuring the total fluorescence from the third state for several choices of the excitation pulses.

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.

Dynamics of Excited Electrons in Copper and Ferromagnetic Transition Metals: Theory and Experiment
(2000)

Both theoretical and experimental results for the dynamics of photoexcited electrons at surfaces of Cu and the ferromagnetic transition metals Fe, Co, and Ni are presented. A model for the dynamics of excited electrons is developed, which is based on the Boltzmann equation and includes effects of photoexcitation, electron-electron scattering, secondary electrons (cascade and Auger electrons), and transport of excited carriers out of the detection region. From this we determine the time-resolved two-photon photoemission (TR-2PPE). Thus a direct comparison of calculated relaxation times with experimental results by means of TR-2PPE becomes possible. The comparison indicates that the magnitudes of the spin-averaged relaxation time t and of the ratio t_up/t_down of majority and minority relaxation times for the different ferromagnetic transition metals result not only from density-of-states effects, but also from different Coulomb matrix elements M. Taking M_Fe > M_Cu > M_Ni = M_Co we get reasonable agreement with experiments.

We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS) which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic properties of the tripod scheme, such as the solution for coincident pulses, the behaviour of the system in the adiabatic limit for delayed pulses, the conditions for no ionization and for maximal ionization, and the optimal conditions for population transfer between the discrete states via the continuum. In the case when one of the discrete states is strongly coupled to the continuum, the population dynamics reduces to a standard two-state LICS problem (involving the other two states) with modified parameters; this provides the opportunity to customize the parameters of a given two-state LICS system.

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.

Abstract: Let H_1 , H_2 be complex Hilbert spaces, H be their Hilbert tensor product and let tr_2 be the operator of taking the partial trace of trace class operators in H with respect to the space H_2 . The operation tr_2 maps states in H (i.e. positive trace class operators in H with trace equal to one) into states in H_1 . In this paper we give the full description of mappings that are linear right inverse to tr_2 . More precisely, we prove that any affine mapping F(W) of the convex set of states in H_1 into the states in H that is right inverse to tr_2 is given by W -> W x D for some state D in H_2 . In addition we investigate a representation of the quantum mechanical state space by probability measures on the set of pure states and a representation - used in the theory of stochastic Schrödinger equations - by probability measures on the Hilbert space. We prove that there are no affine mappings from the state space of quantum mechanics into these spaces of probability measures.

Abstract: It is shown that nonvacuum pseudoparticles can account forquantum tunneling and metastability. In particular the saddle-point nature of the pseudoparticles is demonstrated, and the evaluation of path-integrals in their neighbourhood. Finally the relation between instantons and bounces is used to derive a result conjectured by Bogomolny andFateyev.

Abstract: The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.

Abstract: The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N)-Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d = 2 and d = 4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so. (To appear in the Proceedings of the XXII Conference on Differential Geometry Methods in Theoretical Physics, Ixtapa, Mexico, September 20-24, 1993)

Abstract: Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields "doubble Phi", CC and "Phi"C, the conformal fields which are symmetric traceless tensors of rank l and have dimensions "delta" = 2+l or 8+l+ "eta"(l) and "eta"(l) = O(N ^ -2) are identified. The unidentified field have dimension "delta" = "lambda"+l+eta(l) with "lambda" >= 10. The anomalous dimensions eta(l) are calculated at order O(N ^ -2) for both 2 ^ -1/2(-"doubble Phi" + CC) and 2 ^ -1/2(-"Phi"C + C"Phi") and are found to be the same, proving U(1)_Y symmetry. The relevant coupling constants are given at order O(1).

Abstract: We analyse 4-dimensional massive "phi" ^ 4 theory at finite temperature T in the imaginary-time formalism. We present a rigorous proof that this quantum field theory is renormalizable, to all orders of the loop expansion. Our main point is to show that the counterterms can be chosen temperature independent, so that the temperature flow of the relevant parameters as a function of T can be followed. Our result confirms the experience from explicit calculations to the leading orders. The proof is based on flow equations, i.e. on the (perturbative) Wilson renormalization group. In fact we will show that the difference between the theories at T > 0 and at T = 0 contains no relevant terms. Contrary to BPHZ type formalisms our approach permits to lay hand on renormalization conditions and counterterms at the same time, since both appear as boundary terms of the renormalization group flow. This is crucial for the proof.

Abstract: We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schrödinger operator. We prove the feasibility of our method by constructing an " AG_3 model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the B_3 model. In order to better understand features of our construction we exhibit the F_4 rational model with our method.

Abstract: We calculate exact analytical expressions for O(alpha s) 3-jet and O (alpha^2 s ) 4-jet cross sections in polarized deep inelastic lepton nucleon scattering. Introducing an invariant jet definition scheme, we present differential distributions of 3- and 4-jet cross sections in the basic kinematical variables x and W^2 as well as total jet cross sections and show their dependence on the chosen spin-dependent (polarized) parton distributions. Noticebly differences in the predictions are found for the two extreme choices, i.e. a large negative sea-quark density or a large positive gluon density. Therefore, it may be possible to discriminate between different parametrizations of polarized parton densities, and hence between the different physical pictures of the proton spin underlying these parametrizations.

Abstract: We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis.

Magnetic anisotropies of MBE-grown fcc Co(110)-films on Cu(110) single crystal substrates have been determined by using Brillouin light scattering(BLS) and have been correlated with the structural properties determined by low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). Three regimes of film growth and associated anisotropy behavior are identified: coherent growth in the Co film thickness regime of up to 13 Å, in-plane anisotropic strain relaxation between 13 Å and about 50 Å and inplane isotropic strain relaxation above 50 Å. The structural origin of the transition between anisotropic and isotropic strain relaxation was studied using STM. In the regime of anisotropic strain relaxation long Co stripes with a preferential [ 110 ]-orientation are observed, which in the isotropic strain relaxation regime are interrupted in the perpendicular in-plane direction to form isotropic islands. In the Co film thickness regime below 50 Å an unexpected suppression of the magnetocrystalline anisotropy contribution is observed. A model calculation based on a crystal field formalism and discussed within the context of band theory, which explicitly takes tetragonal misfit strains into account, reproduces the experimentally observed anomalies despite the fact that the thick Co films are quite rough.

We report on the observation of quantized surface spin waves in periodic arrays of magnetic Ni81Fe19 wires by means of Brillouin light scattering spectroscopy. At small wavevectors (q_1 = 0 - 0.9*100000 cm^-1 ) several discrete, dispersionless modes with a frequency splitting of up to 0.9 GHz were observed for the wavevector oriented perpendicular to the wires. From the frequencies of the modes and the wavevector interval, where each mode is observed, the modes are identified as dipole-exchange surface spin wave modes of the film with quantized wavevector values determined by the boundary conditions at the lateral edges of the wires. With increasing wavevector the separation of the modes becomes smaller, and the frequencies of the discrete modes converge to the dispersion of the dipole-exchange surface mode of a continuous film.

Absract: We report on measurements of the two-dimensional intensity distribtion of linear and non-linear spin wave excitations in a LuBiFeO film. The spin wave intensity was detected with a high-resolution Brillouinlight scatteringspectroscopy setup. The observed snake-like structure of the spin wave intensity distribution is understood as a mode beating between modes with different lateral spin wave intensity distributions. The theoretical treatment of the linear regime is performed analytically, whereas the propagation of non-linear spin waves is simulated by a numerical solution of a non-linear Schrödinger equation with suitable boundary conditions.

Abstract: The calculation of absorption cross sections for minimal scalars in supergravity backgrounds is an important aspect of the investigation of AdS/CFT correspondence and requires a matching of appropriate wave functions. The low energy case has attracted particular attention. In the following the dependence of the cross section on the matching point is investigated. It is shown that the low energy limit is independent of the matching point and hence exhibits universality. In the high energy limit the independence is not maintained, but the result is believed to possess the correct energy dependence.

Abstract: A Born-Infeld theory describing a D2-brane coupled to a 4-form RR field strength is considered, and the general solutions of the static and Euclidean time equations are derived and discussed. The period of the bounce solutions is shown to allow a consideration of tunneling and quantum-classical transitions in the sphaleron region. The order of such transitions, depending on the strength of the RR field strength, is determined. A criterion is then derived to confirm these findings.

Abstract: The functional relation between interquark potential and interquark distance is explicitly derived by considering the Nambu-Goto action in the AdS5 X S 5 background. It is also shown that a similar relation holds in a general background. The implications of this relation for confinement are briefly discussed.

A new method is used to investigate the tunneling between two weakly-linked Bose-Einstein con- densates confined in double-well potential traps. The nonlinear interaction between the atoms in each well contributes to a finite chemical potential, which, with consideration of periodic instantons, leads to a remarkably high tunneling frequency. This result can be used to interpret the newly found Macroscopic Quantum Self Trapping (MQST) effect. Also a new kind of first-order crossover between different regions is predicted.

Abstract: The transition from the instanton-dominated quantum regime to the sphaleron-dominated classical regime is studied in the d = 2 abelian-Higgs model when the spatial coordinate is compactified to S1. Contrary to the noncompactified case, this model allows both sharp first-order and smooth second-order transitions depending on the size of the circle. This finding may make the model a useful toy model for the analysis of baryon number violating processes.

Abstract: Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born-Infeld theory. In particular the equation of small fluctuations about the D-brane is derived and converted into a modified Mathieu equation and - complementing earlier low-energy investigations in the case of the dilaton-axion system - studied in the high-energy domain. Explicit expressions are derived for the S-matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.