Siegert pseudostates: completeness and time evolution

Within the theory of Siegert pseudostates, it is possible to accurately calculate bound states and resonances. The energy continuum is replaced by a discrete set of states. Many questions of interest in scattering theory can be addressed within the framework of this formalism, thereby avoiding the need to treat the energy continuum. For practical calculations it is important to know whether a certain subset of Siegert pseudostates comprises a basis. This is a nontrivial issue, because of the unusual orthogonality and overcompleteness properties of Siegert pseudostates. Using analytical and numerical arguments, it is shown that the subset of bound states and outgoing Siegert pseudostates forms a basis. Time evolution in the context of Siegert pseudostates is also investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's function, the time-dependent expansion of a wave packet in terms of Siegert pseudostates is derived. In this expression, all Siegert pseudostates--bound, antibound, outgoing, and incoming--are employed. Each of these evolves in time in a nonexponential fashion. Numerical tests underline the accuracy of the method

Theory of x-ray absorption by laser-dressed atoms

An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2). The laser dresses the core-excited atomic states, which introduces a dependence of the cross section on the angle between the polarization vectors of the two linearly polarized radiation sources. We use the Hartree-Fock-Slater approximation to describe the atomic many-particle problem in conjunction with a nonrelativistic quantum-electrodynamic approach to treat the photon-electron interaction. The continuum wave functions of ejected electrons are treated with a complex absorbing potential that is derived from smooth exterior complex scaling. The solution to the two-color (x-ray plus laser) problem is discussed in terms of a direct diagonalization of the complex symmetric matrix representation of the Hamiltonian. Alternative treatments with time-independent and time-dependent non-Hermitian perturbation theories are presented that exploit the weak interaction strength between x rays and atoms. We apply the theory to study the photoabsorption cross section of krypton atoms near the K edge. A pronounced modification of the cross section is found in the presence of the optical laser.Comment: 13 pages, 3 figures, 1 table, RevTeX4, corrected typoe

All-optical microscope autofocus based on an electrically tunable lens and a totally internally reflected IR laser

Funding Information: Deutsche Forschungsgemeinschaft (SFB 688); NIH (Prime Grant No. 5 R01 DA038882-02); University of Wuerzburg.Microscopic imaging at high spatial-temporal resolution over long time scales (minutes to hours) requires rapid and precise stabilization of the microscope focus. Conventional and commercial autofocus systems are largely based on piezoelectric stages or mechanical objective actuators. Objective to sample distance is either measured by image analysis approaches or by hardware modules measuring the intensity of reflected infrared light. We propose here a truly all-optical microscope autofocus taking advantage of an electrically tunable lens and a totally internally reflected infrared probe beam. We implement a feedback-loop based on the lateral position of a totally internally reflected infrared laser on a quadrant photodetector, as an indicator of the relative defocus. We show here how to treat the combined contributions due to mechanical defocus and deformation of the tunable lens. As a result, the sample can be kept in focus without any mechanical movement, at rates up to hundreds of Hertz. The device requires only reflective optics and can be implemented at a fraction of the cost required for a comparable piezo-based actuator.Publisher PDFPeer reviewe

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Iso-XFEM method is an evolutionary optimization method developed in our previous studies to enable the generation of high resolution topology optimised designs suitable for additive manufacture. Conventional approaches for topology optimization require additional post-processing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this time-consuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this paper, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test-cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated

Properties of metastable alkaline-earth-metal atoms calculated using an accurate effective core potential

The first three electronically excited states in the alkaline-earth-metal atoms magnesium, calcium, and strontium comprise the (nsnp) triplet P^o_J (J=0,1,2) fine-structure manifold. All three states are metastable and are of interest for optical atomic clocks as well as for cold-collision physics. An efficient technique--based on a physically motivated potential that models the presence of the ionic core--is employed to solve the Schroedinger equation for the two-electron valence shell. In this way, radiative lifetimes, laser-induced clock shifts, and long-range interaction parameters are calculated for metastable Mg, Ca, and Sr.Comment: 13 pages, 9 table

Linescan microscopy data to extract diffusion coefficient of a fluorescent species using a commercial confocal microscope

We are grateful to the Max Delbrück Center for Molecular Medicine in the Helmholtz Association for core support and funding. P.A. and M.J.L. would like to acknowledge funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 421152132-SFB1423 subproject C03.We report here on the measurement of the diffusion coefficient of fluorescent species using a commercial microscope possessing a resonant scanner. Sequential linescans with a rate of up to 12 kHz yield a temporal resolution of 83 μs, making the setup amenable to measure diffusion rates over a range covering at least three orders of magnitude, from 100 μm2/s down to 0.1 μm2/s. We share representative data sets covering (i) the diffusion of a dye molecule, observed in media of different viscosities and (ii) the diffusion of a prototypical membrane receptor.  The data can be valuable for researchers interested in the rapid diffusion properties of nuclear, cytosolic or membrane bound proteins fused to fluorescent tags.Publisher PDFPeer reviewe