Resonances in Mie scattering by an inhomogeneous atomic cloud

Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that resonances in Mie theory can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. At odds with uniform clouds which show a complex structure including narrow peaks, these densities show resonances, yet only under the form of quite regular and contrasted oscillations. Copyright (C) EPLA, 2012

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

The calculation of photoelectron angular distributions with jet-like structure from scattering theory

Photoelectron angular distributions produced in above-threshold ionization (ATI) are analysed using a nonperturbative scattering theory. The numerical results are in good qualitative agreement with recent measurements. Our study shows that the origin of the jet-like structure arises from the inherent properties of the ATI process and not from the angular momentum of either the initial or the excited states of the atom.

Plasma inverse scattering theory

The object of this report is to calculate the electron density profile of plane stratified inhomogeneous plasmas. The electron density profile is obtained through a numerical solution of the inverse scattering algorithm.

The inverse scattering algorithm connects the time dependent reflected field resulting from a δ-function field incident normally on the plasma to the inhomogeneous plasma density.

Examples show that the method produces uniquely the electron density on or behind maxima of the plasma frequency.

It is shown that the δ-function incident field used in the inverse scattering algorithm can be replaced by a thin square pulse.

The 90-degree problem of scattering theory revisited: dynamical turbulence effects versus nonlinear effects

The 90° problem of cosmic-ray transport theory is revisited in this paper. By using standard forms of the wave spectrum in the solar wind, the pitch-angle Fokker–Planck coefficient and the parallel mean free path are computed for different resonance functions. A critical comparison is made of the strength of 90° scattering due to plasmawave effects, dynamical turbulence effects and nonlinear effects. It is demonstrated that, only for low-energy cosmic particles, dynamical effects are usually dominant. The novel results presented here are essential for an effective comparison of heliospheric observations for the parallel mean free path with the theoretical model results.

Scattering theory of cooling and heating in optomechanical systems

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

Role of Mie scattering in the seeding of matter-wave superradiance

Matter-wave superradiance is based on the interplay between ultracold atoms coherently organized in momentum space and a backscattered wave. Here, we show that this mechanism may be triggered by Mie scattering from the atomic cloud. We show how the laser light populates the modes of the cloud and thus imprints a phase gradient on the excited atomic dipoles. The interference with the atoms in the ground state results in a grating that in turn generates coherent emission, contributing to the backward light wave onset. The atomic recoil "halos" created by the Mie-scattered light exhibit a strong anisotropy, in contrast to single-atom scattering.

激光尘埃粒子计数器微型光学传感器的研究

研制成功便携式激光尘埃粒子计数器的核心部件——微型光学传感器。该传感器采用直角散射光收集形式。以高功率半导体激光器作为光源，同时采用高性能的PIN型光电二极管作为光电探测器。散射光收集系统为单一大数值孔径的球面反射镜，其对粒子散射光的收集角范围从20°到160°。粒子散射光信号是脉冲信号，其频谱成份主要在高频段，所以在PIN型光电二极管后用一个带通式前置放大器来消除外界的低频噪声．根据米氏散射理论计算了该光学传感器的光散射响应特性，并用聚苯乙烯标准粒子实测了该光学传感器的性能。结果表明，该系统具有高的信噪

尘埃粒子计数器中光源对传感器光通量的影响分析

在Mie散射理论基础上，由单分散射的光强表达式导出在偏振光的入射条件下一定立体角内的散射光通量的表达式，并与自然光入射作比较。计算了在相同强度不同光源入射下，尘埃粒子计数器的两种常用散射光收集系统收集的散射光通量。结果表明：采用近前向散射光收集系统得到的光通量相等；而采用直角方向散射光收集系统时两者并不相等，且在平面偏振光入射时，收集的散射光通量还跟探测器中心与入射光偏振方向夹角有关。用MATLAB编程计算，得出了在探测器中心与偏振方向的夹角成90°或270°位置时，收集的散射光通量有极值的结论，为激光尘

Laser-vapour interaction in high-power cw Nd:YAG laser welding

During high-power cw Nd:YAG laser welding a vapour plume is formed containing vaporised material ejected from the keyhole. Spectroscopic studies of the vapour emission have demonstrated that the vapour can be considered as thermally excited gas with a stable temperature (less than 3000K), not as partially ionised plasma. In this paper, a review of temperatures in the vapour plume is presented. The difficulties in the analysis of the plume spectroscopic results are reviewed and explained. It is shown that particles present in the vapour interact with the laser beam, attenuating it. The attenuation can be calculated with Mie scattering theory, however, vaporisation and particle formation also both play a major role in this process. The laser beam is also defocused due to the scattering part of the attenuation mechanism, changing the energy density in the laser beam. Methods for mitigating the effects of the laser beam-vapour interaction, using control gases, are presented together with their advantages and disadvantages. This 'plume control' has two complementary roles: firstly, the gas must divert the vapour plume from out of the laser beam path, preventing the attenuation. Secondly, the gas has to stabilise the front wall of the keyhole, to prevent porosity formation.