A Population Model of Thermal Radiation

Abstract

The population model of cavity photons previously introduced is analysed by identifying the non-Markov evolution in terms of phases whose durations are themselves independent and exponentially distributed random variables. The resulting radiation is shown to have thermal characteristics for an appropriate choice of the population parameters. The detection process is explicitly introduced and its characteristics are obtained. The model is shown to be viable enough to produce intensity spectra of different shapes corresponding to the resulting radiation.     

Free-space diffraction and the fractional fourier transform

Abstract

An explicit expression is derived for free-space propagation in terms of the fractional Fourier transform. The expression contains two arbitrary parameters, which can be, for example, an original phase curvature together with a scaling parameter or, alternatively, the order of fractional transformation. Appropriate choice of these parameters is discussed. This approach is then applied to the free-space propagation of Gaussian beams.     

The standard model in cavity quantum electrodynamics. II. Coupling constants and atom field interaction

Abstract

Specific forms of the travelling and trapped vector mode functions for a three-dimensional Fabry-Perot cavity are developed from the general results of the preceding paper, with parameters describing the output cavity mirror chosen for a typical high Q cavity case. Cavity and external quasi-mode functions associated with the quasi-mode theory of macroscopic canonical quantization are then obtained via an idealized choice of output mirror parameters. The coupling constants describing photon exchange processes between the single cavity quasi-mode associated with each Fabry-Perot resonance and various external quasi-modes are calculated, and their slow dependence on the external quasi-mode frequency shows that the conditions for irreversible Markovian damping of the cavity quasi-mode are satisfied. For radiative atoms placed in the cavity the coupling constants for energy exchange processes with sideways travelling external quasi-modes also vary slowely, so that Markovian spontaneous emission damping occurs for the radiative atoms. However, their coupling with the isolated cavity quasi-modes is associated with reversible photon exchanges as represented via one photon Rabi frequencies. The standard model in cavity quantum electrodynamics, in which the basic processes are described by a cavity damping rate, a radiative atom spontaneous decay rate and an atom-cavity mode coupling constant has now been justified in terms of the quasi-mode theory of macroscopic canonical quantization.     

Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

Control of superluminal transit through a heterogeneous medium

Abstract

We consider pulse propagation through a two component composite medium (metal inclusions in a dielectric host) with or without cavity mirrors. We show that a very thin slab of such a medium, under conditions of localized plasmon resonance, can lead to significant superluminality with detectable levels of the transmitted pulse. A cavity containing the heterogeneous medium is shown to lead to subluminal-to-superluminal transmission depending on the volume fraction of the metal inclusions. The predictions of the phase time calculations are verified by explicit calculations of the transmitted pulse shapes. We also demonstrate the independence of phase time on system width and the volume fraction under specific conditions.     

The Density-matrix Approach to Cavity Radiation and Population Point Process Models

Abstract

The problem of cavity radiation and its detection is reviewed and in particular the evolution equation of Scully and Lamb is studied with special reference to coarse-graining. It is shown that the resulting evolution equation corresponds to that of a Markov process representing the cavity population. The approximations corresponding to oscillations below and above threshold reduce the process to a branching process with immigration. The effect of the detector is also studied and the photocount statistics are shown to correspond to those of an emigration process superposed on the branching process. The identification of the evolution as a branching process is shown to result in considerable simplicity and ease in the determination of the statistical characteristics of the cavity population. In particular the Shepherd model is identified as a special case; a complex situation like the multi-mode oscillation is also identified and the corresponding statistical characteristics obtained.     

Adiabatic state preparation in a cavity

Abstract

The paper discusses the single-mode Jaynes-Cummings model with time-dependent parameters. Solvable models for two-level systems are utilized to consider the changes in the photon distribution effected by the passage of atoms through the cavity. It is suggested that such systems may be used as filters to modify the photon distribution. The effect can be enhanced by repeatedly sending new atoms through the cavity. We show that such filters can cut out either small or large photon numbers. It is also shown that the method can be used to narrow down photon distributions and in this way achieve highly non-classical sub-Poissonian states. Some limitations and applications of the method are presented.     

X-ray microtomography study of cavity coalescence during superplastic deformation of an Al–Mg alloy

Abstract

Coalescence between cavities induced during superplastic deformation of an Al–Mg alloy was studied, in particular by X-ray microtomography, which can provide three-dimensional images of the population of cavities through the volume of the material. From such images, the variation with strain of the number of cavities per unit volume was measured for various strain rates. For a given strain, the number of cavities increases with strain rate, but for a given strain rate, it is shown that significant interlinkage between cavities takes place in a large strain interval. Moreover, although the cavity volume fraction increases with strain, it becomes difficult to describe the population of cavities by a mean volume since the largest cavity may concentrate more than 70% of the total volume of cavities. For such circumstances, an interlinkage parameter was introduced as the ratio between the volume of the largest cavity and the total volume of cavities for given experimental conditions (strain and strain rate). This work illustrates the uncertainty of some conclusions directly drawn from data obtained using only two-dimensional techniques, such as quantitative metallography performed on polished sections.     

Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

Abstract

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.     

Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose–Einstein condensate: a new tool to measure weak force

Abstract

We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.     

Spontaneous emission from a planar microcavity below threshold and the wolf effect

Abstract

Equivalence between a planar microcavity below threshold and a partially coherent primary source is pointed out for the first time. Spatial coherence properties of spontaneous emission from the planar microcavity are controllable by varying two cavity parameters of the cavity length and the mirror reflectivity. The spontaneous emission gives rise to the Wolf effect which is spectral changes induced by the spatial coherence. It is clearly shown from our theoretical analyses that the spectrum in the far field shifts toward higher frequencies than that on the emitting plane of the planar microcavity. In particular, the blue shift of the far-field spectrum takes a maximum value at the centre of the far-field plane and decreases gradually far away from the centre. Moreover, the blue shift increases with decreasing values of the two cavity parameters.     

Numerical study of superplastic deformation with superimposed pressure for cavity sensitive materials

Abstract

The non-uniform deformation (necking and thinning) development and fracture of superplastic materials under both uniaxial tension and circular sheet bulging are numerically analysed by considering the effects of strain rate sensitivity and cavity growth with superimposed pressure. It is found that the fracture mode, which is controlled by both strain rate sensitivity and cavity growth rate, can be changed by superimposed pressure from fracture without external necking for cavity sensitive alloys at zero pressure to fracture with necking development or extensive thinning at pressure large enough to completely suppress cavity growth. Fracture mechanism diagrams are presented which enable prediction of the fracture mode to be made as a function of material parameters and pressure conditions for uniaxial tension and bulging.

MST/724     

Development of nanocrystalline Fe–Co alloys using mechanical alloying

Abstract

Nanostructured alloys have considerable potential as soft magnetic materials. In these materials a small magnetic anisotropy is desired, which necessitates the choice of cubic crystalline phases of Fe, Co, Ni, etc. In the present work, Fe–50 at.-%Co alloys were prepared using mechanical alloying (MA) in a planetary ball mill under a controlled environment. The influence of milling parameters on the crystallinity and crystal size in the alloys was studied. The particle size and morphology were also investigated using SEM. In addition, a thermal treatment was employed for partial sintering of some of the MA powders. The crystal size in both MA powders and compacted samples was measured using X-ray diffraction. It was shown that the crystal size could be reduced to less than 15 nm in these alloys. The nanocrystalline material obtained was also evaluated for magnetic behaviour.     

Granulation in a Fluidized Bed II Effect of Binder Amount on the Final Granules

Abstract

There are many parameters affecting the properties of the final granules prepared in a fluidized bed. In this study one of the product parameters, quantity of the binder, has been studied for its effect on the final granule size, size distribution and friability

Determination of granule size change as a function of binder quantity leaded us to study the growth mechanisms during fluidized bed granulation. Two mechanisms are suggested;

1) Snowballing of primary granules (nuclei)

2) Agglomeration of primary granules

It has been shown that there is a critical amount of binder at which the formation of the primary granules comes to an end if more binder is added to the system. Then granule growth occurs by agglomeration of the primary granules. The physical properties of the granules formed before and after this critical binder concentration varies significantly     

Edge Stress Intensity Functions in Polyhedral Domains and their Extraction by a Quasidual Function Method

The solution to elastic isotropic problems in three-dimensional (3-D) polyhedral domains in the vicinity of an edge is provided in an explicit form. It involves a family of eigen-functions with their shadows, and the associated edge stress intensity functions (ESIFs), which are functions along the edges. Utilizing the explicit structure of the solution in the vicinity of the edge we use the quasidual function method, recently presented in [Omer et al. (2004). International Journal of Fracture 129:97–130] for scalar elliptic problems and in [Costabel et al. (2004). SIAM Journal of Mathematical Analysis 35(5), 1177–1202] in a general theoretical framework, for the extraction of ESIFs. This method provides a polynomial approximation of the ESIF along the edge whose order is adaptively increased so to approximate the exact ESIF. It is implemented as a post-solution operation in conjunction with the p-version finite element method. Numerical examples are provided in which we extract ESIFs associated with traction free or homogeneous Dirichlet boundary conditions in 3-D cracked domains or 3-D V-Notched domains. These demonstrate the efficiency, robustness and high accuracy of the proposed quasi-dual function method.     

TOTAL PARTICLE MONITORING AND DETECTION

ABSTRACT

One of the methods of detecting particles in the ultrafine size range (diameter <0.05 μm) is by condensation nuclei counters. Such condensation nuclei counters have a broad range of application including clean room monitoring, the characterization of contaminants in fossil energy process streams, and atmospheric monitoring. Based on the condensation of a saturated vapor, the method can amplify the size of the particles which are being studied by several orders of magnitude so that they can be detected by standard optical methods. However, the lower size limit of detectability is dependent on the proper choice of parameters that create the saturation conditions.

This paper presents results of the counting sensitivity tests of two condensation-type counters (the Pollak and the Sinclair continuous-flow counters). The results indicate that these instruments should be operated close to the self-nucleation limit in order to ensure total particle counting.     

Bragg Cell Diffraction in Resonant Cavities

Abstract

Steier et al. [1] have shown that the diffraction efficiency of a stationary grating may be improved by placing the grating in a resonant cavity. In this paper we describe the diffraction of light by a Bragg cell in a resonant cavity. Large improvements in diffraction efficiency are shown to be possible if scattering losses on the surface of the cell can be kept small. The effects of introducing gain into the cavity are calculated and the changes in bandwidth, resolution and dynamic range are discussed for the system when used as a radiofrequency spectrum analyser. A multichannel fibre optic system has been designed and is described.     

Photon filters in a microwave cavity

Abstract

In an earlier paper we concluded that time-dependent parameters in the atom-mode interaction can be utilized to modify the quantum field in a cavity. When an atom shoots through the cavity field, it is expected to experience a trigonometric time dependence of its coupling constant. We investigate the possibilities this offers to modify the field. As a point of comparison we use the solvable Rosen-Zener model, which has parameter dependences roughly similar to the ones expected in a real cavity. We do confirm that by repeatedly sending atoms through the cavity, we can obtain filters on the photon states. Highly non-classical states can be obtained. We find that the Rosen-Zener model is more sensitive to the detuning than the case of a trigonometric coupling.     

Field-dipole orientation mechanism and higher order modes in atom guides

Abstract

In cavity quantum electrodynamics (CQED), cavity size, dipole position and dipole orientation are the main factors controlling cavity effects, for example, suppression and enhancement of spontaneous emission. However, the dynamical effects of dipole orientation in CQED have, to date, remained largely unexplored, with most treatments simply concentrating on two (or three) orthogonal directions to illustrate the variations of CQED effects with dipole orientation. No mechanism which determines the evolution of the dipole orientation has been put forward to describe typical situations where atoms move in the field of an excited cavity mode. We emphasize here that in the presence of a cavity mode, the average dipole orientation is automatically determined at every point to be parallel to the direction of the electric field vector of the cavity mode. Besides giving rise to a single value for the spontaneous emission rate, this mechanism is shown to have important consequences for the dynamics of atoms in atom guides. In particular, it determines the average trapping potential distributions and the average radiation forces which guide the atoms along a cylindrical cavity. The effects of the field-dipole orientation mechanism are illustrated with reference to typical situations involving sodium atoms in sub-micron cylindrical guides. The role of a higher order cavity mode of the cylinder in the dynamics is highlighted in terms of its influence on the rotational and vibrational motions in such guides.