Cooperative effects in the two atom resonance fluorescence spectrum

We consider the resonance fluorescence spectrum of two similar interacting atoms in the limit of high photon densities. The excitation spectrum of the symmetric modes contains two sidebands in addition to the usual three peaks which are analogous to those of the isolated atom. These two new sidebands are due entirely to the cooperative behaviour of the two atoms and vanish when the atoms are far apart. The energy shifts and spectral widths for these two sidebands are two and five times larger than those for the isolated atom respectively. The probability of occurrence of these sidebands depends on the parameters V_AB/Ω and γ²₀/Ω², where V_AB is the dipole-dipole interaction energy, γ₀ is the spontaneous emission probability and Ω is the Rabi frequency. The asymmetric broadening of both sidebands depends on the parameter γ₀/Ω. The possibility to measure the dipole-dipole energy through the observation of these sidebands is discussed.     

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities

The excitation spectrum of two identical three-level atoms is considered when a strong electromagnetic field operates resonantly between two levels of the atoms. While undergoing the transition into the excited state, the atoms interact through their dipole-dipole interaction and radiate to each other as well, and subsequently, they decay radiatively into another excited state. For such a system, the spectral functions are calculated describing the cooperative and interference spectra for the symmetric and antisymmetric modes arising from the decay of the atoms from one excited state into another. In the absence of the pump field, the spectral function for the symmetric modes consists of two peaks, which are described by Lorentzian lines peaked at the frequencies ω = ω₂₃ + V_AB and ω = ω₂₃ ? V_AB and having spectral widths of the order of γ⁰₂₁ + γ⁰₂₃ and γ⁰₂₃, respectively, where ω₂₃ is the transition frequency between the two excited states, V_AB is the dipole-dipole interaction and $\text{1}\text{2}\text{γ}{}^0{}_{21}$ is the natural width for a photon spontaneously emitted from the 2 → 1 transition of an isolated atom. The splitting of the central peak for the transition in question and the broadening of the spectral widths are due entirely to the dipole-dipole and radiative interactions between the atoms. The spectral function for the antisymmetric modes describes a stable mode at the frequency ω = ω₂₃ ? V_AB, which has a delta-function distribution, and a Lorentzian line peaked at the frequency ω = ω₂₃ + V_AB and has a spectral width of the order of γ⁰₂₁. In the presence of the pump field, the spectral function for the symmetric modes contains, in addition to the central peaks, two pairs of sidebands, one pair of which is induced by the pump field with an energy shift equal to $\text{Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, while the other pair of sidebands is due to the dipole-dipole interaction between the atoms; the probability of occurrence of the latter pair of sidebands is proportional to $\text{V}{}_{\mathrm{AB}}\text{/Ω}{}_{\mathrm{<mtext>a</mtext>}}$, while the induced energy shift is equal to $\text{3Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, where $\text{√2Ω}{}_{\mathrm{<mtext>a</mtext>}}$ is the induced by the laser field energy shift (Rabi frequency) for a single two-level atom. The spectral widths for both pairs of sidebands are of the order of γ⁰₂₁ + γ⁰₂₃. The excitation spectrum of the antisymmetric modes consists of, in addition to the central peaks, a pair of stable sidebands, which have delta-function distributions, and two pairs of sidebands, which are similar but sharper than those for the symmetric modes. Detail comparisons are given between the one- and two-atom excitation spectra for the systems under investigation.     

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities: II. Numerical results

Numerical calculations are presented for the excitation spectrum of two identical three-level atoms interacting with a strong resonant laser field. The atoms interact through their dipole-dipole interaction and radiate to each other as well. The spectrum of the symmetric and antisymmetric modes due to the radiative decay from the higher to the lower excited state of the interacting atoms is considered without and with taking into account the effects of the strong pumping process. In the absence of strong pumping, the dipole-dipole interaction in the spectrum of the symmetric modes gives rise to an asymmetric doublet whose ratio of intensities is 2:1, while the spectrum of the antisymmetric modes consists of two peaks one of which represents a stable mode indicating the trapping of a photon between the atoms and a radiative one which has a lifetime one-half that of the isolated atom. In the presence of strong pumping, asymmetries due to the dipole-dipole interaction arise enhancing certain peaks while diminishing the intensity of others and a new pair of sidebands is induced as well. The computed spectra are presented graphically for different values of the Rabi frequencies and the dipole-dipole interaction, respectively.     

Quantum beats in two-photon resonance fluorescence

The two-photon resonance fluorescence spectrum of a three-level atom is shown to consist of the low frequency modes in addition to the high frequency ones in the limit of high photon densities. The spectral function for the low frequency modes consists of two lorentzian lines describing: the peak occuring at the renormalized beat frequency Δ₊ and that of the zero-photon excitation at the frequency Δ_-, where Δ_±=Δ-3Ω²/2ω_a±Ω²u/2ω_a, u²=1+(2Δω_a/Ω ²)². Here, 2Δ is the energy splitting between the two excited states, ω_a is the photon energy of the pump field and Ω is the Rabi frequency. The peak at the renormalized beat frequency Δ₊ occurs provided that the condition (2Δω_a/Ω²)² > 1 is satisfied. The two-photon laser spectroscopy is expected to be a useful tool for the observation of the low frequency modes in question.     

Two-atom two-photon resonance fluorescence

The excitation spectrum arising from the interaction between two identical two-level atoms, one of which is excited in the presence of a strong electromagnetic field (pump field), is investigated when the atomic transition frequency is nearly twice the frequency of the pump field. The excitation spectrum consists of those describing the symmetric and antisymmetric modes, respectively. The spectral functions for the symmetric and antisymmetric modes are derived and discussed in detail. The possibility to measure directly the magnitude of the dipole-dipole interaction energy is discussed.     

Mode dispersion in the optical-phonon spectra of mixed crystals ZnS1−x Sex

The IR reflection and the Raman spectra of ZnS_1?x Se_x crystals (0≤ x ≤ 1) are measured. The mode dispersion of the solid solutions is found to deviate from that calculated using an isodisplacement model. The reasons behind this deviation are discussed. Two additional modes are found in the frequency range between the ZnS-like TO and LO modes. It is assumed that one of them is a line of the second-order spectrum amplified by the Fermi resonance and the other is linked to the resonance (additional local) mode of Se impurity atoms. The latter conclusion is confirmed by calculating the spectrum of a Se impurity in a ZnS crystal in terms of the microscopic lattice dynamics theory in the low impurity concentration approximation. The oscillator strengths of the main and additional optical phonons in ZnS_1?x Se_x solid solutions are discussed.     

Unified geometry of antisymmetric tensor gauge fields and gravity

Vector gauge fields are known to be related to connections on principal fibre bundles P(M,G) over space-time M. Here we relate abelian antisymmetric tensor gauge fields of rank r to constrained connections on P(Ω_r?1M,U(1)), the U(1) bundles over the space of all (r?1)-dimensional closed submanifolds of M. In particular, the Kalb-Ramond field (r=2) is seen as such a connection on the bundle over the space of all loops in space-time. Moreover, a Kaluza-Jordan construction on P(Ω₁M,U(1)) leads to the bosonic sector of the N = 1 supergravity action in ten dimensions. This result is highly reminiscent of the α′→ 0 limit of the closed string dual model.     

Resonances of orientation and alignment of atoms in the case of inclined optical pumping

It is shown that, with pumping inclined relative to a constant magnetic field H₀, the radio-frequency (RF) magnetic field rotating at frequency Ω induces new resonances ω₀ = γ H ₀ and 2Ω for the Fourier components of orientation and ω₀ = ?Ω, Ω/2, 3Ω/2, 2Ω, and 3Ω for the components of alignment. New resonances excited by the oscillating RF field are also considered.     

Collision frequency shift of hyperfine transitions in atomic hydrogen at a low temperature

The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S. For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets (S= 1) and singlets (S = 0), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of b → c and b → a transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state b). The comparison is performed with experiments in ultracold alkali vapors.     

Relaxationsphänomene in Mössbauerspektren von magnetisierten paramagnetischen Substanzen

The Mössbauer spectra of partly magnetized FeNH₄(SO₄)₂·12 H₂O show a broadening and a shift of the hyperfine structure lines, reflecting the paramagnetic spin fluctuations. These fluctuations and their influence on the γ-spectrum may be treated in a spin wave model without introducing phenomenological parameters. By means of a simple diagram technique we get a line broadening γ and line shift δ, proportional to second and third order polynomials of the magnetization and to ∫g ² dΩ and ∫g ³ dΩ, respectively.g(Ω) is the frequency spectrum of spin waves. The values of the two frequency integrals, as deduced from the measured Mössbauer data γ and δ of ferric alum, are in reasonable agreement with the results obtained from the calculated spin wave spectrum, assuming pure magnetic dipole-dipole coupling (long wave length approximation of Holstein-Primakoff). A small contribution of non-magnetic dipole-dipole interaction (van Vleck) cannot be excluded.     

大小周期正方格子复合结构的光子带隙特性

把具有宽完全带隙的粗锐复合的周期常数为a的二维正方格子再与周期常数为a₂的大周期简单正方格子复合，发现大周期正方格子起缺陷作用.并发现当a₂<5a时,缺陷态明显地随入射角度变化.此变化随a₂的增大而减少.用FDTD方法计算了其透射和反射谱,结果表明缺陷峰透射率与a₂的大小成反比.另外还发现: 缺陷峰结构与大周期正方格子的圆柱直径的关系曲线与a₂关系不大.通过调节大周期正方格子的圆柱的直径，可获得单 关键词： 光子晶体 光子能隙 复式结构 缺陷态     

Generalized thermoelastic Lamb waves in a plate bordered with layers of inviscid liquid

The propagation of thermoelastic waves in a homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides is investigated in the context of generalized theories of thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases. The different regions of secular equations are obtained and special cases, such as Lame modes, thin plate waves and short wavelength waves of the secular equations are also discussed. The secular equations for thermoelastic leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for an aluminum-epoxy composite and aluminum materials plate bordered with water. The dispersion curves for symmetric and antisymmetric thermoelastic wave modes and amplitudes of displacement and temperature change in case of fundamental symmetric (S₀) and skew symmetric (A₀) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The results have been deduced and compared with the relevant publications available in the literature at the relevant stages of the work.     

Spherically compressed helium atom described by perturbative and variational methods

We analyze the energy spectrum of the three lowest-lying S symmetry states for the spherically confined helium atom as a function of the box radius by using an approach based on a time independent perturbation theory and two variational methods. The first treatment depends on exact solutions for confined one-electron atoms, whereas in the latter two methods exponents and linear coefficients are variationally optimized via {s,t,u}-Hylleraas functions and Generalized {r₁,r₂,r₁₂}-Hylleraas basis sets that fulfill appropriate boundary conditions. Although it is found that throughout most of the box radii here analyzed the variational energies for the three states lie below those perturbatively obtained, an opposite trend occurs toward the weak and strong confinement regions for the singlet excited and triplet states, respectively.     

手性分子2, 3-丁二醇的旋光拉曼光谱研究

本文从拉曼峰和旋光拉曼峰出发,通过键极化率和微分键极化率分析研究(2R, 3R)-2, 3-丁二醇. 通过分子C₁和C₂两种点群的优化结构,获得不依赖于这两种结构的结果 和有关这个手性系统物理图像的丰富信息.对分子拉曼键极化率分析,得出在拉曼弛豫过程中, 电荷主要从外围流向骨架结构.对分子微分键极化率的分析,显示在不对称C原子和与其相联系的H原子 两侧化学键, C-O和C-CH₃的微分键极化率的符号正好相反,意味着这个分子具有相当好的手性 不对称性质.对比对称和反对称的键极化率、微分键极化率,本文得到这样的结论: 对于(特别是键伸缩的)键极化率,(大体上是)对称的大于反对称的; 而对于微分键极化率则是反对称的大于对称的. 关键词： 旋光拉曼 键极化率 微分键极化率 2,3-丁二醇     

Embedding theorem for weighted Sobolev classes on a John domain with weights that are functions of the distance to some h-set

Let Ω be a John domain, let Γ ? ?Ω be an h-set, and let g and v be weights on Ω that are distance functions to the set Γ of special form. In the paper, sufficient conditions are obtained under which the Sobolev weighted class W _p,g ^r (Ω) is continuously embedded in the space L _q,v (Ω). Moreover, bounds for the approximation of functions in W _p,g ^r (Ω) by polynomials of degree not exceeding r ? 1 in L _q,v ( $\tilde \Omega $ ) are found, where $\tilde \Omega $ is a subdomain generated by a subtree of the tree T defining the structure of Ω.     

Second order resonance Raman scattering in As2S3 glass

First and second order resonance enhanced Raman scattering has been observed for As₂S₃ glass. First order scattering is dominated by a peak at 340 cm^-1 due to the symmetric stretch of the AsS₃ pyramidal group. Two partially resolved second order peaks are observed at about 630 and 710 cm^-1 whose relative intensities are highly temperature dependent and which are due respectively to overtones of the antisymmetric and symmetric AsS₃ stretching modes.     

Embedding theorem for weighted Sobolev classes with weights that are functions of the distance to some h-set

The paper continues the first part (Russ. J. Math. Phys. 20 (3), 360–373). Let Ω be a John domain, let Γ ? ?Ω be an h-set, and let g and υ be weights on Ω that are distance functions to the set Γ of special form. In the paper, sufficient conditions are obtained under which the Sobolev weighted class W _p,g ^r (Ω) is continuously embedded in the space L _q,v (Ω). Moreover, bounds for the approximation of functions in W _p,g ^r (Ω) by polynomials of degree not exceeding r ? 1 in L _q,v ( $\tilde \Omega $ ) are found, where $\tilde \Omega $ is a subdomain generated by a subtree of the tree T defining the structure of Ω.     

Raman spectroscopic study of the arsenite minerals leiteite ZnAs2O4, reinerite Zn3(AsO3)2 and cafarsite Ca5(Ti,Fe,Mn)7(AsO3)12·4H2O

The selected arsenite minerals leiteite, reinerite and cafarsite have been studied by Raman spectroscopy. Density functional theory (DFT) calculations enabled the position of the AsO₂²⁻ symmetric stretching mode at 839 cm⁻¹, the antisymmetric stretching mode at 813 cm⁻¹ and the deformation mode at 449 cm⁻¹ to be calculated. The Raman spectrum of leiteite shows bands at 804 and 763 cm⁻¹ assigned to the As₂O₄²⁻ symmetric and antisymmetric stretching modes. The most intense Raman band of leiteite is the band at 457 cm⁻¹ and is assigned to the ν₂ As₂O₄²⁻ bending mode. A comparison of the Raman spectrum of leiteite is made with the arsenite minerals reinerite and cafarsite. Copyright © 2009 John Wiley & Sons, Ltd.     

A new representation of the interaction between an atom and an intense elliptically polarized electromagnetic field

A new representation of the interaction between a laser field and an atom is obtained. The Fourier component of the interaction is represented as a multipole expansion dependent on the force parameter of the field, a ₀=F/ω², and the degree of its ellipticity, η. This representation provides the analytical separation of the angles in the time-dependent Schrödinger equation. The stationary spherically symmetric part of the potential V ₀(r, a ₀, η) of a “field-dressed” atom is singled out. The application of the new representation to the calculation of nonlinear effects and electron scattering by an atom in a field are discussed