Determination of the s-wave scattering length and the C6 van der Waals coefficient of 174Yb via photoassociation spectroscopy

We report photoassociation spectroscopy of 174Yb for the 1S(0)-1P1 transition at 1 microK, where only the s-wave scattering state contributes to the spectra. The wave function of the s-wave scattering state is obtained from the photoassociation efficiency, and we determine that the C6 potential coefficient is 2300+/-250 a.u. and the s-wave scattering length is 5.53+/-0.11 nm. Based on these parameters, we discuss the scattering properties of s- and d-wave states.     

Ultra-high resolution trap-loss spectroscopy of ultracold <Superscript>133</Superscript>Cs atom long-range states in a magnetooptical trap

We present an ultra-high resolution spectroscopic study of the photoassociation of cesium atoms inside a magnetooptical trap using trap-loss detection with photoassociation laser slow scanning. The photoassociation spectra show vibrational levels of three molecular symmetries below the 6S _1/2 + 6P _3/2 dissociation limit. A dynamic model is derived to extract the photoassociation rate from the trap-loss spectrum. Many observed rotational levels are well resolved, which indicate d-wave and higher partial wave contributions to the photoassociation cross section.     

Photoassociative spectroscopy as a self-sufficient tool for the determination of the Cs triplet scattering length

In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the s-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f = 4, m(f) = 4. We analyzed the intensities of the lines associated with the Cs2 0(-)(g) state dissociating to the 6s(1/2)+6p(3/2) asymptote. This yields a value of the Cs triplet state scattering length, a(T) = -530a(0), while consistency requirements impose a value of the multipole ground state molecular coefficient, C6 = 6510 a.u.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

The laser-intensity dependence of the photoassociation spectrum of the ultracold Cs_2(6S_(1/2) + 6P_(1/2))0_u~+ long-range molecular state

The high-resolution photoassociation spectrum of the ultracold cesium molecular 0_u~+ state below the 6S 1/2 + 6P 1/2 limit is presented in this paper. The saturation of the photoassociation scattering probability is observed from the dependence of the trap-loss probability on the photoassociation laser intensity. The corresponding resonant line width is also demonstrated to increase linearly with increasing photoassociation laser intensity. Our experimental data have good consistency with the theoretical saturation model of Bohn and Julienne Bohn J L and Julienne P S 1999 Phys. Rev. A 60 1].     

Saturation of Photoassociation in Cs Magneto-optical Trap

An ultrahigh resolution photoassociation spectrum of caesium atoms in a magneto-optical trap is presented. Hyperfine structure of the excited state molecule is obtained by using the lock-in method based on modulated cold atoms in this spectrum. Amplitude of resonant lines related to the rotational levels increases with photoassociation laser intensity, and saturation effect of photoassociation of cold atoms is observed in our experiment. The saturation intensity of photoassociation is deduced by fitting the experimental data to asaturation model based on scattering theory. Differences among saturation intensities of different rotational progressions in the υ=55 vibrational state of the caesium molecular long-range 0_g^- state have been found.     

Finite difference computation of acoustic scattering by small surface inhomogeneities and discontinuities

The use of finite difference schemes to compute the scattering of acoustic waves by surfaces made up of different materials with sharp surface discontinuities at the joints would, invariably, result in the generations of spurious reflected waves of numerical origin. Spurious scattered waves are produced even if a high-order scheme capable of resolving and supporting the propagation of the incident wave is used. This problem is of practical importance in jet engine duct acoustic computation. In this work, the basic reason for the generation of spurious numerical waves is first examined. It is known that when the governing partial differential equations of acoustics are discretized, one should only use the long waves of the computational scheme to represent or simulate the physical waves. The short waves of the computational scheme have entirely different propagation characteristics. They are the spurious numerical waves. A method by which high wave number components (short waves) in the wave scattering process is intentionally removed so as to minimize the scattering of spurious numerical waves is proposed. This method is implemented in several examples from computational aeroacoustics to illustrate its effectiveness, accuracy and efficiency. This method is also employed to compute the scattering of acoustic waves by scatterers, such as rigid wall acoustic liner splices, with width smaller than the computational mesh size. Good results are obtained when comparing with computed results using much smaller mesh size. The method is further extended for applications to computations of acoustic wave reflection and scattering by very small surface inhomogeneities with simple geometries.     

Scattering from a Multi-Layered Sphere Located in a High-Order Hermite-Gaussian Beam

Scattering of a high-order Hermite-Gaussian beam by a multi-layered sphere is analyzed. The incident high- order Hermite-Gaussian beam field is expressed by the complex-source-point method and expanded in terms of spherical vector wave functions. The beam shape coefficients of the Hermite-Gaussian beam are obtained. Under electromagnetic field boundary conditions, coefficients in the expressions of scattering fields are derived. Results of the numerical calculation of scattering intensity are presented. The effects of the particle parameters and beam parameters on scattering intensity are discussed in detail.     

Control of photoassociation reaction F+H→HF with ultrashort laser pulse

The laser-induced vibrational state-selectivity of product HF in photoassociation reaction H+F$\rightarrow$HF is theoretically investigated by using the time-dependent quantum wave packet method. The population transfer process from the continuum state down to the bound vibrational states can be controlled by the driving laser. The effects of laser pulse parameters and the initial momentum of the two collision atoms on the vibrational population of the product HF are discussed in detail. Photodissociation accompanied with the photoassociation process is also described.     

Photoassociation spectroscopy of laser-cooled ytterbium atoms

We report the photoassociation spectroscopy of laser-cooled ytterbium atoms in an optical trap. We observed more than 90 photoassociation resonances of vibrational levels in the (1)Sigma(+)(u) state, including 80 consecutive series, up to 490 GHz detuning with respect to the atomic resonance. From the resonance frequencies we derived the atomic radiative lifetime of the (6s6p) 1P1 state to be 5.464+/-0.005 ns, which is about 2 orders of magnitude improvement over previous results. We also observed line broadening of resonances, which is ascribed to the predissociation to the triplet states, and estimated the transition probability to be 0.2. Furthermore, we observed the decrease of the photoassociation signal intensity, from which the scattering length is estimated to be equal to or less than 3 nm.     

Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α

The scalar wave theory of nondiffracting electromagnetic (EM) high-order Bessel vortex beams of fractional type α has been recently explored, and their novel features and promising applications have been revealed. However, complete characterization of the properties for this new type of beam requires a vector analysis to determine the fields' components in space because scalar wave theory is inadequate to describe such beams, especially when the central spot is comparable to the wavelength (k(r)/k≈1, where k(r) is the radial component of the wavenumber k). Stemming from Maxwell's vector equations and the Lorenz gauge condition, a full vector wave analysis for the electric and magnetic fields is presented. The results are of particular importance in the study of EM wave scattering of a high-order Bessel vortex beam of fractional type α by particles.     

Log-Periodic Oscillations in the Photo Response of Efimov Trimers

The photoassociation of Efimov trimer, composed of three identical bosons, is studied using the long wavelength approximation. It is shown that for identical particles the leading contribution comes from the r ² s-mode operator and from the quadrupole d-mode operator. Log-periodic oscillations are found in the photoassociation response function, both near the energy threshold for the leading s-wave reaction, and in the high frequency tail for all partial waves.     

Scattering of a Bessel beam by a sphere

The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.     

Nearside—farside theory of elastic angular scattering for strongly absorptive collisions

A systematic investigation has been made of ways for combining the method of Yennie, Ravenhall and Wilson (YRW) for the resummation of a partial wave Legendre series with the nearside—farside (NF) angular decompositions of Fuller and Hatchell. Of the resulting four procedures, the most useful one first applies the YRW resummation method m times (m = 0,1,2,…) to the partial wave scattering amplitude, followed by the Fuller NF decomposition. This NF procedure performs best for the physical interpretation of structure in the angular scattering of strongly absorptive elastic collisions. Numerical results from all four NF procedures are reported for a partial wave series possessing a simple parametrized scattering matrix element. The theory and calculations are relevant to atom—atom and atom—molecule elastic scattering in the presence of other open channels, for example, chemical reaction.     

The effect of field modulation on the vibrational population of the photoassociated NaK and its dynamics

This paper presents calculation results for the photoassociation of a NaK molecule with a two-color modulated laser and gives a detailed analysis about them.For the two-step photoassociation process in intense fields,the effect of two-color modulated laser parameters,such as relative phase,envelope period,and laser intensity,on the population of the molecular electronic state can be obtained by solving the time-dependent Schrodinger equation through the quantum wave packet method.The numerical simulation shows not only that the influence of laser parameters on the vibrational distribution presents some regularity,but also that a higher population in the ground electronic state can be realized through adjusting these laser parameters.     

Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: Example of a high-order Bessel beam of quasi-standing waves

The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves’ amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.     

Computational simulation of wave propagation problems in infinite domains

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.     

Photoassociation of NaRb with an asymmetric laser pulse

We investigate the photoassociation dynamics of cold NaRb molecule controlled by an asymmetric laser pulse called slowly-turned-on and rapidly-turned-off (STRT) laser pulse. This new shaped laser pulse has a remarkable merit, compared with the typical Gauss-type pulses, so that we can efficiently associate molecules with the state expected instead of going back to the continuum state. Using the three-state model, we solve the quantum mechanical equation with the “split operator-Fourier transform” method under the rotating-wave approximation (RWA) in propagation of the wave packet. By the projection of the obtained wave function onto each vibrational state, we can get the vibrational population of the ground electronic state. The results reveal that, with the STRT laser pulse, an efficient photoassociation process can be achieved and the vibrational distribution in the ground state can be controlled by the laser parameters.     

Optical Super-Resonances in Mesoscale Dielectric Cenosphere: Giant Magnetic Field Generations

Resonant light scattering by mesoscale dielectric spheres has received enormous attention and found many interesting applications. The recently emerged field of Mesotronics provides novel opportunities for wavelength-scaled optics and new fundamental aspects are still being uncovered. It has recently been demonstrated that high-order Mie resonances can be excited in homogeneous low-dissipation mesoscale dielectric spheres, leading to the generation of intense magnetic fields. This article describes a simple and effective way to drastically enhance the superresonance effect. Proof-of-principle results for the first time show that yet one more novel phenomenon of increasing the intensity of the magnetic field without changing the resonant Mie size parameter of the sphere by introducing an air cavity. In such a dielectric cenosphere (from two Greek words “kenos”-hollow and “sphaira”-sphere), by correct choice of the air cavity size, it is possible to increase the intensity of the electromagnetic fields at the poles of the sphere by an order of magnitude due to increasing of the amplitude of resonant partial wave coefficient.