Coherence of bose condensates

Abstract

We study the coherence of interacting Bose condensates in recent magnetic trap experiments. The coherent evolution manifests itself in the macroscopic interference of two independent Bose condensates. The theoretical predictions from the time-dependent Gross–Pitaevskii equation are in excellent agreement with the measured interference patterns. A coherent coupling of two condensates represents the atomic analogon of a Josephson junction. The dependence of the magnetic confinement on the nuclear spin orientation allows one to build a controllable beam splitter by magnetic resonance. The application of this beam splitter to realize an atom laser is studied theoretically. The coherence of the output beam is limited only by phase diffusion of the condensate.     

梁结构耦合点的纵向弹性波传播

采用波动分析法研究了纵向弹性波在两半无限梁耦合点的传播。应用梁的一维波动方程，耦合点模拟为质量弹簧系统，根据耦合点的连续条件和平衡条件，计算得到了纵向波传输至耦合点的振动功率传播效率和反射效率。传播效率和反射效率确定为梁纵向波阻抗和耦合点阻抗的函数，分析了梁纵向波阻抗和耦合点阻抗对纵向波传播效率和反射效率的影响。研究表明通过合理的选择激励梁、耦合梁和耦合点阻抗之间的匹配关系，可有效控制耦合点的纵向波传播。本研究对于振动控制和结构优化设计具有重要的意义。     

A study of the coherent beam–beam effect in the framework of the Vlasov perturbation theory

A number of factors which can influence coherent beam–beam oscillations are studied on the basis of the Vlasov equation: difference in the intensities and single-particle tunes in the beams; difference in the phase advances between interaction points; long-range interactions; synchro-betatron coupling due to betatron phase advance variation in the vicinity of IP, chromatic tune modulation and crossing angle.

The synchro-betatron coupling appears to have a principal stabilizing effect: at synchrotron tune values in the neighborhood of half the beam–beam parameter it provides Landau damping of the discrete spectral lines by overlapping sidebands; the damping rate being higher with negative chromaticity. At smaller synchrotron tune values a specific mode of the head-tail damping sets in which is not sensitive to chromaticity.

Application to LHC shows that with the design values of parameters the coherent beam–beam oscillations should be Landau damped, probably with the help of negative chromaticity of a moderate absolute value.     

矩形螺旋线慢波电路高频特性的数值分析

介绍了用ANSOFT公司提供的HFSS 10.0软件模拟计算色散特性和耦合阻抗的理论方法,并对矩形螺旋线慢波结构的高频特性进行了数值模拟.结果表明:和传统的圆螺旋线结构相比,矩形结构具有更高的耦合阻抗,能有效减小器件体积;在横截面厚度和螺旋角一定的情况下,当矩形螺旋线的宽高比大于4时,相速几乎不变,但是耦合阻抗随着宽度的增加而下降;同时螺旋角的减小可以降低系统的相速,减小工作电压.由于可利用微电子机械系统(MEMS)印制技术制作,具有可与带状电子束作用,提高效率等优点,矩形螺旋线在紧凑型行波管(TWT)领域有广阔的应用前景.     

Coherent and incoherent off-axis Hermite-Gaussian beam combinations

A detailed study of the coherent and the incoherent combinations of two-dimensional off-axis Hermite-Gaussian beams with rectangular symmetry is made. The closed-form propagation formulas of the resulting beam are derived, and the resulting beam quality in terms of the M(2) factor and power in the bucket is discussed and compared for the coherent and the incoherent combinations. In addition, it is shown that the resulting astigmatic beam can be symmetrized in the sense of the second-moment definition of beam width. However, the symmetrizing transformation of the resulting astigmatic beams is incomplete, because there exist different irradiance profiles.     

Recording schedule for partially coherent hologram multiplexing in a photorefractive medium

The exposure schedule for partially coherent hologram multiplexing, in which data pages are multiplexed by multiple signal beams and a single reference beam, is investigated in detail for the case of a pi/2 phase-shifted photorefractive medium. We found that the optimum recording schedule for partially coherent multiplexing cannot be determined by the classical recording schedule theory because of time-constant errors induced by partially coherent interaction between a reference beam and self-diffraction signal beams. To overcome the issue, we derive a modified recursion equation that accounts for the time-constant errors, and we also propose a novel iterative recording-schedule correction algorism for finding the optimum solution. In the calculation with hologram multiplicity of 30 and photorefractive coupling strength of 3.0, we could successfully obtain a flat diffraction-efficiency profile after the second recursion.     

计及变形耦合项的平面柔性梁动力学建模及频率分析

考虑了变形产生的几何非线性效应对作大范围运动的平面柔性梁的影响，在其纵向、横向的变形位移中均考虑了变形的二次耦合变量，从非线性应变-变形位移的原理出发，说明增加耦合变量后。使得剪应变近似为零，由此得出的变形模式更符合工程实际和简化需要。考虑两个方向的变形耦合后，采用有限元离散，通过Lagrange方程导出系统的动力学方程。最后对一作旋转运动的平面柔性梁进行仿真计算，并对其固有频率进行分析研究。将本文模型所得的结论。与一次耦合动力学模型、零次近似模型进行比较，说明了三种模型的差异。得到了作旋转运动的平面柔性梁的一些新特点。     

Beam wander of partially coherent Airy beams

The beam wander of a partially coherent Airy beam in a turbulent atmosphere was investigated. By using the extended Huygens–Fresnel integral, as analytical expression is derived for the second-order moment of a partially coherent Airy beam. Based on the theory proposed by Andrews, a general expression is obtained for the beam wander of a partially coherent Airy beam. With the help of the expression, various factors which impact on the beam wander are illustrated numerically. The results show that the beam wander of a partially coherent Airy beam decreases with the increase of the characteristic scale and the decrease of the coherent length or the exponent truncation factor. The value of the beam wander is a maximum when the exponent truncation factor is 0.63, no matter what the coherent lengths are. Our results provide an effective way to control the beam wander of a partially coherent Airy beam in practice.     

Microstrip coupling techniques applied to thin-film Josephson junctions at microwave frequencies

Three different schemes for coupling to low impedance Josephson devices have been investigated. They all employ superconducting thin-film microstrip circuit techniques. The schemes are: (i) a quarterwave stepped impedance transformer, (ii) a microstrip resonator, (iii) an adjustable impedance transformer in inverted microstrip. Using single microbridges to probe the performance we found that the most primising scheme in terms of coupling efficiency and useful bandwidth was the adjustable inverted microstrip transformer.     

One-dimensional description of cylindrically symmetric laser beams: application to bessel-type nondiffracting beams

We introduce a new representation of coherent laser beams that are usually described in circular cylindrical coordinates. This representation is based on the decomposition of a laser beam of a given azimuthal order into beams exhibiting Cartesian symmetry. These beams, which we call constituent waves, diffract along only one of their transverse dimensions and propagate noncollinearly with the propagation axis. A cylindrically symmetric laser beam is then considered a coherent superposition of constituent waves and is represented by an integral over an angular variable. Such a representation allows for the introduction of the propagation factor M2, defined in terms of one-dimensional root-mean-square (rms) quantities, in the treatment of two-dimensional beams. The representation naturally leads to the definition of a new rms parameter that we call the quality factor Q. It is shown that the quality factor defines in quantitative terms the nondiffracting character of a laser beam. The representation is first applied to characterize Laguerre-Gauss beams in terms of these one-dimensional rms parameters. This analysis reveals an asymptotic link between Laguerre-Gauss beams and one-dimensional Hermite-Gauss beams in the limit of high azimuthal orders. The representation is also applied to Bessel-Gauss beams and demonstrates the geometrical and one-dimensional characters of the Bessel-Gauss beams that propagate in a nondiffracting regime. By using two separate rms parameters, Q and M2, our approach gives an alternative way to describe laser beam propagation that is especially well suited to characterize Bessel-type nondiffracting beams.     

基于本征方程求解复合材料梁几何非线性静力平衡

对基于本征梁理论求解复合材料梁的几何非线性大变形屈曲问题进行了研究,根据材料属性利用渐近变分法确定复合材料梁的刚度矩阵,再根据本构方程和平衡方程求得其静力学行为,结果表明：对单层铺层的复合材料梁来说,刚度矩阵的耦合项可以忽略,其变形构型及梁末端的位移及转角的变化趋势与各项同性材料相同;对一个一般的复合材料梁来说,其刚度矩阵的耦合项不可忽略,耦合项对位移和转角的影响与施加在梁上的载荷大小有关,在载荷小于30N,以耦合项50%的变化量为界,当变化量小于50%时,位移和转角的变化趋势与初始时相同,当变化量大于50%时,位移和转角的变化趋势发生很大的改变,但与解耦后的变化趋势相似。     

Estimate for the effect of forward scattering on the measurement of extinction for particles by cavity ringdown spectroscopy

An analytical model is formulated for the extinction of light by particles in a cavity ringdown spectroscopy measurement. The electromagnetic field inside the cavity is assumed to be the lowest-order Gaussian beam, and the scattering by the particles is incorporated using van de Hulst's approximation for the scattering by a sphere. This model includes both coherent scattering in the forward direction and strong scattering in the forward direction for electrically large particles. The model is used to estimate the amount of energy scattered by the particles that is coupled back into the incident beam. The consequences of this coupling for the measurement of the extinction cross section of spherical particles are examined.     

Propagation of doughnut-shaped super-Gaussian beams,convolution theorem and Hankel transform

The most direct and simple method to calculate analytically the propagation in the far field of a coherent beam with a rectangular symmetry and a super-Gaussian-like irradiance profile involves the use of the convolution theorem. In this paper we extend this method to a circularly symmetric beam, and hence from the Fourier transform to the zero-order Hankel transform. Then, we examine the more complex case of super-Gaussian-like beam irradiance shapes with an axial shadow, as those emitted by unstable resonators with diffraction output coupling or with a variable-reflectivity mirror. The analytical results obtained by approximating the super-Gaussian-like beam with a convolution function and applying the Hankel transform are in excellent agreement with those obtained by numerical simulations.     

The effect of plasmon field on the coherent lattice phonon oscillation in electron-beam fabricated gold nanoparticle pairs

By using electron beam lithography, we fabricated pairs of gold nanoparticles with varying interparticle separation. Double-beam femtosecond transient absorption spectroscopy was used to determine the coherent lattice oscillation frequency as a function of the interparticle separation in the presence of the plasmon field excited by the monitoring probe light. We found that the fractional shift in the coherent lattice phonon oscillation frequency follows an exponential decay with respect to the interparticle gap scaled by the disc diameter with the same decay constant as that previously observed for the fractional shift in the surface plasmon electronic oscillation resonance frequency. This strongly suggests that it is the near-field coupling between the particles that shifts both the coherent electronic oscillation (plasmon) frequency and the coherent lattice oscillation (phonon) frequency. The similar trend in the effect of interparticle coupling on the plasmon frequency and the phonon frequency is essentially a reflection of the universal scaling behavior of the distance decay of the interparticle plasmonic near-field. It is shown that the observed decrease in the lattice oscillation frequency with decrease in the interparticle distance is the result of a reduction in the effective free electron density within each nanoparticle pair partner as a result of the polarizing perturbation of the plasmonic field of the other nanoparticle in the pair.     

A consistent finite element formulation for non-linear dynamic analysis of planar beam

A co-rotational finite element formulation for the dynamic analysis of planar Euler beam is presented. Both the internal nodal forces due to deformation and the inertia nodal forces are systematically derived by consistent linearization of the fully geometrically non-linear beam theory using the d'Alembert principle and the virtual work principle. Due to the consideration of the exact kinematics of Euler beam, some velocity coupling terms are obtained in the inertia nodal forces. An incremental-iterative method based on the Newmark direct integration method and the Newton–Raphson method is employed here for the solution of the non-linear dynamic equilibrium equations. Numerical examples are presented to investigate the effect of the velocity coupling terms on the dynamic response of the beam structures.     

Effect of turbulence on the beam quality of apertured partially coherent beams

The effects of turbulence on the beam quality of apertured partially coherent beams have been studied both analytically and numerically. Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, closed-form expressions for the average intensity, mean-squared beam width, power in the bucket, beta parameter, and Strehl ratio of apertured partially coherent beams propagating through atmospheric turbulence are derived. It is shown that the smaller the beam truncation parameter is, the less affected by turbulence the apertured partially coherent beams are. Furthermore, the apertured partially coherent beams are less sensitive to the effects of turbulence than unapertured ones. The main results are interpreted physically.     

Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems

Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems is investigated based on the generalized Collins formula for treating the propagation of a partially coherent beam through such optical systems. Analytical formulas for the cross-spectral density of a partially coherent Hermite-Gaussian beam propagating through such optical systems are derived. As an application example, we derive the propagation formulas for a partially coherent flattened Gaussian beam by expressing it as a superposition of a series of partially coherent Hermite-Gaussian beams by using polynomial expansion. The focusing properties of a partially coherent Hermite-Gaussian beam focused by a thin lens are studied as a numerical example.     

Average characteristics of partially coherent electromagnetic beams

Average characteristics of partially coherent electromagnetic beams are treated with the paraxial approximation. Azimuthally or radially polarized, azimuthally symmetric beams and linearly polarized dipolar beams are used as examples. The change in the mean squared width of the beam from its value at the location of the beam waist is found to be proportional to the square of the distance in the propagation direction. The proportionality constant is obtained in terms of the cross-spectral density as well as its spatial spectrum. The use of the cross-spectral density has advantages over the use of its spatial spectrum.     

温度场中的柔性梁系统动力学建模

研究温度场下带集中质量的柔性梁系统的动力学问题。考虑几何非线性，在纵向变形与轴向伸长的关系式中计及了与横向变形有关的二次耦合项。考虑温度变化对系统动力学性态的影响，在本构关系式中计及了热应变。用假设模态法对各柔性梁进行离散，从虚功原理出发，根据各柔性梁之间的运动学约束关系，建立了带集中质量的柔性梁系统的动力学方程。仿真结果表明．即使在转速较低的情况下，随着集中质量的增大和温度的急剧变化，纵向变形的二次耦合项的影响不容忽视，此外，温度的变化还引起轴向变形和轴向约束力高频振荡。     

Evolution properties of a partially coherent Lorentz-Gauss vortex beam in a uniaxial crystal

The propagation properties of a partially coherent Lorentz-Gauss vortex beam propagating in a uniaxial crystal orthogonal to the optical axis were studied. The analytical expressions of the partially coherent Lorentz-Gauss vortex beam propagating in a uniaxial crystal were derived. Based on the derived formulae, the average intensity properties and evolution properties of the coherent vortex of the partially coherent Lorentz-Gauss vortex beam propagating in a uniaxial crystal were illustrated using numerical examples. The influences of the uniaxial crystal and the parameters of the beam at the source plane of z?=?0 on the average intensity and evolution properties of the coherent vortex for the partially coherent Lorentz-Gauss vortex beam are analyzed in detail.