Spectral invariance and non-invariance of light generated by partially coherent sources

A basic formula is derived for the spectrum of the field generated by a planar source of any state of spatial coherence. The formula shows clearly the contribution due to diffraction and due to source correlations. The distinction between these two contributions has not been appreciated in some previous publications. Examples are presented illustrating the effect of source correlations on the spectrum of the far field. A brief preliminary account is also presented of a recent investigation by H. Chen and E. Wolf which has shown that it is possible to produce a source whose degree of coherence will act on the spectrum of the source as a low-pass filter with a sharp frequency cut-off.Dedicated to H. Walther, with best wishes, on the occasion of his 60th birthday     

内禀退相干下薛定谔猫态光场与原子相互作用系统的场熵演化

通过求解系统的Milburn方程,研究了二能级原子与薛定谔猫态光场相互作用系统中的场熵演化特性.讨论了内禀退相干,光场强度,相干态间的相位角对场熵演化的影响.结果表明: 内禀退相干下,随着时间的演化,场熵振荡逐渐减弱,光场与原子的纠缠度逐渐趋于恒值.并且光场与原子的最大纠缠度值只取决光场强度和相干态间的相位角,与内禀退相干因子无关.光场强度较小时,奇相干态光场与原子的纠缠度最大;偶相干态光场与原子的纠缠度值为最小;Yurke-Stoler相干态光场与原子的纠缠度值介于两者之间. 当内禀退相干因子不变、光场强度较大时,分别处于Yurke-Stoler相干态、偶相干态和奇相干态的光场与原子的纠缠度值趋近于相同.     

内禀退相干下薛定谔猫态光场与原子相互作用系统的场熵演化

通过求解系统的Milburn方程,研究了二能级原子与薛定谔猫态光场相互作用系统中的场熵演化特性.讨论了内禀退相干,光场强度,相干态间的相位角对场熵演化的影响.结果表明: 内禀退相干下,随着时间的演化,场熵振荡逐渐减弱,光场与原子的纠缠度逐渐趋于恒值.并且光场与原子的最大纠缠度值只取决光场强度和相干态间的相位角,与内禀退相干因子无关.光场强度较小时,奇相干态光场与原子的纠缠度最大;偶相干态光场与原子的纠缠度值为最小;Yurke-Stoler相干态光场与原子的纠缠度值介于两者之间. 当内禀退相干因子不变、光场强度较大时,分别处于Yurke-Stoler相干态、偶相干态和奇相干态的光场与原子的纠缠度值趋近于相同.     

任意态无反转的激光

研究一个外场驱动上能级相干的能级系统。它可用来在任意态(裸态和缀饰态)均无粒子数反转时获得激光。 关键词：     

Nearly smooth granular gases

Hydrodynamic equations for nearly smooth granular gases are derived from the pertinent Boltzmann equation. The angular velocity distribution field needs to be included in the set of hydrodynamic fields. The angular velocity distribution is strongly non-Maxwellian for the homogeneous cooling state and any homogeneous steady state. In the case of steady wall-bounded shear flows the average spin (created at the boundaries) has a finite penetration length into the bulk.     

Observation of Ramsey fringes in nonlinear Faraday rotation

The evolution of Δm = 2 ground state coherences was investigated in a thermal Rb atomic beam using spatially separated laser beams. The coherence was created by optical pumping with a linearly polarized light beam and was probed, after evolving in a homogeneous magnetic field via the rotation of the plane of polarization of a second light beam. The observed signal shows dispersively shaped Ramsey fringes with a fringe width of 6 kHz.     

New spectral representation of random sources and of the partially coherent fields that they generate

It is shown that, contrary to general belief, it is possible to construct a statistical ensemble of monochromatic oscillations, all of the same frequency, that yields rigorously the spectral and cross-spectral densities of a fluctuating, statistically stationary source and of the field that the source generates. New mode representations are also introduced. The modes may be interpreted as natural oscillations of sources and fields of any state of coherence.     

稀薄等离子体中超辐射的发展过程及相干特性

用量子Ｍａｘｗｅｌｌ－ＢｌｏｃｈＣ－数方程讨论了存在均匀消相阻尼的一维稀薄等离子体系统中电场和极化的发展过程及相干特性，给出了线性阶段的解析结果和非线性阶段的数值结果。数值结果显示了电场和极化的发展过程及随机源对它们的影响。最后给出了电场和极化的相干度及自由电子对相干度的影响。当等离子体频率远小于辐射频率时，自由电子的作用可以忽略。     

高激发态原子的相干效应

本文以高激发态原子为研究对象, 由基态、激发态和高激发态能级形成阶梯型三能级系统, 理论上求解阶梯型三能级系统的密度矩阵方程, 研究了高激发态原子的相干效应, 计算获得探测光的吸收和色散曲线. 并研究了高激发态原子间相互作用以及外加电场对相干效应的影响. 结果表明, 外加场可以使吸收和色散曲线产生频移.     

Scanning tunneling spectroscopy in the superconducting state and vortex cores of the beta-pyrochlore KOs2O6

We performed the first scanning tunneling spectroscopy measurements on the pyrochlore superconductor KOs2O6 (T(c)=9.6 K) in both zero magnetic field and the vortex state at several temperatures above 1.95 K. This material presents atomically flat surfaces, yielding spatially homogeneous spectra which reveal fully gapped superconductivity with a gap anisotropy of 30%. Measurements performed at fields of 2 and 6 T display a hexagonal Abrikosov flux line lattice. From the shape of the vortex cores, we extract a coherence length of 31-40 A, in agreement with the value derived from the upper critical field H(c2). We observe a reduction in size of the vortex cores (and hence the coherence length) with increasing field which is consistent with the unexpectedly high and unsaturated upper critical field reported.     

Near-field spatial correlations from partially coherent homogeneous planar sources: effects on surface wave excitation

We show that an increase of the coherence length of a statistically homogeneous planar source diminishes the contribution of surface waves to the spatial coherence of the near field, as well as producing changes in the enhancement of the near-field spectrum.     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Spatial coherence properties of light from optical fibres

The mutual intensity of the optical field in the Fraunhofer diffraction region produced from the end of an optical fibre under illumination of a coherent beam, is theoretically analysed by using an optical fibre-end source model. In this source model, the optical field at the end of the fibre is expressed as an aggregation of independent plane waves with random directions and phases, because the guided modes propagating through the fibre may be regarded as a stochastic process. It is found that the optical field in the diffraction region from the multimode optical fibre is not homogeneous butquasi homogeneous in a statistical sense. The spatial coherence properties in the field are discussed in connection with theV number (the normalized frequency) of the fibre and in comparison with those in the field produced from an incoherent source obeying the van Cittert-Zernike theorem.     

Creation and manipulation of coherences in molecules with a pulsed magnetic field

We demonstrate the application of a pulsed magnetic field for the creation and manipulation of coherences in molecular systems, using quantum beat spectroscopy for the detection of the dynamics of the molecular superposition states. In all cases, the experiments are performed on energy levels in electronically excited states of the (jet-cooled) CS₂ molecule populated by a short laser pulse. In the basic experiment, following excitation of initially degenerate Zeeman sublevels under zero field conditions with suitable laser polarization, quantum beats are generated at the moment the magnetic field is switched on, even when the field is delayed by several excited state lifetimes. By quenching of the field, it is shown that the molecule may be “frozen” in any superposition state of the participating sublevels. Using a combination of static and pulsed fields with different orientations, the molecule can be prepared in a more general state, described by coherences among all Zeeman substrates. This is achieved by choosing an appropriate time delay for the switched field, without any change to the geometrical parameters of the experiment such as laser polarization or detection direction. Numerical simulations of these dynamical coherence phenomena have been performed to support assignment and interpretation of the experimental results. Received: 8 April 1998 / Accepted: 3 June 1998     

光场诱导的原子激光的量子相干性

基于伞量子理论,分别研究了几种重要的光场作用下,从原子玻色-爱因斯坦凝聚(BEC)体耦合输出的原子激光的量子相干特性.结果表明,粒子数态光场诱导的原子激光总是反聚束的,相干态光场诱导的原子激光是任意阶相干的,而压缩相干态光场诱导的原子激光总是聚束的.表明用光场诱导产生的原子激光具有与初始光场完全相间的量子相干性质.     

Quantum Speed Limit for Dynamics of Central Spin Model with Initial System-Bath Correlations

We investigate the quantum speed limit (QSL) time of an electronic spin coupled to a bath of nuclear spins. We consider three types of initial states with different correlations between the system and bath, i.e., quantum correlation, classical correlation, and no any correlation. Interestingly, we show that the QSL times of the central spin for these three types of initial correlations are identical when the couplings are homogeneous. However, it is remarkable different for inhomogenous couplings. The QSL time of the central spin is sensitive to the initial states, the average coupling strength, the distribution of the couplings between the system and bath and the number of the nuclear spins in the bath. Furthermore, we find that the coherence in the initial state has significant influences on the QSL time of the system, and can lead to the increase of QSL time for homogeneous couplings.     

Modal expansion for spherical homogeneous sources

The modal expansion of a class of stochastic spherical scalar sources is studied. At the surface of these sources the cross-spectral density is assumed to be homogeneous, in the sense that the power spectrum is position-independent and the spectral degree of coherence depends on the angular distance between points only. It is shown that for any such source the modes are given by the spherical harmonics and the associated eigenvalues can be evaluated by solving simple integrals. Three examples of the spectral degree of coherence for this type of sources are given for which the eigenvalues can be found in closed form.     

The effect of degenerate atomic levels on the field state dissipation in two—photon Jaynes—Cummings model

The dissipation of the field in the two-photonJaynes-Cummings model (JCM) with degenerate atomic levels was studied.The initial degenerate atomic state affects the field coherence loss,when the degenerate atom is initially in an equal probability superposition state,the field coherence loss is smallest,It is found that the degeneracy of the atomic level increases the period of entanglement between the atom and the field.When the degeneracy was considered,the coherence properties of the field could be affected by the reservoir qualitatively,if a nonlinear two-photon process is involved.This is different from the dissipation of one-photon JCM with degenerate atomic levels.     

Spatial correlations in the near field of random media

The conventional coherence theory suggests that the fields radiated by statistically homogeneous sources correlate over spatial regions of the order of the wavelength irrespective of the distance from the surface of the source. Contrary to these predictions, we show that the spatial correlations of optical fields in close proximity of highly scattering, randomly inhomogeneous media depend on this distance and, moreover, their extent can be significantly smaller than the wavelength. The contribution of evanescent fields is experimentally demonstrated and the coherence length in the near field is shown to relate to the coherence properties at the surface which are, in turn, determined by the structural characteristics of the random media.     

A radiometric generalization of the Van Cittert-Zernike theorem for fields generated by sources of arbitrary state of coherence

New formulae are derived for the cross-spectral density function and the complex degree of coherence of light in the far zone of a field generated by a planar source of any state of coherence. The formulae are analogous to those encountered in the far-zone formulation of the Van Cittert-Zernike theorem that applies to light from a spatially incoherent source; the only essential difference is that the average light intensity across the source is replaced by the generalized radiance function of the source, with a symmetrized directional variable. In the limiting case of a spatially incoherent source our formulae reduce to expressions that are in agreement with the Van Cittert-Zernike theorem. In the other limiting case, that of spatially fully coherent source, they reduce to results that are to be expected on the basis of the Huygens-Fresnel principle.