Laser Cooling and Trapping of Sodium Atoms in Magneto-optical Trap

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Control of orbital angular momentum of light with optical fibers

We present a fiber-based method for generating vortex beams with a tunable value of orbital angular momentum from -1? to +1? per photon. We propose a new (to our knowledge) method to determine the modal content of the fiber and demonstrate high purity of the desired vortex state (97% after 20 m, even after bends and twists). This method has immediate utility for the multitude of applications in science and technology that exploit vortex light states.     

The Influence of Particles Interaction in Low-Temperature Plasma on its Composition and Optical Properties

A model theory of the influence of particles interaction in plasma on its composition and optical properties is developed. The interaction of charged particles in plasma reduces the ionization energy of atoms and ions. The action of internal microfields in plasma on atoms and ions reduces the statistical weight of electron levels which affects the populations of excited states. The latter effect leads to an effective cutoff of partition functions and determines the behaviour of optical properties of plasma (of absorption coefficient and emissivity) at increased number densities of charged particles. The formulas are obtained for calculation of the continuous and discrete spectrum in plasma taking into account the particles interaction. A non-monotonic dependence of optical plasma density upon number density of charged particles is quantitatively explained. A satisfactory agreement is obtained with a large number of experimental data some of which were considered to be contradictory. The method developed can be used for calculations in the field of atomic spectroscopy and low-temperature plasma physics including increased densities of charged particles. The use of the formulas obtained in plasma diagnostics will enable one to avoid considerable errors.     

Instanton liquid at a finite density of quark matter

For the case of finite quark and baryon densities, the interaction of light quarks with an instanton liquid is considered in a phase that involves a nonvanishing chiral condensate. The generating functional is considered in the tadpole approximation, and the behavior of the dynamical quark mass and the behavior of the chiral condensate, as well as the behavior of the instanton-liquid (gluon-condensate) density, which grows slightly with the quark chemical potential, are explored. Arguments are presented in favor of the statement that the quark-density threshold for the emergence of a diquark condensate grows sizably owing to interaction with the instanton liquid.     

The concept of effective density and the closed integrofunctional equation for a radial function of a simple liquid

The thermodynamically consistent concept of effective density, similar to the idea of an acting field in statistical thermodynamics, is introduced. Assuming a linear functional relation between the effective and true densities (the packet approximation), a generating functional is constructed and from it, in the usual way, the closed integrofunctional equation for a radial function is obtained. Some properties of the obtained equation are investigated, including its relation to known integral equations, and a possible scheme for its solution, by the method of iteration, is presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 96–100, September, 1975.     

Changes in statistics of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam on propagation

The changes in the probability density functions (PDFs) are discussed, of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam propagating in free space. Such changes may be caused by correlations between the components of the electric field at a pair of points in the source plane. When the fluctuations of the electric field are governed by Gaussian statistics the PDFs of the instantaneous Stokes parameters at any distance from the source are completely determined by the two-point correlation properties of the field in the source plane. These results can be used for synthesis of sources generating random beams with prescribed statistical properties. They also may find applications in remote sensing, tomography and communications with partially coherent and partially polarized light.     

Fourier synthesization of optical pulses and “polar” light

It is shown that the direct Fourier synthesization of light beams allows one to create polarity-asymmetric waves, which are able, in the process of nonlinear interaction with a medium, to break its inversion symmetry. As a result, these “polar” waves may show the effect of optical rectification in nonlinear centrosymmetric media by generating light-induced dc electric polarization. At the same time, waves of this type, due to their unusual symmetry properties, can be used for detecting the direction and sign of a dc electric field applied to the medium. The prospects of application of polar waves to data recording and processing are discussed.     

Spatial and temporal electron and ion density variations within the focal region of an intense laser beam in a tenuous plasma

The recent availability of focussed laser beams with flux densities well in excess of 10¹⁵ watts/cm² at 1.06 μm has led to experimental investigations of direct interaction between intense electromagnetic fields and charged particles. In this paper the relevant hydrodynamic two-fluid mode equations for a singly ionized tenuous plasma eveloped by an intense spatially varying electromagnetic field at the focus of a pulsed laser beam is solved by computer simulations for a cylindrically symmetric geometry. Radial, axial and temporal variations of electron and ion densities are given for different laser intensities and particle number densities. Fluctuations in electron density are found due to the bulk oscillation of electrons relative to what is essentially a static array of massive ions. The possibility of generating intense electromagnetic fields devoid of charged particles is discussed.     

Generating of squeezed atom laser via stimulated Raman transition

We present a scheme to generate a squeezed atom laser via stimulated Raman transition of the atoms in Bose-Einstein condensate (BEC) interacting with two light beams, including a weaker squeezed coherent probe light and a stronger classical pump light. The results show that the quantum fluctuation of this atom laser can be periodically squeezed. The squeezing depth of such atom laser is determined by the initial squeezing factor of the probe light, and the squeezing period of that is related to the mean number of atoms in the trap, the strength of interaction between squeezing light and BEC atoms, and the detuning of the light.     

磁光阱中单原子荧光信号的优化及单原子的高效装载

实验中首先通过增大四极磁场梯度、提高背景真空度、缩小冷却俘获激光光束直径的方法获得了磁光阱中单原子的装载.其次,通过减小冷却光失谐量、适当增加其光强、同时使用偏振光谱锁频技术抑制冷却光噪声的方法得到了磁光阱中高信号背景比的单原子荧光信号.此外,通过实时反馈控制磁光阱四极磁场梯度的方法,在实验中实现了单原子98%的装载概率.使用Hamburg Brown-Twiss方案测量了磁光阱中的单原子在连续光激发下所辐射荧光的光子统计特性,得到二阶关联度g(2)(τ=0)=0.09.     

Stationary source of nonclassical or entangled atoms

A scheme for generating continuous beams of atoms in nonclassical or entangled quantum states is proposed and analyzed. For this the recently suggested transfer technique of quantum states from light fields to collective atomic excitation by stimulated Raman adiabatic passage [M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000)] is employed and extended to matter waves.     

The detection of atmospheric turbulence using two ultrasonic light modulators and heterodyne signal processing

The use of double diffraction of coherent light, passing through a pair of ultrasonic light modulators (ULM) with slightly different frequencies, has been studied for optical heterodyne detection processing. A beat signal can be generated with a difference or sum sound frequency between the two ULM's when a pair of diffracted light beams of first order, produced after passage through the two ULM's are photomixed with each other. This system has the merit that it requires no optical components except the two ULM's. It is also convenient for heterodyning techniques that the alignment of the two light beams to be photomixed is not critical. As an application of this system the phase fluctuations of the beat caused by atmospheric turbulence have been processed electronically to obtain its statistical properties.     

Statistical similarity and cross-spectral purity of stationary stochastic fields

In practical situations, one often generates a beam by superposition of two or more light beams. The beam generated by superposition displays, in general, different spectral properties than do the original beams. However, there are some optical beams, called cross-spectrally pure beams, which can generate a light beam of identical spectral distribution on superposition. The relationship between cross-spectral purity and spatial coherence has been the subject of investigations for some time. Recently, a concept of so-called statistical similarity has been introduced which provides a new way to elucidate complete spatial coherence. In this Letter, we discuss some implications of statistical similarity of an optical field on its cross-spectral purity.     

Diffractive Beam-Shaping Element for Generating Multiple Structured Beams with Distinct Spatial Structures

This paper presents a novel approach for generating structured light using a diffractive beam-shaping element that can generate multiple beams with distinct spatial structures in the focal plane. The element is constructed by restructuring a spiral zone plate with fork gratings, providing a tunable and controllable means for generating structured light. The element can create linear and 2D arrays of various structured beams, including vortices with adjustable charge and vorticity, petallike beams, and ring-lattice structures. To control the generation of these beams, it introduces several parameters of the fork gratings, enabling tailoring of the beam properties to specific applications. The proposed approach involves significant mathematical analysis, including the derivation of complex equations and expressions to understand the behavior of the proposed element and its impact on the generated beams. It conducts simulations and experiments to validate the mathematical analysis and demonstrate the feasibility of the proposed approach.     

Scattering of atoms by light

This review discusses the latest theoretical and experimental achievements in the resonant light pressure acting on the translational motion of atoms. Alongside with the effects due to the spontaneous light pressure (atomic deflection, velocity bunching, cooling), various manifestations of the effects of induced light pressure are considered in detail. This paper provides the theory and experiments of atoms scattering by a standing light wave under the conditions of coherent and non-coherent interaction, diffraction and interference of atomic beams. The problems where atomic motion along two trajectories and Landau-Zener transitions between them are essential, are studied. The kinetic phenomena (scattering, cooling, channeling) due to the motion of the particles exposed to gradient force and also friction and diffusion caused by spontaneous emission are considered. The influence of the recoil effect under spontaneous emission of atoms on non-linear polarization phenomena is discussed.     

相互作用原子玻色-爱因斯坦凝聚体诱导的光场压缩效应

给出了光场与二能级原子玻色-爱因斯坦凝聚体(BEC)相互作用系统的哈密顿量，研究了原子 间相互作用对压缩相干态光场与原子BEC相互作用系统中光场正交压缩特性的影响.结果表明 ：光场两正交分量的涨落均随时间按余弦规律周期性地变化，其压缩性质依赖于光场的初始 压缩因子和压缩方向角，而原子间的相互作用影响光场正交分量的涨落随时间变化的幅度和 周期. 关键词： 玻色-爱因斯坦凝聚 压缩相干态 光场的正交压缩     

Cosmic Structure Formation with Kinetic Field Theory

Kinetic field theory (KFT) is a statistical field theory for an ensemble of classical point particles in or out of equilibrium. Its application to cosmological structure formation is reviewed. Beginning with the construction of a generating functional, it is described in detail how the theory needs to be adapted to an expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, three approaches are developed to nonlinear cosmic structures, which rest either on expanding an interaction operator, averaging the interaction term, or resumming perturbation terms. An analytic, parameter‐free equation for the nonlinear cosmic power spectrum is presented. It is explained how density profiles of bound structures and velocity power spectra can be derived from the theory. It is clarified how KFT relates to the BBGKY hierarchy. Kinetic field theory is then applied to fluids, reformulating KFT in terms of macroscopic quantities. The resulting resummation scheme is used to describe mixtures of gas and dark matter. Finally, it is discussed how KFT can be combined with modified theories of gravity. As an example for a noncosmological application, results are shown on the spatial correlation function of cold Rydberg atoms derived from KFT.     

Interaction of soliton-like light beamsin second-order non-linear materials

We investigate numerically the interaction between two light beams, initially monochromatic, during the excitation of solitary waves in quadratically non-linear media. We show that the result of the interaction is strongly dependent on soliton oscillations occurring during excitation, generating a new class of threshold phenomena.     

Generating Functionals in Nonequilibrium Statistical Mechanics

The main ideas and methods of calculations within the framework of the generating functional technique are considered in a systematical way. The nonequilibrium generating functionals are defined as functional mappings of the nonequilibrium statistical operator and so appear to be dependent on a certain set of macroscopic variables describing the nonequilibrium state of the system. The boundary conditions and the differential equation of motion for the generating functionals are considered which result in an explicit expression for the nonequilibrium generating functionals in terms of the so-called coarse-grained generating functional being the functional mapping of the quasiequilibrium statistical operator. Various types of integral equations are derived for the generating functionals which are convenient to develop the perturbation theories with respect to either small interaction or small density of particles. The master equation for the coarse-grained generating functionals is obtained and its connection with the generalized kinetic equations for a set of macrovariables is shown. The derivation of the generalized kinetic equations for some physical systems (classical and quantum systems of interacting particles, the Kondo system) is treated in detail, with due regard for the polarization effects as well as the energy and momentum exchange between the colliding particles and the surrounding media.     

A general modal approach for the development of optimal multi-layer stacked vibration energy harvesters

Piezoelectric vibration energy harvesters with multi-layer stacked structures have been developed. They consist of multi-layer beams, of zigzag configurations, with rigid masses attached between the beams. The rigid masses, which also serve as spacers, are attached to each layer to tune the frequencies of the harvester. Close resonance frequencies and considerable power output can be achieved in multiple modes by varying the positions of the masses. A modal approach is introduced to determine the modal performance conveniently using the mass ratio and the modal electromechanical coupling coefficient, and the required modal parameters are derived using the finite element method. Mass ratio represents the influence of modal mechanical behaviour on the power density. Since the modes with larger mass ratios cause the remaining modes to have smaller mass ratios and lower power densities, a screening process using the modal approach is developed to determine the optimal or near-optimal performance of the harvesters when altering mass positions. This procedure obviates the need for full analysis by pre-selecting the harvester configurations with close resonances and favourable values of mass ratio initially. Furthermore, the multi-layer stacked designs using the modal approach can be used to develop harvesters with different sizes with the power ranging from microwatts to milliwatts.