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1.
由电子绕原子核的经典轨道运动出发,对电子的椭圆轨道初始坐标参数求平均,得到空间密度分布。这分布与经典极限条件下氢原子中定态几率密度相同。类似的比较也推广到相空间进行。由这一比较得出结论:定态氢原子波函数不描述单个原子而描述一个系综。
关键词: 相似文献
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3.
K. B. Korotchenko 《Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques》2010,4(4):599-602
A new type of combinational channeling radiation induced by subbarrier (interband) transitions for the transverse motion of
relativistic electrons (positrons) is studied. It is known as diffracted channeling radiation (DCR). The formula describing
the DCR angular distribution in the case of axial channeling is obtained by taking into account the band structure of energy
levels for the transverse motion of electrons (positrons). It is shown that, in the two-wave approximation of the wave function
A(r) of virtual photons, the DCR matrix elements in the dipole approximation for axial and plane channeling coincide formally
(with the dimension of the problem taken into account). However, the formulas for DCR angular distributions in the cases of
axial and plane channeling differ considerably. 相似文献
4.
Analytical estimates and computer simulations were undertaken to perceive the motion of negative particles through a lattice structure, the interaction being classical binary scattering. Three distinct modes of particle motion along atomic strings were found depending on the magnitude of the transverse energy and the angular momentum L of the particle with regard to the string axis. At small and large L increased scattering on the strings as compared with random penetration dominates. At medium L and negative transverse energy (bound state particles in the attractive potential) a rosette motion along the string occurs. In this case small impact parameters to the string atoms are avoided and thus an increased penetrability of the negative particles results. The influence of thermal lattice vibrations on these motions was studied. Experimentally, the negative particle motion modes manifested themselves in the penetration profiles of 20 MeV electrons through an 8 μm MgO single crystal. 相似文献
5.
基于半经典理论,分析了中性钠原子在激光驻波场中的受力特征,以此为基础分别对不同纵向运动速度和横向运动速度条件下中性钠原子的运动轨迹进行了仿真运算,得到了不同速度条件下中性钠原子的运动轨迹特征,基于累计算法进一步对不同速度条件下中性钠原子的沉积特性进行了仿真,当钠原子的纵向运动速度符合最可及速度(740 m/s)时,纳米沉积条纹的半高宽为2.78 nm,条纹对比度为38.5 ∶1,当纵向运动速度偏离最可及速度(350 m/s)时,纳米沉积条纹的半高宽为29.1 nm,其对比度下降为15 ∶1.而当中性钠原子
关键词:
原子光刻
激光驻波场
条纹半高宽
条纹对比度 相似文献
6.
The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type
of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves
with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain
large splittings (>100ℏk) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in
these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation
of such a splitter.
Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 386–391 (25 September 1997) 相似文献
7.
研究了冷原子与法布里-珀罗腔内拉盖尔-高斯横模强耦合相互作用体系的透射光谱, 分析了透射光谱与原子在腔中运动轨迹的关系. 结果表明, 与厄米特-高斯横模相比, 拉盖尔-高斯横模的腔场与原子的最大耦合系数几乎不随阶数的增加而变化, 使得探测光谱的对比度受模式阶数的影响较小. 在拉盖尔-高斯横模场分布的圆环边缘附近, 原子运动轨迹的微小偏移会引起透射光谱的很大变化, 因此在这些位置可以实现原子运动轨迹的高精度探测. 相似文献
8.
In this paper we present a mathematical procedure to analytically calculate the output signal of a pulsed atom interferometer in an inertial field. Using the well-known ABCDξ method we take into account the full wave dynamics of the atoms with a first order treatment of the wavefront distortion by the laser pulses. Using a numerical example we study the effect of both the length of the beam splitting laser pulses and of the width of the initial spatial distribution of the atoms. First, we find that in a general inertial field the interferometer only has a limited window in terms of the initial width (centered around 100 μm in the example calculation) in which interference fringes are visible at all. This effect is caused by the inevitable statistical spread in atomic parameters, such as initial position and momentum, and the dependence of the interferometer phase on these. In the optimum case, the useful range of the initial width is formed by the range in which both the spatial distribution and the diffraction limited momentum spread are small enough to avoid large phase differences over the atomic wavefunction. As a second result we find that the interferometer phase depends strongly on the length of the laser pulses and, to a smaller extent, on the initial width of the atomic cloud. This spatial dependency is relatively small (~10?5 rad) and justifies semiclassical approximations, as used in other calculations, for most experiments. New high-accuracy experiments, however, will come in the range where this effect is no longer negligible. 相似文献
9.
Dennis Lorek Andreas Wicht Claus Lämmerzahl 《General Relativity and Gravitation》2011,43(7):2053-2064
We present an orientational quantum interferometer sensitive to gravitational waves that is based on orienting quantum objects
like molecules, atoms, or nuclei in space. The detection principle is based on inducing non-sphericity to the corresponding
wave functions by light-pulses. In the field of a gravitational wave these objects then possess spectra that depend on their
orientation in space. In our measurement scheme we investigate the adiabatic influence of a monochromatic gravitational wave
over a quarter gravitational wave period and compare the corresponding frequencies at instances with maximal and vanishing
gravitational wave elongation. We therefore explore the effect over a quarter gravitational wave period (or wavelength) and
the resulting frequency shift scales with the binding energy of the system times the amplitude of the gravitational wave.
In particular, a gravitational wave with amplitude h = 10−23 will induce a frequency shift of the order of 110 μHz for an atom interferometer based on a 91-fold charged uranium ion. 相似文献
10.
M. D. Hoogerland J. P. J. Driessen E. J. D. Vredenbregt H. J. L. Megens M. P. Schuwer H. C. W. Beijerinck K. A. H. van Leeuwen 《Applied physics. B, Lasers and optics》1996,62(4):323-327
Using a three-step transverse laser cooling scheme, a strongly diverging flow of metastable Ne(3s
3
P
2] atoms is compressed into a well-collimated, small diameter atomic beam (e.g., 1.4 mrad HWHM divergence at 3.6 mm beam diameter) with an unmodified axial velocity distribution centered at 580 m/s. The maximum increase in beam flux 1.04 m downstream of the source is a factor 1400; the maximum increase in phase space density, i.e., brightness, is a factor 160. The laser power used is only 140 mW. The scheme is extendable to a large variety of atomic species and enables the application of bright atomic beams in many areas of physics. 相似文献
11.
Two-level atoms bouncing in a stable gravitational cavity are considered, where the atomic mirror at the bottom of the bounces is an evanescent wave caused by an internally reflected intense Gaussian-mode laser beam. We consider the broadening mechanisms of the atoms from their initially tightly spaced position distribution, using a phenomenological semi-classical model, which includes spontaneous emission. A fully quantum model, which neglects spontaneous emission, is derived, and the broadening of the atomic wave function in the quantum model is compared with the broadening of the atomic distribution in an analogous classical simulation where spontaneous emission is similarly neglected. We find that the broadening is correctly described by the classical simulations in the horizontal directions, while it significantly underestimates the broadening in the vertical direction.Dedicated to H. Walther on the occasion of his 60th birthday 相似文献
12.
We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high-Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical
Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow,
in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this
solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons
in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode.
The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation
is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire
energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of
Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in
this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first
in the area of the fundamental parametric resonance, δ/2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance,
generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical
experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high-Q microwave cavity are possible objects for observing parametric instability and dynamical chaos.
Zh. éksp. Teor. Fiz. 115, 740–753 (February 1999) 相似文献
13.
We consider the usual Jaynes–Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω0 and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. 相似文献
14.
《Journal of Nonlinear Mathematical Physics》2013,20(1):50-53
Abstract We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? 4 type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics. 相似文献
15.
Lajos Molnár 《Communications in Mathematical Physics》2001,217(2):409-421
Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated,
for example, in the following way: Every bijective transformation on the set ℒ of all 1-dimensional subspaces of a Hilbert
space H which preserves the angle between the elements of ℒ is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigner's result from the 1-dimensional case to the case of n-dimensional subspaces of H with n∈ℕ fixed.
Received: 28 August 2000 / Accepted: 30 October 2000 相似文献
16.
We consider a simple model of the lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. The internal dynamics of the atom is governed by the laser field, which is treated as classical with a large number of photons. The center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degrees of freedom. The resulting Hamilton-Schrö dinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion, and the total atomic energy and the Bloch vector length are conserved during the interaction. In our previous papers, the motion of the atom has been shown to be regular or chaotic (in the sense of exponential sensitivity to small variations of the initial conditions and/or the system’s control parameters) depending on the values of the control parameters, atom-field detuning, and recoil frequency. At the exact atom-field resonance, the exact solutions for both the external and internal atomic degrees of freedom can be derived. The center-of-mass motion does not depend in this case on the internal variables, whereas the Rabi oscillations of the atomic inversion is a frequency-modulated signal with the frequency defined by the atomic position in the optical lattice. We study analytically the correlations between the Rabi oscillations and the center-of-mass motion in two limiting cases of a regular motion out of the resonance: (1) far-detuned atoms and (2) rapidly moving atoms. This paper is concentrated on chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that an atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential, or fly ballistically with weak chaotic oscillations of its momentum, or wander in the optical lattice, changing the direction of motion in a chaotic way. In the regime of chaotic wandering, the atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion-Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincaré mappings are constructed using the translational invariance of the standing laser wave. We find common features with typical nonhyperbolic Hamiltonian systems-chains of resonant islands of different sizes imbedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of the atomic trajectories sticking to boundaries of regular islands, which should have a great influence on atomic transport in optical lattices, is found and demonstrated numerically. 相似文献
17.
The motion of a collisionless plasma is modeled by solutions to the Vlasov–Maxwell system. The Cauchy problem for the relativistic
Vlasov–Maxwell system is studied in the case when the phase space distribution function f = f(t,x,v) depends on the time t, and . Global existence of classical solutions is obtained for smooth data of unrestricted size. A sufficient condition for global
smooth solvability is known from [12]: smooth solutions can break down only if particles of the plasma approach the speed
of light. An a priori bound is obtained on the velocity support of the distribution function, from which the result follows.
Received: 18 March 1996/Accepted: 29 July 1996 相似文献
18.
The Wigner's Theorem states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex
Hilbert space which preserves orthogonality is induced by either a unitary or an anti-unitary operator. There exist many Wigner-type
theorems, in particular in indefinite metric spaces, von Neumanns algebras and Banach spaces and we try to find a common origin
of all these results by using properties of the lattice subspaces of certain topological vector spaces. We prove a Wigner-type
theorem for a pair of dual spaces which allows us to obtain, as particular cases, the usual Wigner's Theorem and some of its
generalizations.
PACS: 02.40.Dr, 03.65.Fd,03.65.Ta
AMS Subject Classification (1991): 06C15, 46A20, 81P10. 相似文献
19.
S. V. Prants 《Journal of Experimental and Theoretical Physics》2009,109(5):751-761
A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed. 相似文献