Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate

In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order of magnitude.     

Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included

We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct a highly accurate and simple analytic approximation describing the time dynamics of the coupled atom-molecule system. We show that the approximation describing time evolution of the molecular state probability can be written as a sum of two distinct terms; the first one, being a solution to a limit first-order nonlinear equation, effectively describes the process of the molecule formation while the second one, being a scaled solution to the linear Landau-Zener problem (but now with negative effective Landau-Zener parameter as long as the strong coupling regime is considered), corresponds to the remaining oscillations which come up when the process of molecule formation is over.     

Transfer reactions induced by 17, 18O on 12, 13C at c.m. energies between 12.6 TO 14.0 MeV

Angular distributions for one-neutron and many-nucleon transfer reactions were measured in the systems ^{17, 18}O and ^{12, 13}C at c.m. energies between 12.6 to 14.0 MeV. All the cross sections were analyzed in terms of the full-recoil finite-range DWBA model. For multi-nucleon transfer processes an inert cluster transfer was assumed. The sensitivity of DWBA calculations to various parameter sets is discussed, and the effect of the no-recoil approximation on the phase and magnitude of the transfer amplitude is studied. For one-neutron transfer reactions the forward part of the angular distributions was reproduced reasonably well by the DWBA model, yielding satisfactory spectroscopic information. The rise of the cross section at the backward angles was not reproduced by the DWBA model. Possible contributions of cluster-exchange and compound-nucleus reactions are discussed. For multi-nucleon transfer reactions poorer fits were obtained, particularly in the ¹⁸O+¹²C system.     

Polarization effects for elastic and inelastic scattering with an adiabatic-propagator approximation

The effective coupling potentials derived from Feshbach's projection formalism can be significantly simplified with an adiabatic approximation in the propagator. For the diagonal and non-diagonal correction terms we derive perturbation series that lead to prominent shifts in both excitation energies and transition probabilities. We give a comparison between the conventional DWBA treatment and our modified analysis for¹⁶O+¹⁶O scattering.     

Finite-range DWBA analysis of (p, α) reactions on Be and B

The ground state angular distributions of the reactions ⁹Be(p, α)⁶Li and ¹¹B(p, α)⁸Be are analyzed by means of the DWBA theory. One-step direct mechanisms only are considered, but for both reactions the inclusion of the heavy-particle pick-up is found to be essential. DWBA fits to the data are obtained (a) in the zero-range approximation, (b) in the “fixed-range” approximation and (c) by an exact finite-range calculation. Only the latter method yields both an acceptable fit and reasonable values for the spectroscopic factors.     

Dynamics of interacting qubits in a strong alternating electromagnetic field

The populations of energy levels of interacting qubits have been studied as functions of the field amplitude and other control parameters for a constant frequency of the external electromagnetic field. It has been found that the qubit coupling constant strongly affects the quantum-coherent Landau-Zener transitions between the qubit states and the formation of an interference pattern in level populations, depending on the field parameters. It has been demonstrated that it is possible to determine the qubit coupling constant by Landau-Zener interferometry.     

Dispersion theory of nucleon transfer reactions induced by heavy ions

A new approach, the distorted wave pole approximation (DWPA) with the three-body Coulomb effects, is developed by combining the dispersion method and DWBA to analyse the heavy ion-induced neutron transfer reactions. The influence of the three-body Coulomb dynamics on the peripheral partial wave amplitudes is investigated. Differential cross sections of the neutron transfer reactions are calculated to compare the proposed model with the conventional DWBA. The values of nuclear vertex constants for virtual separation of neutron from various nuclei are obtained. The results of the calculations show that DWPA can be applied to analyse the heavy ion-induced neutron transfer reactions and that the three-body Coulomb effects are taken into account with acceptable accuracy in DWBA.     

M_(αβ) X-ray production cross sections of Pb and B iby 9–40 keV electron impact

The experimental data of Mαβ X-ray production cross sections for Pb and Bi by 9–40 keV electron impact have been given. Thin films with thick carbon substrates are used in the experiment. The effects of target structure on the Mαβ X-ray production cross sections are corrected by using the Monte Carlo method. The corrected experimental data are compared with calculated cross sections in terms of the distorted-wave Born approximation(DWBA) theory. The measured Mαβ X-ray production cross sections for Pb and Bi are lower than the DWBA calculations. The atomic relaxation parameters used in comparing the DWBA values with experimental results affect the degree of difference.     

共面不对称条件下Ar原子(e,2e)反应的三重微分截面

采用修正的扭曲波玻恩近似(DWBA)方法,计算了共面、大能量损失和小动量转移这一特殊几何条件下电子碰撞Ar(3p6)(e,2e)反应的三重微分截面.理论方法对(e,2e)反应过程近程极化势进行了修正,并引入Gamow因子表示后碰撞相互作用(PCI).将计算结果与实验结果、标准DWBA计算结果及Gamow因子修正后的DWBA-G计算结果进行了比较,发现极化效应起着重要的作用.     

光学势在(e, 2e)反应动力学过程的作用

将光学势包含到畸变波Bohn近似(DWBA)方法的畸变势中,修正了DWBA理论.计算了共面高非对称动力学条件下Ar原子2p壳层的三重微分截面,并与标准的DWBA计算得到的结果进行了比较.计算结果表明,光学势在Ar (2p)的电离过程中起着重要的作用. 关键词： 光学势 畸变波Bohn近似 三重微分截面     

Study of (e, 2e) process on potassium at 6 eV—60 eV above threshold in second-order Born approximation

The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for alkali target potassium at excess energies of 6 eV-60 eV. Comparing with the first-order DWBA calculations before, the present theoretical model improves the degree of agreement with experiments, especially for backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e, 2e) problems in low and intermediate energy range.     

Gauging a quantum heat bath with dissipative Landau-Zener transitions

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.     

Simulation of Neutron Reflection from the Surface of a Nanostructured Object in the Modified Kinematic Approximation

The applicability of the modified kinematic approximation for simulation of the specular reflection and the diffraction of a neutron beam from regularly ordered nanostructured objects on the surface and in the surface material layer is analyzed. The obtained results are compared with those of the real experiment and simulation of the distorted-wave Born approximation (DWBA). The influence of various factors on the obtained results is analyzed. These factors include the effect of neutron-wave refraction at the interfaces between media, the spectrometer-resolution function, and renormalization of the results for a nonspecular scattering signal based on data obtained for a specular channel. It is shown that, in many cases, it is possible to obtain rather good agreement with the experimental data and with the results of calculations using DWBA methods and of calculations using the Parratt algorithm.     

Adiabatic transport of Bose-Einstein condensates in a double-well trap: Case of weak nonlinearity

A complete adiabatic transport of Bose-Einstein condensate in a double-well trap is investigated within the Landau-Zener (LZ), and Gaussian Landau-Zener (GLZ) schemes for the case of a small non-linearity, when the atomic interaction is weaker than the coupling. The schemes use the constant (LZ) and time-dependent Gaussian (GLZ) couplings. The mean field calculations show that LZ and GLZ suggest essentially different transport dynamics. Significant deviations from the case of a strong coupling are discussed.     

Solution to the Landau-Zener problem via Susskind-Glogower operators

We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.     

电子碰撞激发氢原子和氦离子散射微分截面的计算

本文详细介绍计算电子碰撞激发散射截面的扭曲波玻恩近似（DWBA）理论模型,并对低能DWBA模型进行修正。利用修正的DWBA模型计算了电子碰撞激发氢原子和氦离子1s-2s 和1s-2p的散射微分截面。将关于氢原子由基态到n=2态的电子碰撞激发散射微分截面与绝对实验测量数据比较,发现二者符合得很好,这验证了我们对DWBA修正的正确性。本文工作为拟合强场诱导的氦原子非序列双电离关联电子动量谱提供了有效的理论方法。     

Theoretical calculation of the triple differential cross sections of the 2p orbital of argon in a coplanar highly asymmetric（e,2e） reaction

The triple differential cross sections of the 2p electron of argon in a coplanar highly asymmetric geometry have been calculated with the modified distorted wave Born approximation (DWBA) and the target Hartree－Fock approximation methods. The damping polarization of the semi-classical short-range potentials and the M_ee factor are included in the distorting potentials of the modified DWBA. Theoretical results are compared with a recent experiment. The dynamic mechanism of inner shell ionization in a coplanar highly asymmetric geometry (e, 2e) reaction are also discussed.