Bragg spectroscopy and Ramsey interferometry with an ultracold Fermi gas

We report on the observation of Bragg scattering of an ultracold Fermi gas of ⁶Li atoms at a dynamic optical potential. The momentum states produced in this way oscillate in the trap for time scales on the order of seconds, nearly unperturbed by collisions, which are absent for ultracold fermions due to the Pauli principle. In contrast, interactions in a mixture with ⁸⁷Rb atoms lead to rapid damping. The coherence of these states is demonstrated by Ramsey-type matter wave interferometry. The signal is improved using an echo pulse sequence, allowing us to observe coherence times longer than 100 μs. Finally, we use Bragg spectroscopy to measure the in-situ momentum distribution of the ⁶Li cloud. Signatures for the degeneracy of the Fermi gas can be observed directly from the momentum distribution of the atoms inside the trap.     

Dynamic multipole polarizabilities of Li and Na atoms interacting with Debye potentials

The effects of Debye potentials on the dynamic multipole polarizabilities of Li and Na atoms are investigated using the symplectic algorithm. Frequency-dependent multipole polarizabilities of Li(2s ²S) and Na(3s ²S) are reported in terms of scaled number density of the plasma electrons for arbitrary plasma temperature.     

Electron-pair densities of group 2 atoms in their and terms

Electron-pair intracule (relative motion) and extracule (center-of-mass motion) densities are studied in both position and momentum spaces for the ¹ P and ³ P terms of the group 2 atoms Be (atomic number Z =4), Mg (Z =12), Ca (Z =20), Sr (Z =38), Ba (Z =56), and Ra (Z =88). In position space, the ¹ P - ³ P difference in the intracule densities shows that the probability of a small interelectronic distance is larger in the triplet for all the six atoms, as reported for the lightest Be atom in the literature. The position-space extracule density clarifies that the triplet electrons are more likely to be at opposite positions with respect to the nucleus than the singlet electrons for all the atoms. In momentum space, the singlet generally has a larger probability of a small relative momentum between two electrons as a na?ve manifestation of the Fermi hole in the triplet. The extracule density in momentum space shows that the ¹ P term has a distribution larger in a large center-of-mass momentum region than the ³ P term. Received: 26 August 1998 / Received in final form: 1 February 1999     

幻数尺寸Li-n-1,Lin,Li+ n+1(n=20,40)团簇的几何结构、电子与光学性质的第一性原理研究

基于密度泛函理论,采用第一性原理分子动力学模拟退火方法,对Li^-_n-1,Li_n,Li⁺_n+1 (n=20,40)的最低能量结构进行了全局搜索. 发现锂团簇的生长模式是以单个或多个嵌套的正多面体为核心,其余原子以五角锥为基本单元围绕核心生长. 基于最低能量结构的第一性原理电子结构计算得到锂团簇的分子轨道能级分布与无结构凝胶模型给出的电子壳层完全一致. 在总电 关键词： 团簇 电子结构 极化率 光吸收     

Halo structure of 11Li in proton scattering: A folding model description with isospin,density and momentum dependent effective interaction

Recent ¹¹Li+p elastic scattering data at 62, 68.4, and 75 MeV and inelastic scattering data at 68.4 MeV, taken at RIKEN, are analysed with an isospin, density and momentum dependent finite range effective interaction (SBM) and M3Y interaction in a single folding model. The M3Y folded ¹¹Li+p potentials are found to be almost similar to the folded ⁹Li+p potentials. But the SBM folded ¹¹Li+p potentials are distinctly different, causing small but significant change in the angular distribution. Folded potentials need appreciable reduction factors indicating possible effects of strong breakup channel coupling. No significant change in results is found if ⁹Li core + Gaussian two-neutron halo density is used instead of the COSM density of ¹¹Li although the radial extent of the latter is much larger. The angular distribution of the recently discovered excited state at 1.3 MeV, well reproduced by the SBM folded potential, is found to be predominantly dipole in nature.     

Elastic scattering of e∓ by Na atoms

ABSTRACT

The differential, integrated elastic, momentum transfer, viscosity and total cross-sections along with Sherman function for the elastic scattering of electrons and positrons by sodium atoms have been calculated within the framework of complex projectile–atom optical potential model at the impact energies 0.1 ≤ E_i ≤ 10⁴ eV for both the projectiles. The relativistic Dirac partial wave techniques, with accurate analytical charge densities, are used to obtain the scattering amplitudes. The present results produce satisfactory agreement with the experimental measurements and other theoretical calculations available in the literature.     

硅烯饱和吸附碱金属原子的第一性原理研究

基于密度泛函理论的第一性原理计算, 研究了硅烯饱和吸附碱金属元素原子的稳定性、微观几何结构和电子性质, 并与纯硅烯及其饱和氢化结构进行了对比分析. 研究发现复合物SiX(X=Li, Na, K, Rb)的形成能都是负的, 相对于纯硅烯来说可以稳定存在. Bader电荷分析表明, 电荷从碱金属原子转移至硅原子. 从成键方式来看, 硅烯与氢原子形成共价键, 而与碱金属原子之间形成的键主要是离子性成键, 但还存在部分共价关联成分. 能带计算表明, 锂原子饱和吸附在硅烯形成的复合物SiLi是直接带隙的半导体, 带隙大小为0.34 eV. 其他碱金属饱和吸附在硅烯上形成的复合物都表现为金属性.     

双层石墨烯吸附碱金属原子的第一性原理研究

基于密度泛函的第一性原理方法,研究了Li、Na、K和Rb碱金属原子吸附在双层石墨烯(BLG)表面的吸附能、迁移行为、电子性能.研究发现,Li和Na原子在BLG表面吸附易形成团簇,K和Rb原子能够分散吸附.碱金属原子在BLG表面的扩散能垒随原子半径的增加而减小.碱金属原子吸附使电子部分转移至BLG,使体系Fermi能级贯穿导带,表现出金属性.电荷密度差和电荷转移的分析表明,Li、Na、K和Rb与BLG表面以离子键结合.     

双层石墨烯吸附碱金属原子的第一性原理研究

基于密度泛函的第一性原理方法,研究了Li、Na、K和Rb碱金属原子吸附在双层石墨烯(BLG)表面的吸附能、迁移行为、电子性能. 研究发现,Li和Na原子在BLG表面吸附易形成团簇,K和Rb原子能够分散吸附. 碱金属原子在BLG表面的扩散能垒随原子半径的增加而减小. 碱金属原子吸附使电子部分转移至BLG,使体系Fermi能级贯穿导带,表现出金属性. 电荷密度差和电荷转移的分析表明,Li、Na、K和Rb与BLG表面以离子键结合.     

First-principles study on the structural and electronic properties of LiB and its hydrides (Li2BnHn, n=5, 8, 12, LiBH4)

Structural, electronic and vibrating properties of LiB and its hydrides (Li₂B_nH_n, n=5, 8, 12, LiBH₄) were calculated by the first-principles using density functional theory in its generalized gradient approximation. The calculated results are in good agreement with experimental studies. The deviation between theory and experimental results are also discussed. With the increasing of H atoms in range of 5-12, the band gap energy increases and the width of the conduction band decreases. Comparing with LiB, the band gap of LiBH₄ is broadened, which indicates the enhancement of Li-B and Li-H bond strength. Valence electrons mainly transfer from Li atoms to B and H atoms. As a result, Li atoms are thought to be partially ionized as Li⁺ cations. There is little contribution of Li orbital to the occupied states, resulting in Li-H and Li-B bond exhibiting an ionic nature, and B-H bond showing a covalent nature.     

Acceleration of cold Rb atoms by frequency modulated light pulses

The displacement of Rb atoms in a magneto-optical trap (MOT) caused by the force of a finite time series of counter-propagating frequency modulated light pulse pairs is measured as a function of the chirp of the pulses. The frequency modulated light pulses induced ⁸⁵Rb 5²S_1/2 F=3 ↔ ⁸⁵Rb 5²P_3/2 F'=2, 3, 4 excitation and de-excitation of the atoms. The result of this excitation de-excitation process is a force causing the acceleration and, consequently, the displacement of the maximum of the spatial distribution of the trap atoms. The time dependence of the populations of the levels of the atom are calculated — including also the ⁸⁵Rb 5²S_1/2 F=2 and F'=1 states — as the result of the interaction with the finite train of counter propagating frequency modulated light pulses by the solution of the Bloch equations. As the result of the measurement the interval of the chirp of the frequency modulated light of given intensity where the transitions take place, are determined. The results of the experiment and the expectation on the basis of model calculations are in qualitative agreement.     

Electronic structure and magnetic properties of the N monodoping and (Li, N)-codoped ZnO

Using first-principles calculations based on density functional theory, we investigated systematically the electronic structures and magnetic properties of N monodoping and (Li, N) codoping in ZnO. The results indicate that monodoping of N in ZnO favors a spin-polarized state with a magnetic moment of 0.95 μ_B per supercell and the magnetic moment mainly comes from the unpaired 2p electrons of N and O atoms. In addition, it was found that monodoping of N in ZnO is a weak ferromagnet and it is the spin-polarized O atoms that mediate the ferromagnetic exchange interaction between the two N atoms. Interestingly, by Li substitutional doping at the cation site (Li_Zn), the ferromagnetic stability can be increased significantly and the formation energy can be evidently reduced for the defective system. Therefore, we think that the enhancement of ferromagnetic stability should be attributed to the accessorial holes and the lower formation energy induced by Li_Zn doping.     

Electronic and magnetic properties of SiC nanoribbons by F termination

By using the first-principles calculations, the electronic properties are studied for the F-terminated SiC nanoribbons (SiCNRs) with either zigzag edges (ZSiCNRs) or armchair edges (ASiCNRs). The results show that the broader F-terminated ZSiCNRs are metallic and the edge states appear at the Fermi level, while the F-terminated ASiCNRs are always semiconductors independent of their width but the edge states do not appear due to the Si-C dimer bonds at the edges. The charge density contours analyses shows that the Si-F and Si-C bonds are all ionic bonds due to the much stronger electronegativities of the F and C atoms than that of the Si atom. However, the C-F bonds display a typical non-polar covalent bonding feature because of the electronegativity difference between the F and C atoms of 1.5 is a much smaller than that of between the F and Si atoms of 2.2, as well as the tighter bounded C 2s ²2p ² electrons with smaller orbital radius than the Si 3s ²3p ² electrons. For both the F- and the H-terminated ZSiCNRs, the ground state is a ferromagnetic semiconductor.     

Higher orders in residual two-electron interaction

Precise methods of calculations of many-electron atoms are under intensive development. In such calculations, higher orders of the perturbation theory in regard to residual interaction of electrons should be taken into account. In this study, a model of an atom with two electrons in its core and two valence electrons is considered. In terms of this model, expansion with respect to residual interaction is analyzed for two initial approximations based on the potentials V ⁽²⁾ and V ⁽⁴⁾. It turns out that the higher order corrections are nearly the same in both cases. At the same time, the potential V ⁽²⁾ has a number of advantages.     

One-nucleon spectroscopic factors and momentum distributions of nucleons in the 6Li and 9Be nuclei within three-body models

Within the three-body α2N and 2αN models of the ⁶Li and ⁹Be nuclei, respectively, the spectroscopic factors and the momentum distributions of nucleons are computed for the cases where residual nuclei can be formed both in the ground and in excited states. The impact of model parameters on the values of one-nucleon features is discussed. The results of the calculations performed in the present study are compared with available experimental data.     

Electronic and geometric properties of alkali-C60 molecules

First-principle electronic structure calculations are carried out for M_xC ₆₀ ^q , where M = Li, Na, K and ( x , q ) = (1, 0),(1,±1),(2, 0),(3, - 1),(6, 0),(6, - 1),(12, 0) using the local density functional. The electric dipole moment for MC₆₀ agrees with the experimental results. The calculated Mulliken charge indicates that the bonding of the alkali atom with C₆₀ is mostly ionic except for lithium. The alkali atom prefers to make many bonds with the carbon atoms rather than a single bond with the neighbor carbon atom. The calculated adsorption energy suggest that the metal-metal bonding of sodiums and potassiums on C₆₀ arises for more than the six valence electrons in the alkali atoms. The lithium-lithium bond is, on the other hand, not appeared for x ? 12. The difference in the most stable geometry between lithiums and the other alkali atoms on C₆₀ comes from the covalent character of the lithium-carbon bond.     

Spin polarization of electrons elastically scattered from europium and bismuth atoms

We present calculations of differential, integrated elastic, total, momentum transfer cross-sections and spin-polarization parameters S, T and U for scattering of electrons from Eu and Bi atoms in the energy range 2.0 to 500.0 eV using semi-relativistic approach. The target-projectile interaction is represented both by real and complex parameter-free optical potentials in the solution of Dirac equation for the scattered electrons. The results for the differential cross-sections and spin-polarization parameters have been compared with the available calculations and experimental results. Received 17 February 2000 and Received in final form 15 June 2000     

Analytic calculation of the lineshapes in polarization spectroscopy of rubidium

This paper reports on analytic calculations of the lineshapes for polarization spectroscopy of rubidium atoms. Under the use of a weak circularly polarized pump beam, the time-dependent population of each magnetic sublevel was obtained analytically from the rate equations up to the lowest order of the pump beam intensity, and the associated circular birefringence experienced by a counterpropagating probe beam was calculated. In particular, analytic forms of the polarization spectroscopy spectra were obtained for ⁸⁷Rb and ⁸⁵Rb atoms using the mean transit time crossing the pump beam, and the analytic results were compared with the numerical data, experimental results and Nakayama model’s results, showing a good agreement one another.     

Defects in ion-implanted hcp-titanium: A first-principles study of electronic structures

The electronic structures of hexagonal closed-packed (h.c.p) titanium containing a vacancy and krypton impurity atoms at various insertion sites are calculated by first-principles methods in the framework of the density-functional theory (DFT). The density of states (DOS) for titanium containing a vacancy defect shows resonance-like features. Also, the bulk electron density decreases from ∼0.15/ų to ∼0.05/ų at the vacancy centre. Electronic structure calculations have been performed to investigate what underlies the krypton site preference in titanium. The DOS of the nearest-neighbour (NN) titanium atoms to the octahedral krypton appears to be less distorted (relative to pure titanium) when compared to the NN titanium atoms to the tetrahedral krypton. The electronic density deformation maps show that polarization of the titanium atoms is stronger when the krypton atom is located at the tetrahedral site. Since krypton is a closed-shell atom, thus precluding any bonding with the titanium atoms, we may conclude that the polarization of the electrons in the vicinity of the inserted krypton atoms and the distortion of the DOS of the NN titanium atoms to the krypton serve to indicate which defect site is preferred when a krypton atom is inserted into titanium. Based on these considerations, we conclude that the substitutional site is the most favourable one, and the octahedral is the preferred interstitial site, in agreement with recent DFT calculations of the energetics of krypton impurity sites.