激光冷却和捕陷中性原子③

6 激光冷却和捕陷中性原子技术的应用 前面已经提到,激光冷却和捕获中性原子技术最主要的应用是在精密计量和超冷原子物理两个方面.在精密计量方面最为典型的是可用于原子频标的"原子喷泉"(atomic fountain)技术;而在超冷原子物理方面最为典型的是玻色-爱因斯坦凝聚(Bose-Einstein condensation)和原子波激射器(atom laser)的实现.     

A Nucleophilic Addition of Acetone Enolate to (<Emphasis Type="Italic">E</Emphasis>)-Alkyloxindolylideneacetates

Summary. The reaction of (E)-(2-oxo-1,2-dihydroindol-3-ylidene)acetic acid esters with dry acetone at 70°C in presence of aluminum oxide as a catalyst led to the formation of an addition product as a mixture of two isomers. When the same reaction was carried out in presence of morpholine as a base, the unexpected spiro-product was obtained beside the two isomers. Methylation of the latter with methyl iodide in acetone in presence of anhydrous potassium carbonate yielded the corresponding methylated products, whereas methylation of the starting material by the same procedure gave an N-methylated product and the unexpected dispiro-compound. The reaction mechanisms are considered and the structural assignments of the new compounds are based on the chemical and spectroscopic evidences. The structure of the dispiro-product was derived by X-ray analysis.     

噪声对双势阱玻色-爱因斯坦凝聚体系自俘获现象的影响

研究了对称双势阱玻色-爱因斯坦凝聚体系(BEC)存在均匀噪声或高斯噪声时的自俘获现象.结果发现噪声的存在破坏了自俘获现象的临界行为特征，使得原来约瑟夫森振荡和自俘获之间的临界点变成了一个过渡区域，而且噪声强度越大，这个过渡区域展得越宽.同时发现，对于确定的相互作用强度，当噪声强度增大到一定程度时，相平面会出现混乱，如果这时固定噪声强度增大相互作用强度，相平面中的轨道会重新出现.对纯量子系统加噪声后，自俘获同样不存在临界值，而是存在一个临界区域，且随噪声的增强临界区域会展宽.与平均场近似情况下不同的是，纯量子情况下噪声促进自俘获的产生，且噪声越强自俘获越明显. 关键词： 玻色-爱因斯坦凝聚 自俘获 双势阱 噪声     

两个玻色-爱因斯坦凝聚体间相互作用的数值研究

本文采用辛算法数值求解一维含时Gross-Pitaevskii(GP)方程.研究了存在陷俘势和撤掉陷俘势时两个凝聚体间的相互作用.发现当存在陷俘势时两个凝聚体间发生弹性碰撞;在零时刻撤掉陷俘势时两个凝聚体间发生干涉现象;当t=2时撤掉陷俘势两个凝聚体间发生了复杂现象.     

Phase of a Bose-Einstein Condensate in a Double-Well Potential Modulated Periodically in Time

By using of the invariant theory, we have studied phase of a Bose-Einstein condensate in a double-well potential modulated periodically in time when the on-site interaction energy of a single pair of bosons occupying the same well equals the collision energy between two condensates, the dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained in the case of the cyclical evolution. PACS:03.65.Vf; 03.75.Mn     

Critical temperature and condensed fraction of Bose-Einstein condensation in optical lattices

Critical temperature and condensate fraction of Bose-Einstein condensation in the optical lattice are studied. The results show that the critical temperature in optical lattices can be characterized with an equivalent critical temperature in a single lattice, which provide a fast evaluation of critical temperature and condensate fraction of Bose-Einstein condensation confined with pure optical trap. Critical temperature can be estimated with an equivalent critical temperature. It is predicted that critical temperature is proportional to q in q number lattices for superfluid state and should be equal to that in a single lattic for Mott insulate state. Required potential depth or Rabi frequency and maximum atom number in the lattices both for superfluid state and Mott state are presented based on views of thermal mechanical statistics.     

Analysis of Japanese banks’ historical tree diagram

By using the historical data from the Japanese banks’ database at “The Bankers Library” of Japanese Banker Association, we analyze the historical network of banks from 1868 to 2006. Firstly, we define a bank every year by a particle and draw a space-time evolution process of merger, division, establishment, and failure by a tree diagram structure. We found that the distribution of the tree basin size of real data and simulation result are mostly fitting well. Secondly, we analyze the raw data of financial statements of banks collected by the National Diet library. We confirm that the distributions of the amount of deposits have fat-tail every year, however, small deviations are observed relating to governmental policy.     

Facile Assembly of Dispersed ZrMCM‐41 Nanoparticles Promoted in‐situ by Zirconium Salt

Mesoporous ZrMCM‐41 nanoparticles were synthesized by a usual way where tetraethyl‐orthosilicate (TEOS) and zirconium nitrate were used as the inorganic precursors. The obtained nanoscale ZrMCM‐41 was characterized by X‐ray diffraction, N₂ physis‐sorption, scanning electron microscopy and transmission electron microscopy. Characterization results revealed that zirconium salt added in the synthesis had a crucial effect on the assembly of nanoscale ZrMCM‐41 with relatively uniform particle size, which was rarely observed in reported studies for ZrMCM‐41 synthesized using the similar method. Meanwhile, the possible mechanism behind the synthesis was discussed based on the character of hydrolysis and condensation of TEOS and the mild acidic environment induced by the hydrolysable zirconium salt under aqueous conditions. Thus obtained nanoscale ZrMCM‐41 with developed pore structures may be advantageous to general applications in catalysis or adsorption host‐guest chemistry in terms of efficient mass transport of guest molecules.     

A new strategy for the synthesis of benzoxanthenes catalyzed by proline triflate in water

Catalyzed by proline triflate, benzoxanthenes were obtained in good yields from the condensation of naphthols, aldehydes, and 1,3-dicarbonyl compounds in water. A possible mechanism of this reaction is proposed.     

Spectrophotometric determination and kinetic studies of condensation of aromatic aldehydes with 1,3-dimethylbarbituric acid

The condensation reaction of 1,3-dimethylbarbituric acid with aromatic aldehydes in ethanol has been investigated spectrophotometrically at 25–35°C. The reaction follows overall second-order kinetics, first-order each in reactant. From the dependence of the rate constants on temperature, activation parameters have been calculated. The rate of condensation increases with the presence of electron donating groups on the aromatic ring of the aldehyde. The rate-determining step involves dehydration of the aldol intermediate. The reaction was found to be catalyzed by HCl solutions. Based on this reaction, determination of 10 aromatic aldehydes in a concentration range of 0.13–70.25 μg/ml is proposed. The method was applied for determination of barbituric and 1,3-dimethylbarbituric acids also.