光晶格中玻色-爱因斯坦凝聚体的自旋和磁研究

近年应用光晶格（optical lattice)控制原子玻色－爱因斯坦凝聚体（BEC）的研究取得了突破性的进展。德国Munich研究小组首次在三维光晶格中观察到了超冷原子从BEC超流状态向Mott insulator状态的量子相变。这样的量子相变现象不仅具有重大的理论研究价值，而且为BEC的实际应用提供了新的途径。文章介绍了作者近来在光晶格中BEC的自旋和磁特性方面的一些研究进展，并探讨了它们在磁传感器及量子计算中的可能应用。     

稀薄原子气体玻色-爱因斯坦凝聚近期研究进展简介

论述了自1999年涡旋态在稀薄碱金属原子气体的玻色-爱因斯坦凝聚体(BEC)中成功实现以来有关的BEC理论和实验研究的进展及作近期的部分探索，并介绍了相关的基本概念和理论。     

Characterization and control of phase fluctuations in elongated Bose–Einstein condensates

Quasi-one-dimensional Bose–Einstein condensates (BECs) in elongated traps exhibit significant phase fluctuations even at very low temperatures. We present recent experimental results on the dynamic transformation of phase fluctuations into density modulations during time of flight and show the excellent quantitative agreement with the theoretical prediction. In addition we confirm that, under our experimental conditions, in the magnetic trap density modulations are strongly suppressed even when the phase fluctuates. We also discuss our theoretical results on control of the condensate phase by employing a time-dependent perturbation. Our results set important limitations on future applications of BECs in precision atom interferometry and atom optics, but at the same time suggest pathways to overcome these limitations. Received: 17 August 2002 / Published online: 15 January 2003 RID="*" ID="*"Corresponding author. Fax: +49-511/762-3023, E-mail: Helge.Kreutzmann@ITP.uni-hannover.de     

Quasi-Two-Dimensional Diffusion in Adherent Cells Revealed by Three-Dimensional Single Quantum Dot Tracking

Intracellular diffusion is critical for molecule translocation in cytoplasm and mediates many important cellular processes.Meanwhile,the diffusion dynamics is affected by the heterogeneous cytoplasm.Previous studies on intracellular diffusion are mainly based on two-dimensional(2 D) measurements under the assumption that the three-dimensional(3 D) diffusion is isotropic.However,the real behaviors of 3 D diffusion of molecules in cytoplasm are still unclear.Here,we have built a 3 D single-particle tracking(SPT) microscopy and studied the 3 D diffusion of quantum dots(QDs) in adherent A549 cells.Notably,we found that the intracellular diffusion of QDs is quasi-2 D,with the axial motion being severely confined.Further investigations demonstrated that disrupting the cytoskeleton component or endoplasmic reticulum(ER) does not alter the quasi-2 D diffusion pattern,although ER reduces the diffusion rates and slightly relieves the constraint in the axial diffusion.The preferred quasi-2 D diffusion is quite robust and attributed to the complex cytoarchitectures in the flat adherent cells.With the aid of 3 D SPT method,the quasi-2 D diffusion in cells was revealed,shedding new light on the physical nature of cytoplasm.     

Quantum coherent oscillations between two coupled bose-einstein condensates

The theoretical investigation of quantum coherent atomic oscillations between two coupled Bose-Einstein condensates(BECs) is studied. We apply the inseparable wave function of time-space to describe two trapped BECs in a double-well magnetic trap. According to Thomas-Fermi approximation, dynamical equations of the interwell phase difference and population imbalance are obtained. Using numerical method, coherent atomic tunneling and macroscopic quantum self-trapping(MQST) effect are investigated.     

两耦合玻色-爱因斯坦凝聚体间的量子相干振荡

理论上考察了两耦合玻色-爱因斯坦凝聚体间的相干原子振荡,我们用时空不能完全分离的波函数去描述囚禁在双磁阱中的玻色-爱因斯坦凝聚体,根据托马斯-费米近似,得到两凝聚体的相位差和布局数随时间的演化方程,应用数值计算的方法,考察了相干原子遂穿和宏观量子自囚禁效应.这些研究结果和采用双模时空分离波函数近似法得到的结果进行了比较.     

Matter-wave vortices and solitons in anisotropic optical lattices

Using numerical methods, we construct families of vortical, quadrupole, and fundamental solitons in a two-dimensional (2D) nonlinear-Schrödinger/Gross-Pitaevskii equation which models Bose-Einstein condensates (BECs) or photonic crystals. The equation includes the attractive or repulsive cubic nonlinearity and an anisotropic periodic potential. Two types of anisotropy are considered, accounted for by the difference in the strengths of the 1D sublattices, or by a difference in their periods. The limit case of the quasi-1D optical lattice (OL), when one sublattice is missing, is included too. By means of systematic simulations, we identify stability limits for two species of vortex solitons and quadrupoles, of the rhombus and square types. In the attraction model, rhombic vortices and quadrupoles remain stable up to the limit case of the quasi-1D lattice. In the same model, finite stability limits are found for vortices and quadrupoles of the square type, in terms of the anisotropy parameter. In the repulsion model, rhombic vortices and quadrupoles are stable in large parts of the first finite bandgap (FBG). Another species of partly stable anisotropic states is found in the second FBG, subfundamental dipoles, each squeezed into a single cell of the OL. Square-shaped quadrupoles are completely unstable in the repulsion model, while vortices of the same type are stable only in weakly anisotropic OL potentials.     

Efficient numerical methods for computing ground states and dynamics of dipolar Bose–Einstein condensates

New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose–Einstein condensates (BECs) described by a three-dimensional (3D) Gross–Pitaevskii equation (GPE) with a dipolar interaction potential. Due to the high singularity in the dipolar interaction potential, it brings significant difficulties in mathematical analysis and numerical simulations of dipolar BECs. In this paper, by decoupling the two-body dipolar interaction potential into short-range (or local) and long-range interactions (or repulsive and attractive interactions), the GPE for dipolar BECs is reformulated as a Gross–Pitaevskii–Poisson type system. Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blow-up of the dynamics in different parameter regimes of dipolar BECs. In addition, a backward Euler sine pseudospectral method is presented for computing the ground states and a time-splitting sine pseudospectral method is proposed for computing the dynamics of dipolar BECs. Due to the adoption of new mathematical formulation, our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem. Extensive numerical examples in 3D are reported to demonstrate the efficiency and accuracy of our new numerical methods for computing the ground states and dynamics of dipolar BECs.     

Single-electron spin-dependent transport in split-gate structures containing self-assembled quantum dots

Study of split-gate structures, in which self-assembled InAs quantum dots (QDs) are located near the region of 2D electron gas, has revealed Coulomb oscillations in the dependence of the tunnel current through a limited number of InAs QDs in a channel on the gate voltage, which correspond to the excited states of QDs with opposite spins. The Coulomb oscillations of the current were observed up to a temperature of ～20 K. The Coulomb energy ΔE _C was found to be 12.5 meV, a value corresponding to the theoretical estimates for p states of QDs in our experimental structures.     

Quantum Entanglement of Many Particles in Spinor Bose–Einstein Condensates

We present a theoretical treatment of the proposal for creating maximally entangled states of many particles in spin-1 Bose–Einstein condensates (BECs) by applying a single atom Raman transition [You. L. (2003). Physical Review Letters 90, 030402]. It is shown that the three-mode model suggested by You can be further reduced to an efficient two-mode one by a simple method. We also suggest a scheme for generating the atom-atom continuous-variable entangled states in this system. PACS number: 03.75.Gg, 03.75.Mn, 05.30.JP, 03.75.Hh     

On-chip multiphoton Greenberger–Horne–Zeilinger state based on integrated frequency combs

One of the most important multipartite entangled states, Greenberger–Horne–Zeilinger state (GHZ), serves as a fundamental resource for quantum foundation test, quantum communication and quantum computation. To increase the number of entangled particles, significant experimental efforts should been invested due to the complexity of optical setup and the difficulty in maintaining the coherence condition for high-fidelity GHZ state. Here, we propose an ultra-integrated scalable on-chip GHZ state generation scheme based on frequency combs. By designing several microrings pumped by different lasers, multiple partially overlapped quantum frequency combs are generated to supply as the basis for on-chip polarization-encoded GHZ state with each qubit occupying a certain spectral mode. Both even and odd numbers of GHZ states can be engineered with constant small number of integrated components and easily scaled up on the same chip by only adjusting one of the pump wavelengths. In addition, we give the on-chip design of projection measurement for characterizing GHZ states and show the reconfigurability of the state. Our proposal is rather simple and feasible within the existing fabrication technologies and we believe it will boost the development of multiphoton technologies.     

Production of a chromium Bose–Einstein condensate

The recent achievement of Bose–Einstein condensation of chromium atoms [1] has opened longed-for experimental access to a degenerate quantum gas with long-range and anisotropic interaction. Due to the large magnetic moment of chromium atoms of 6 μ_B, in contrast to other Bose–Einstein condensates (BECs), magnetic dipole-dipole interaction plays an important role in a chromium BEC. Many new physical properties of degenerate gases arising from these magnetic forces have been predicted in the past and can now be studied experimentally. Besides these phenomena, the large dipole moment leads to a breakdown of standard methods for the creation of a chromium BEC. Cooling and trapping methods had to be adapted to the special electronic structure of chromium to reach the regime of quantum degeneracy. Some of them apply generally to gases with large dipolar forces. We present here a detailed discussion of the experimental techniques which are used to create a chromium BEC and allow us to produce pure condensates with up to 10⁵ atoms in an optical dipole trap. We also describe the methods used to determine the trapping parameters.     

Bessel型光晶格中双组分玻色-爱因斯坦凝聚体的基态解

研究了平面Bessel型光晶格(BL)中双组分玻色-爱因斯坦凝聚(BECs)体系的基态解.从描述三维(3D)BECs体系的动力学方程Gross-Pitaevskii方程(GPE)出发,当垂直方向囚禁频率远大于平面上囚禁频率时,得到了描述2D-BECs体系的动力学方程.利用双组分BECs体系中原子之间相互作用与BL强度相互平衡的条件,得到了平面BL光晶格中2D-GPE的一组基态精确解,给出了基态的原子数分布,总原子数和能量与原子之间相互作用强度及BL势的关系.相对于单组分BEC体系,由于不同组分原子相互作用的存在,使得BL光晶格中双组分BECs基态具有更丰富的结构.当不存在不同组分原子之间的相互作用时,模型简化到单组分体系,并给出了相应的基态解,原子数分布和能量. 关键词： Bessel型光晶格 基态解 双组分玻色-爱因斯坦凝聚     

The ground states and pseudospin textures of rotating two-component Bose–Einstein condensates trapped in harmonic plus quartic potential

The ground states of two-component miscible Bose–Einstein condensates(BECs) confined in a rotating annular trap are obtained by using the Thomas–Fermi(TF) approximation method.The ground state density distribution of the condensates experiences a transition from a disc shape to an annulus shape either when the angular frequency increases and the width and the center height of the trap are fixed,or when the width and the center height of the trap increase and the angular frequency is fixed.Meantime the numerical solutions of the ground states of the trapped two-component miscible BECs with the same condition are obtained by using imaginary-time propagation method.They are in good agreement with the solutions obtained by the TF approximation method.The ground states of the trapped two-component immiscible BECs are also given by using the imaginary-time propagation method.Furthermore,by introducing a normalized complex-valued spinor,three kinds of pseudospin textures of the BECs,i.e.,giant skyrmion,coaxial double-annulus skyrmion,and coaxial three-annulus skyrmion,are found.     

Spinor Bose–Einstein condensates

An overview of the physics of spinor and dipolar Bose–Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor–dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed.     

Energy spectrum and entanglement of two tunnel- coupled Bose--Einstein condensates

This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose--Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.     

A computational investigation of topological insulator Bi2Se3 film

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.     

Magnetoquantum de Haas-van Alphen oscillations in spin-split two-dimensional Fermi liquid

Theory of magnetoquantum oscillations with spin-split structure in strongly anisotropic (two-dimensional (2D)) metal is developed in the formalism of level approach. Parametric method for exact calculation of oscillations wave forms and amplitudes, developed earlier for spin degenerate levels is generalized on a 2D electron system with spin-split levels. General results are proved: 1) proportionality relation between magnetization and chemical potential oscillations accounting for spin-split energy levels and magnetic field unperturbed levels (states of reservoir), 2) basic equation for chemical potential oscillations invariant to various models of 2D and 1D energy bands (intersecting or overlapping) and localized states. Equilibrium transfer of carriers between overlapping 2D and 1D bands, characterizing the band structure of organic quasi 2D metals, is considered. Transfer parameter, calculated in this model to be of the order of unity, confirms the fact that the wave form of oscillations in organic metals should be quasisymmetric up to ultralow temperature. Presented theory accounts for spin-split magnetization oscillations at magnetic field directions tilted relative to the anisotropic axis of a metal. Theoretical results are compared with available experimental data on organic quasi-2D metal α-(BEDT-TTF)₂KHg(SNC)₄ explaining the appearance of clear split structure under the kink magnetic field and absence above by the corresponding change in the electron g-factor rather than cyclotron mass. Received 20 December 2000 and Received in final form 13 July 2001     

Stranski–Krastanov growth of InGaN quantum dots emitting in green spectra

Self-assembled InGaN quantum dots (QDs) were grown on GaN templates by metalorganic chemical vapor deposition. 2D–3D growth mode transition through Stranski–Krastanov mode was observed via atomic force microscopy. The critical thickness for In_0.67Ga_0.33N QDs was determined to be four monolayers. The effects of growth temperature, deposition thickness, and V/III ratio on QD formation were examined. The capping of InGaN QDs with GaN was analyzed. Optimized InGaN quantum dots emitted in green spectra at room temperature.     

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.