Rotating spin-1 bose clusters

We propose a simple scheme for generating rotating atomic clusters in an optical lattice which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increase, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum L(*) substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect "fermionization" of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reveals the quantum Hall and spin structure of a single cluster.     

Quantum hall states and boson triplet condensate for rotating spin-1 bosons

We propose and analyze two series of clustered quantum Hall states for rotating systems of spin-1 bosons. The first series [labeled SU(4)(k)] includes the exact ground states of a model Hamiltonian at large angular momentum L, and also for N=3k particles at L=N. The latter is a spin-singlet boson-triplet condensate. The second series, labeled SO(5)(k), includes exact ground states at large L for different parameter values.     

Coherent decay of positronium bose condensate

The rate of self-stimulated emission of photon pairs by pseudoscalar particles from Bose condensate is calculated. Growing with density, this rate exceeds the density-independent rate of spontaneous two-photon decay at plausible density values of positronium gas, thus opening, in principle, the way to the annihilation gamma ray laser realization.     

Optimum ground states for spin-3/2 chains

We present a set of optimum ground states for a large class of spin-3/2 chains. Such global ground states are simultaneously ground states of the local Hamiltonian, i.e. the nearest neighbour interaction in the present case. They are constructed in the form of a matrix product. We find three types of phases, namely a weak antiferromagnet, a weak ferromagnet, and a dimerized antiferromagnet. The main physical properties of these phases are calculated exactly by using a transfer matrix technique, in particular magnetization and two spin correlations. Depending on the model parameters, they show a surprisingly rich structure.     

Spinor dynamics in an antiferromagnetic spin-1 condensate

We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts anharmonic oscillations near a critical magnetic field. Measurements of the magnetic phase diagram agree with predictions made in the approximation of a single spatial mode. The oscillation period yields the best measurement to date of the sodium spin-dependent interaction coefficient, determining that the difference between the sodium spin-dependent s-wave scattering lengths a(f=2) - a(f=0) is 2.47+/-0.27 Bohr radii.     

Exact ground states for two new spin-1 quantum chains, new features of matrix product states

We use the matrix product formalism to find exact ground states of two new spin-1 quantum chains with nearest neighbor interactions. One of the models, model I, describes a one-parameter family of quantum chains for which the ground state can be found exactly. In certain limit of the parameter, the Hamiltonian turns into the interesting case . The other model which we label as model II, corresponds to a family of solvable three-state vertex models on square lattices. The ground state of this model is highly degenerate and the matrix product states is a generating state of such degenerate states. The simple structure of the matrix product state allows us to determine the properties of degenerate states which are otherwise difficult to determine. For both models we find exact expressions for correlation functions.     

Macroscopic quantum tunneling of a bose condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.     

Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

We study a class of two-dimensional spin-1/2 Heisenberg antiferromagnets, introduced by Klein [1], in which the nearest-neighbor term is supplemented by next-nearest-neighbor pair and four-body interactions, producing additional frustration. For certain lattices, including e.g. the hexagonal lattice, we prove that any finite subset which admits a dimer covering has a ground state space spanned by valence bond states, each of which consists only of nearest-neighbor (dimer) singlet pairs. We also establish linear independence of these valence bond states. The possible relevance to resonating-valence-bond theories of high-temperature superconductors is briefly discussed. In particular, our results apply both to regular subsets of the lattice and to subsets with static holes.Work supported in part by N.S.F. Postdoctoral Research FellowshipsWork supported by N.S.F. Grant No. DMR-83-18051     

Geometric phase for degenerate states of spin-1 and spin-1/2 pair

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.      

Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube

We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i)?for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii)?for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii)?between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.     

Distribution of spectral widths and preponderance of spin-0 ground states in nuclei

We use a single j-shell model with random two-body interactions to derive closed expressions for the distribution of and the correlations between spectral widths of different spins. This task is facilitated by introducing two-body operators whose squared spectral widths sum up to the squared spectral width of the random Hamiltonian. The spin-0 width is characterized by a relatively large average value and small fluctuations, while the width of maximum spin has the largest average and the largest fluctuations. The approximate proportionality between widths and spectral radii explains the preponderance of spin-0 ground states.     

Dynamical instability and domain formation in a spin-1 Bose-Einstein condensate

We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.     

Large-scale coherence of the bose condensate of spatially indirect excitons

The Bose condensation of spatially indirect (dipolar) excitons in a wide single quantum well in an electric field transverse to the heterolayers is analyzed. Voltage is applied between a metallic film on the surface (Schottky gate) and a conducting electron layer inside a heterostructure (integrated electrode). The excitation of dipolar excitons and observation of their luminescence are performed through circle windows in a metallic mask 5 μm in diameter. Excitons are collected in a ring lateral trap, which is formed along the window perimeter owing to the strongly inhomogeneous electric field. When the critical condensation conditions in pump and temperature are reached, a narrow line of dipolar excitons corresponding to the exciton condensate appears stepwise in the luminescence spectrum. Under these conditions, a spatially periodic structure of equidistant luminescence spots appears in the luminescence pattern that is observed through a window with a resolution of about 1 μm and is selected by means of an interference filter. An in situ optical Fourier transform of spatially periodic structures from the real space to the k space is derived. The resulting Fourier transforms reproducing the pattern of the luminescence intensity distribution in the far field exhibit the result of the destructive and constructive interference, as well as the fact that the luminescence is directed along the normal to the heterolayers. These results are consequences of the large-scale coherence of the condensed exciton state in the ring lateral trap. Direct measurements of double-beam interference from pairs of luminescence spots in the ring show that the spatial coherence length is no less than 4 μm. Such a large scale means that the experimentally observed periodic luminescence structures are described by a common wavefunction under the condition of the Bose condensation of dipolar excitons.     

Dynamics of bright soliton in a spin–orbit coupled spin-1 Bose–Einstein condensate

We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton's spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton's spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.     

自旋轨道耦合的23Na自旋-1玻色-爱因斯坦凝聚体中的涡旋斑图的研究

利用阻尼映射Gross-Pitaevkii方程, 研究了二维体系中自旋轨道耦合的 ²³Na自旋-1 玻色-爱因斯坦凝聚体中的涡旋斑图, 探索自旋轨道耦合强度对涡旋斑图的影响. 研究发现, 较弱的自旋轨道耦合就可以完全破坏不考虑自旋轨道耦合情况下出现的周期性涡旋晶格; 在自旋轨道耦合较强的情况下, 各自旋态的涡旋易形成涡旋组, 它们绕凝聚体中心形成花瓣状涡旋斑图. 关键词： 玻色-爱因斯坦凝聚体 自旋 涡旋     

Production of a bose einstein condensate of metastable helium atoms

We recently observed a Bose-Einstein condensate in a dilute gas of ⁴He in the 2³S₁ metastable state. In this article, we describe the successive experimental steps which led to the Bose-Einstein transition at 4.7 μK: loading of a large number of atoms in a MOT, efficient transfer into a magnetic Ioffé-Pritchard trap, and optimization of the evaporative cooling ramp. Quantitative measurements are also given for the rates of elastic and inelastic collisions, both above and below the transition. Received 15 October 2001     

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.     

Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.