Phases of a polar spin-1 Bose gas in a magnetic field

The two Bose–Einstein condensed phases of a polar spin-1 gas at nonzero magnetizations and temperatures are investigated. The Hugenholtz–Pines theorem is generalized to this system. Crossover to a quantum phase transition is also studied. Results are discussed in a mean field approximation.     

The surface of liquid4He at nonzero temperatures

We outline a general approach to microscopic evaluation of the properties of strongly interacting, spatially inhomogeneous Bose systems at finite temperatures. A minimum principle for the Helmholtz free energy is used together with an appropriate trial density matrix to generalize the correlated variational wave function theory that has proven so successful in the treatment of the ground states and elementary excitations of quantum fluids at zero temperature. Euler-Lagrange equations are obtained that determine the optimal structure through the one-and two-body densities and the optimal density fluctuation operators and energies characterizing the elementary excitations. Some results of an application of this correlated density matrix theory to the⁴He liquid-vapor interface are presented, with particular focus on the characterization of resonant vapor modes.     

Nonlinear Schrödinger equation and superfluid hydrodynamics

We show that it is possible to generalize the Gross-Pitaevskii equation describing superfluidity in order to recover the two-fluid model, in the hydrodynamic limit, when the deviations from the equilibrium state are of long wavelength. When short distances are relevant, it is possible to keep trace of the purely quantum, non-hydrodynamic term of the Gross-Pitaevskii equation, so that the Hills-Roberts model, which describes the healing phenomenon, is finally obtained. Received: 19 August 1997 / Revised: 16 October 1997 / Accepted: 6 November 1997     

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.     

Lifetime of metastable magnesium atoms in superfluid helium

The metastable 3s3p³P_{0, 1, 2} states of the magnesium atom immersed into superfluid helium have been investigated. Absorption-fluorescence measurements were carried out to monitor the population of the³P₀,³P₁ and³P₂ level as a function of time. The population of these levels was found to decrease exponentially with a constant of =15±2 ms. This is about three times as long as the vacuum lifetime of the³P₁ level. In the resonant excitation band of the 3s3p³P states to the 3s4s³S state a blueshift of 70 nm compared to the emission and a large broadening were detected. The³P₂ and³P₀ states are not at all metastable any more. Additionally the weak intercombination transition of the³P₁ state to the¹S₀ ground state was investigated by monitoring this emission line as a function of time and of wavelength. The experiments resulted in the same exponential decay time as the excitation measurement. This outcome indicates a rather effective fine structure mixing of the considered Mg states in superfluid helium. Moreover, this raises the question whether common atomic quantum numbers are conserved and the selection rules are still valid.     

Low-frequency stimulated emission and induced absorption in a three-level atom

Investigations of the motion of conventional negative ions (electron bubbles) in He II under pressures above 11 bar have provided the only means of measuring the Landau critical velocity for roton creation,v _L, and for studying supercritical dissipation at higher velocities. Earlier work on roton creation is reviewed and it is pointed out that there is still no generally agreed explanation of the fact that the rotons seem to be emitted from the moving ionin pairs; nor is it known why the matrix element characterising the pair emission process should decrease rapidly with pressure. The possibility of studying these phenomena through use either of the fast ion (whose nature remains unknown), or of selected ions from the large variety of species that can be injected into He II by the recently developed technique of laser ablation, is discussed.     

Optical studies of atoms and ions in superfluid helium using a ccd-camera system

The spectroscopic study ions and atoms immersed into liquid helium can contribute to the understanding of the structure of pointlike defects in helium and their interaction with the superfluid phase as well. Ions and atoms serve as microprobes in the form of so calledbubble orsnowball type defects in the quantum fluid. The optical emission of these structures is recorded. From the optical spectra of previous experiments the influence of the surrounding helium on the electronic configuration of the impurity atoms or ions was examined. In this experiment the light emitted from the defect atoms is observed by a camera. The pictures obtained yield information about the distribution and the motion of the defect particles in the superfluid. As an example the fluorescence light resulting from the recombination of magnesium, barium and thallium ions with excess electrons in superfluid helium was recorded.     

Atoms and ions in superfluid helium

Optical spectra of atomic impurities in liquid helium have been investigated. Comparison is made between the wavelength of the free atomic and ionic lines and those in the liquid helium matrix. Simultaneously, the line width and a possible asymmetry is recorded. Presence and absence of radiative transitions depend on the species of the atom implanted in the quantum fluid. The absence of any optical transitions from states lying as low as 1,8 eV below the ionization limit will be explained in this paper.     

Landau Damping of Collective Modes in a Disc-Shaped Bose-Einstein Condensate

We investigate the Landau damping of collective modes in an anisotropic Bose Einstein condensate （BEC）, Based on divergence-free analytical solutions for the ground state wavefunction of the condensate and all eigenvalues and eigenfunctions for thermal excited quasiparticles, we make a detailed analytical calculation on coupling matrix elements. We evaluate the Landau damping of a quadrupole collective mode in the BEC with a disc-shaped trap and discuss its dependence on temperature and particle number of the system.     

An Experimental Study of In-Situ Phase Fraction in Jet Pump Using Electrical Resistance Tomography Technique

We perform the experiments to investigate in-situ phase fraction in a jet pump using the electrical resistance tomography （ERT） technique. A new jet pump with ERT sensors is designed to measure in-situ phase fraction and flow regime. The study is based on laboratory experiments that are carried out on a 50-mm vertical flow rig for various gas and liquid phase superficial velocities. The different flow patterns of gas liquid in the jet pump and vertical pipe are studied using the ERT technique. The results suggest that the ERT system can be used to successfully produce images of gas-liquid flow patterns with frames rates of 58 fps and the in-situ phase fraction with frame rates of 5 fps can be obtained. The visualizations of a rapid mixing process in the throat of a jet pump obtained in this work provide a reliable basis for theoretical study and optimal design of jet pumps.     

The shear viscosity of a trapped Bose-condensed gas

By obtaining Kubo formula type and using nonequilibrium Green’s functions, we calculate the shear viscosity of a trapped Bose-condensed gas below and above the Bose-Einstein condensation temperature (T_BEC). The contributions of the interactions between condensate and noncondensate atoms and between noncondensate atoms take into account to the viscous relaxation time, by evaluating second order self-energies in Beliaev approximation.     

Vortex structure of Gross-Pitaevskii model

The vortex line of the Gross-Pitaevskii model is studied. The kinetic helicity of the vortex is discussed, and vortex structure is classified by the Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex lines is given by the method of phase singularity theory. The dynamic behavior of the vortex at the critical points is discussed in detail, and three kinds of length approximation relations at the neighborhood of a critical point are given: l ∝ (t − t^∗)^1/2, l ∝ t − t^∗, l = const.     

Hirota method for the nonlinear Schrödinger equation with an arbitrary linear time-dependent potential

In this paper, a Hirota method is developed for applying to the nonlinear Schrödinger equation with an arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensation. The nonlinear Schrödinger equation is decoupled to two equations carefully. With a reasonable assumption the one- and two-soliton solutions are constructed analytically in the presence of an arbitrary time-dependent linear potential.     

Quantum competitions between the effects of the interlayer exchange couplings and the magnetically structural symmetry in a four-layer ferrimagnetic superlattice

The magnon energy spectra, the sublayer magnetization and the quantum fluctuations in a ferrimagnetic superlattice consisting of four different magnetic sublayers are studied by employing the linear spin-wave approach and Green's function technique. The effects of the interlayer exchange couplings and the spin quantum numbers on the sublayer magnetization and the quantum fluctuations of the systems are discussed for three different spin configurations. The roles of quantum competitions among the interlayer exchange couplings and the symmetry of the different spin configurations have been understood. The magnetizations of some sublayers increase monotonously, while those of others can exhibit their maximum, and the quantum fluctuations of the whole superlattice system can show a minimum when one of the antiferromagnetic interlayer exchange couplings increases. This is due to the quantum competition/transmission of effects of the interlayer exchange couplings. When the spin quantum number of sublayers varies, the system goes through from a quantum region of small spin numbers to a classical region of large spin numbers. The quantum fluctuations of the system exhibit a maximum as a function of the spin quantum number of a sublayer, which is related with higher symmetry of the system. It belongs to the type III Shubnikov group of magnetic groups. This magnetically structural symmetry consists of not only the symmetry of space group, but also the symmetry of the direction and strength of spins.     

Study of elementary excitations of superfluid4He in silica aerogels

We have studied the elementary excitations of superfluid⁴He in a silica aerogel at 1.8 K and various filling fractions. The results do not show any departure from bulk⁴He behaviour, suggesting that previously observed anomalies in heat capacity and superfluid fraction data could be the effect of a distribution of He I and He II liquids inside pores of different sizes.This article was processed by the author using the LATEX style filepljour2 from Springer-Verlag.     

Bose-Einstein condensates with vortices in rotating traps

We investigate minimal energy solutions with vortices for an interacting Bose-Einstein condensate in a rotating trap. The atoms are strongly confined along the axis of rotation z, leading to an effective 2D situation in the x-y plane. We first use a simple numerical algorithm converging to local minima of energy. Inspired by the numerical results we present a variational ansatz in the regime where the interaction energy per particle is stronger than the quantum of vibration in the harmonic trap in the x-y plane, the so-called Thomas-Fermi regime. This ansatz allows an easy calculation of the energy of the vortices as function of the rotation frequency of the trap; it gives a physical understanding of the stabilisation of vortices by rotation of the trap and of the spatial arrangement of vortex cores. We also present analytical results concerning the possibility of detecting vortices by a time-of-flight measurement or by interference effects. In the final section we give numerical results for a 3D configuration. Received 16 December 1998 and Received in final form 18 March 1999     

Spectroscopy and dynamics of neutral atoms in superfluid helium

Optical spectra and radiative lifetimes of neutral atoms in superfluid helium have been studied. The absorption and emission spectra of Ag, Mg, Yb, Al, Ga, and In were found to exhibit shifts and broadening typical of atoms residing in microscopic He bubbles, showing that this type of trapping is fairly general. The radiative lifetimes measured for these atoms are close to the free space values, indicating that the surrounding bubble hardly perturbs the electronic orbitals during photo emission. One exception observed in Sr is discussed, where competing autoionization substantially decreases the lifetime of a high excited triplet state. A transient non-bubble state with sharp, free atom like spectra is seen during the first few s after dispersion for many atomic species. The dynamics of this state are unusual, with for example very short radiative lifetimes measured for light alkali atoms.     

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

The binding of alkali atoms to the surfaces of liquid helium and hydrogen

Alkali atoms have been shown previously to have only unstable binding states inside liquid⁴He. We calculate the equilibrium configurations and binding energies of single alkali atoms near the liquid-vapor interface of⁴He and³He. A simple interface model is used to predict the surface deformation due to the presence of the atoms. A more realistic density functional model yields somewhat higher energies in the case of⁴He. For all alkali atoms, we find the surface binding energies to be around 10 to 20 K. A similar analysis with atom-H₂ interactions finds that alkali atoms tend to submerge into liquid H₂, with the exception of Li.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000