Vacancies in Solid 4He and Bose Einstein Condensation

We find that a finite concentration of vacancies induces Bose Einstein condensation (BEC) of the atoms in solid ⁴ He at density close to the T=0 K melting where vacancies are delocalized. No BEC is present in the perfect crystal and in the defected solid at higher densities. These results are based on variational Monte Carlo method with shadow wave function which allows for relaxation and delocalization of vacancies. Extension of the theory at finite temperature leads to several possibilities. Depending on presence or not of ground state vacancies and on parameters like energy of formation and effective mass of a vacancy one can have a normal transition with BEC at low temperature or an inverted transition with BEC at high T. ⁴ He on graphite appears to be a favorable candidate for a state with BEC and spatial order.     

Bose-Einstein Condensation Measurements and Superflow in Condensed Helium

We review the formulation and measurement of Bose-Einstein condensation (BEC) in liquid and solid helium. BEC is defined for a Bose gas and subsequently for interacting systems via the one-body density matrix (OBDM) valid for both uniform and non-uniform systems. The connection between the phase coherence created by BEC and superflow is made. Recent measurements show that the condensate fraction in liquid ⁴He drops from 7.25±0.75 % at saturated vapor pressure (p≈0) to 2.8±0.2 % at pressure p=24 bars near the solidification pressure (p=25.3 bar). Extrapolation to solid densities suggests a condensate fraction in the solid of 1 % or less, assuming a frozen liquid structure such as an amorphous solid. Measurements in the crystalline solid have not been able to detect a condensate with an upper limit set at n ₀≤0.3 %. Opportunities to observe BEC directly in liquid ⁴He confined in porous media, where BEC is localized to patches by disorder, and in amorphous solid helium is discussed.     

Localization of Bose–Einstein Condensation by Disorder

Recent experiments suggest that Bose–Einstein condensation (BEC) in liquid⁴ can be localized when the liquid is confined in porous media. We demonstrate in a simple model of hard core bosons using Monte Carlo that the condensate can be separated into two parts. The two regions of condensate are separated by a region of uncondensed fluid that forms in response to a local attractive external potential. The aim is to illustrate that separated condensates, and therefore localized BEC, can be created in porous media.     

Curved beam elements to model noncircular coil shapes for tokamak reactor

The detailed stress analysis of the toroidal field superconducting coil is needed to ensure its structural integrity, which includes conductor breakage, insulation breakage, sliding between two turns, or support structure failure. Such detailed-analysis requires that each of the superconducting coil turns be modelled separately. In this paper, a curved beam finite element,¹³ having constant radius of curvature, is considered to model a turn of a noncircular toroidal field coil. Four different coil shapes subjected to electromagnetic body forces due to toroidal magnetic fields are analysed to assess the finite element models: circular, elliptic, Princeton-D⁸ and compound shape⁹. The comparison of analytical and finite element analysis results for resultant forces, tensions and displacements suggest that the proposed approach may be extended to the detailed stress analysis of the noncircular toroidal field superconducting coil.     

Splitting of a Quadruply Quantized Vortex in the Rb Bose-Einstein Condensate

We observed the sudden deformation of a quadruply quantized vortex into a linear shape in a ⁸⁷Rb (F=2,m _F =2) Bose-Einstein condensate (BEC). Multiply quantized vortex is predicted to split into singly quantized vortices and the observed deformation is considered to be the onset of the splitting. The displacement of the vortex with respect to the center of the BEC would induce the observed splitting. Our theoretical simulation qualitatively supports these arguments.     

Quantum Degenerate Fermi Gases of Ytterbium Atoms

We performed evaporative cooling for dilute gases of ytterbium (Yb) isotopes in a crossed optical dipole trap and successfully cooled two fermionic and two bosonic species down to quantum degenerate regime, following the previous realization of Bose-Einstein condensation (BEC) in ¹⁷⁴Yb. The elastic collision rate of fermionic ¹⁷³Yb atoms with 6 spin components was found to be large enough to carry out efficient evaporation, which enables us to cool the atoms down to 0.6 T _F , where T _F is the Fermi temperature. In this regime, a plunge of evaporation efficiency was observed as an effect of the Fermi degeneracy. The other fermionic isotope ¹⁷¹Yb was cooled down to the temperature below T _F by sympathetic cooling with bosonic ¹⁷⁴Yb atoms. The sympathetic cooling technique has also been applied to ¹⁷⁴Yb-¹⁷⁶Yb Bose-Bose mixture. We have observed almost pure BEC of ¹⁷⁴Yb and the bimodal distribution of ¹⁷⁶Yb, showing the formation of BEC-BEC mixture. Moreover, we performed evaporative cooling of ¹⁷⁰Yb atoms and realized the BEC.     

Aspect Ratio Analysis for Ground States of Bosons in Anisotropic Traps

Characteristics of the initial condensate in the recent experiment on Bose-Einstein condensation (BEC) of ⁸⁷Rb atoms in an anisotropic magnetic trap are discussed. Given the aspect ratio R, the quality of BEC is estimated. A simple analytical ansatz for the initial condensate wave function is proposed as a function of the aspect ratio which, in contrast to the Baym-Pethick trial wave function, can be used for any interaction strength, reproduces both the weak and the strong interaction limits, and which is in better agreement with numerical results than the latter.     

Fluctuations and BEC at the Free Surface of 4He

There is some theoretical evidence that full Bose–Einstein condensation (BEC) is achieved at the free surface of superfluid ⁴ He where the density is small. We present new variational results of the BEC and of the density fluctuation spectrum in the surface region of a slab of ⁴ He. We use both a standard wave function (wf) with bulk correlations and one body shape terms and a novel shadow wave function with a glue term (G-SWF). This last one describes the self- binding of ⁴ He only via interparticle correlations. In both cases we find that BEC increases from the bulk like value well inside the slab to a much larger value in the surface region but a striking different behavior is found in the low density region. With a standard wf the BEC reaches essentially 100% in the surface region. With the G-SWF the condensate only increases up to about 51%. Further out of the surface the condensate decreases and correspondingly there is an enhanced population of small momentum states. This different behavior is correlated with the presence in the G-SWF of enhanced density fluctuations in the surface region due to the zero point motion of ripplons. This enhancement is absent in the case of a standard wf.     

Bose-Einstein Condensation in Liquid 4He in Vycor

We present neutron scattering measurements of Bose-Einstein condensation (BEC) in liquid ⁴He confined in Vycor. The data show clear evidence of a condensate in Vycor with a condensate fraction comparable to that of bulk superfluid ⁴He, approximately 7.5% at low temperature and SVP. The temperature dependence of n₀(T) is also similar to that in the bulk with critical temperature for BEC, T_BEC, in the range 1.80BEC<2.05 K. The data are not accurate enough to show whether T_BEC for Vycor is the same or greater than the depressed critical temperature for superfluidity, T_c=1.95 K.     

The Quest for Bose-Einstein Condensation in Solid 4He

Ever since the seminal torsional oscillator (TO) measurements of Kim and Chan which suggested the existence of a phase transition in solid ⁴He, from normal to a ??supersolid?? state below a critical temperature T _c = 200 mK, there has been an unprecedented amount of excitement and research activity aimed at better understanding this phase. Despite much work, this remarkable phase has yet to be independently confirmed by conventional scattering techniques, such as neutron scattering. We have carried out a series of neutron scattering measurements, which we here review, aimed at observing Bose-Einstein condensation (BEC) in solid ⁴He at temperatures below T _c . In bulk liquid ⁴He, the appearance of BEC below T _?? signals the onset of superfluidity. The observation of a condensate fraction in the solid would provide an unambiguous confirmation for ??supersolidity??. Although, our measurements have not yet revealed a non-zero condensate fraction or algebraic off diagonal long-range order n ₀ in solid ⁴He down to 65 mK, i.e. n ₀=(0±0.3)%, our search for BEC and its corollaries continues with improved instrumentation.     

Toroidal solitons in magnetic oxides,Bose-Einstein condensates,and other media

We consider toroidal soliton solutions in a number of nonlinear models of field theory (Skyrme, Faddeev, and Higgs models). Such models are used in various areas of solid-state chemistry and physics, chemical physics, astrophysics, and plasma chemistry and physics. The stability of toroidal solitons is shown to have a topological nature. We examine different methods of generating a nonlinear contribution to the Lagrangian in order to insure stability of the torus to collapse. Using the Faddeev and Skyrme models, we analyze the toroidal ordering in Bose-Einstein condensates of ²³Na, ³⁹K, and ⁸⁷Rb alkali-metal atoms, the toroidal structures recently found in the magnetic oxides BiFeO₃ and GaFeO₃, and potential applications of such structures in spintronics. In addition, we address several critical issues in the chemistry and physics of solitons with high topological charges.     

A double-focusing toroidal mass spectrograph for energetic plasmas: I. First-order theory

A conceptual design for a new type of ion mass spectrograph is presented that is particularly suited for measuring energetic (1 eV to 50 keV/charge) anisotropic space plasmas. The ion optics consist of two toroidal electrostatic analyzers followed by a combined toroidal electric-magnetic sector field. The resultant Mattauch-Herzog type configuration exhibits double-focusing properties for all masses along an oblique line exterior to the magnetic field. Although the focusing properties vary with ion energy, particular field geometries exist which minimize this energy dependence. As a result, good mass resolution and high sensitivity can be maintained over a wide energy range. Mass resolution is adequate to resolve mass/charge values (1, 2, 4, 8, 16) at all energies and can be increased to > 20 in specialized low-energy ( < 5 keV) modes. The spectrographic mass imaging range is > 16 amu at energies above 10 keV. The toroidal geometry focuses in elevation direction, thus minimizing overall instrument and detector sizes while providing limited angular resolution in that direction. Large beam acceptances result in very high overall instrument sensitivity (geometric factor ∼ 10⁻² cm² sr keV).     

Dependence of energy confinement time on toroidal magnetic field in the TUMAN-3M tokamak

The influence of toroidal magnetic field on the energy confinement time ??_E in the ohmic H-mode has been studied in the TUMAN-3M tokamak with low magnetic field. The experiments were performed at a toroidal magnetic field of B _T = 0.68?1.0 T, which is about twice as large as that (0.25?C0.5 T) studied in analogous experiments on the NSTX and MAST spherical tokamaks. The results are indicative of a strong dependence of the energy confinement time on toroidal magnetic field: ??_E ?? B _T ^0.75?C0.8 . This scaling is much stronger than that projected for the ITER (??_{E_IPB98} ?? B _T ^0.15 ), while being somewhat weaker than the scalings observed on the NSTX and MAST devices. The stronger (as compared to the ITER scaling) dependence of ??_E on B _T observed in these experiments should be taken into account in designing thermonuclear facilities with small aspect ratios and toroidal magnetic fields??in particular, fusion neutron sources.     

Ugtracold Alkali Atoms in Optical Lattices: A New Type of Quantum Crystals?

Similarities between alkali gases in optical lattices with non-integer occupation of the lattice sites and quantum crystals are explored. The analogy with the vacancy liquid provides an agternative explanation to the Mott transition for the recent experiment on the phase transition in the lattice. The vacancy liquid can undergo BEC with T _c within experimental reach. Direct and vacancy-assisted mechanisms of the band motion for hyperfine impurities are discussed. The presence of vacancies can resugt in the spatial decomposition of the system into pure hyperfine components. Below BEC for the vacancies, the impurity component resembles ³He in ³He-Hell mixtures.     

Bose-Einstein Condensation and Superfluidity of Strongly Correlated Bose Fluid in a Random Potential

No Heading It was recently observed that liquid ⁴He confined in porous glass lost its superfluidity at high pressures and very low temperatures, causing the quantum phase transition by the strong correlation. Motivated by this experiment, we study the behavior of a strongly correlated Bose fluid in a disordered environment, such as the Bose-Einstein condensate (BEC) and superfluid critical temperatures, by using a model of 3-dimensional Bose fluid in a random potential. For the perturbation of the repulsive interaction between particles, we introduced two-loop renormalized self energy by the self-consistent calculation, which is effective near the BEC critical temperature. Calculating the second order perturbation with respect to the random potential, we found that the BEC disappears at high densities, which is qualitatively consistent with the experimental results.PACS numbers: 67.40 –w, 05.30 Jp, 64.60 Cn     

Generalized Bose–Einstein Condensation in Superconductivity

Unification of the BCS and the Bose–Einstein condensation (BEC) theories is surveyed via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron–phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of T _c (in units of the Fermi temperature T _F ) of 0.01–0.05 empirically reported in the so-called “exotic” superconductors of the Uemura plot, including cuprates, in contrast to the low values of T _c /T _F ≤10⁻³ roughly reproduced by BCS theory for conventional (mostly elemental) superconductors.     

Superfluidity and Vortex Lattice Formation in Quasi Two-Dimensional Exciton System

Bose-Einstein condensation(BEC) and superfluidity of excitons in type-II quantum wells are studied theoretically. As a typical example, we consider GaAs/AlAs quantum wells with each layer thickness L less than 37Å. First, we investigate the interaction between excitons, thus finding it repulsive for L less than about 15Å, which shows the possibility of BEC. Secondly, we study the stationary pattern of the phase of the BEC order parameter under the external current J. The interaction between excitons and the weak laser light violates conservation of number of excitons and fixes that phase. There appears a vortex lattice with net supercurrent when J is larger than a critical value. The experimental observation of this critical current will give an evidence that BEC and superfluidity occur in exciton system.     

Degree of Indistinguishability,Quantum Coherence,and Bose-Einstein Condensation

Thee concept of indistinguishability is the key element in quantum statistics. But, are particles really either indistinguishable or distinguishable? Could there be a grey area? Most works begin with the premise that all the particles, for example, in a quantum gas, are indistinguishable. Can we vary the degree of distinguishability in some controlled, continuous manner and see how it affects the behavior of the quantum gas, such as the Bose-Einstein condensation (BEC)? We have found a complex parameter with a definite phase that does just that. In a gedanken experiment, we consider two boson gases from two independent sourses A and B. The spins of bosons from A lie at an angle θ with the spins of bosons from B. Let them mix thoroughly in a mixing chamber. As θ is changed from zero, the mixed gas of bosons would divide into two distinct species that undergo BEC individually in two successive stages as the temperature is lowered. At each of these stages is a coexistence-region which consists of a mixture of two thermodynamic phases. These two phases usually referred to as the condensed phase (composed purely of particles of p=0, i.e., the BEC) and the normal phase with p>0 can be likened to the liquid phase and the vapor phase of an ordinary liquid at the liquid-vapor phase transition. The experimental ways to observe the BEC in the two different stages of temperature will be thoroughly discussed.     

Prospects for Bose-Einstein condensation in atomic hydrogen and other gases

Current experimental efforts to observe Bose-Einstein condensation in the laboratory are reviewed. New experiments in spin-polarized hydrogen at high density or very low temperatures offer promise of achieving this goal. The possibility of BEC in other elements, H₂,⁴He, and cesium are discussed.     

Current comparators with superconducting shields

In this paper it is shown that the iron cores of conventionál current comparators may be replaced by superconducting shields. Their function is to transmit the magnetic field of the exciting ratio windings regardless of their position and shape to a detector winding. A toroidal shield system with two modifications - a nested one and a helical one - has been combined with a SQUID to build up current comparators for dc and ac applications. The smallest dc error was found to be 5 × 10^?10. Finally a practical example is given of the application of high precision cryogenic current comparators.