We show that binary mixtures of Bose condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of the mixtures within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought 3 He-4 He interpenetrating superfluids in ultralow temperature physics.[S0031-9007 (96)01390-7] PACS numbers: 03.75.Fi, 05.30.JpThe search of Bose condensate in alkali atoms [1-3] has a deep root in ultralow temperature physics. Since the discovery of superfluid 3 He, the searches of the next elemental superfluid have been focusing on spin polarized hydrogen and 3 He-4 He mixture. The former promises another Bose superfluid besides the only known example of 4 He, the latter, the first example of interpenetrating superfluids. The recent discoveries of alkali Bose condensates [1-3] have in essence achieved the goal of the superfluid hydrogen search. Since there are no intrinsic difficulties in loading more than one alkali element and having them cooled in the same trap, it appears highly promising that interpenetrating superfluids may be realized for the first time within the same experimental setting.In this paper, we shall discuss binary mixtures of alkali condensates. Such mixtures may consist of different alkalis such as 87 Rb-23 Na, or different isotopes such as 87 Rb-85 Rb, or different hyperfine states of the same alkali such as the (F 2, M F 2) and (F 1, M F 1) states of 87 Rb. We shall denote the two different alkalis as 1 and 2, and their particle numbers as N 1 and N 2 . Unlike single component systems which are characterized by a single scattering length, alkali binaries are characterized by three scattering lengths a 1 , a 2 , and a 12 , representing interactions between like and unlike alkalis. At present, the scattering lengths between many like alkali atoms are known, whereas those between unlike alkalis have not been measured. As we shall see, this moderate increase in energy scales leads to a proliferation of ground state and vortex structures.In the following, we shall present (a) a simple algorithm for determining the density profiles of the mixtures, (b) the evolution of the ground states and vortex states as a function of N 1 , N 2 . For length reasons, we shall limit ourselves to the vortex states where alkali 1 contains a 2p vortex and alkali 2 is vortex free. Our algorithm, however, can be applied to an arbitrary number of vortices in 1 and 2. As we shall see, the structure of the mixture depends on the ratio of g factors of the two alkalis and the ratios of their interaction parameters. These ratios determine whether alkali 2 when added to an existing cloud of 1 will stay at its exterior or interior. Another general feature of the mixture is that when N 1 ϳ N 2 , it generally contains a large coexisting region of 1 and 2. This is the analog of the long s...
The Bose-Einstein condensates of alkali atomic gases are spinor fields with local "spin-gauge" symmetry. This symmetry is manifested by a superfluid velocity u s (or gauge field) generated by the Berry phase of the spin field. In "static" traps, u s splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency Ω c1 , and can lead to vortex ground states. The inversion symmetry of Ω c1 , however, is not broken in "dynamic" traps. Rotations of the atom cloud can be generated by adiabatic effects without physically rotating the entire trap. The recent discoveries of Bose-Einstein condensation in atomic gases of 87 Rb [1], 7 Li [2], and 23 Na [3] have achieved a long sought goal in atomic physics. They have also provided condensed matter physicists opportunities to study interacting Bose systems at a wide range of densities. The realizations of these condensates are made possible by the invention of a number of special magnetic traps, which trap atoms with hyperfine spin (F = 2) maximally aligned with the local magnetic field B. The reported Bose-Einstein condensations [1] [2][3] are found in these (adiabatic) spin states.An immediate question is whether these alkali condensates differ from the familar 4 He condensate in any fundamental way. Unlike the spinless 4 He atoms, the trapped alkali atoms are in the F = 2 hyperfine spin state. Their condensates are therefore spinors of the form <ψ m (x, t) >= ζ m (x, t)Φ(x, t),
We show that the decay of sinusoidal ripples on crystal surfaces, where mass transport is limited by the attachment and detachment of atoms at the step edges, is remarkably different from the decay behavior that has been reported until now. Unlike the decreasing or at most constant rate of amplitude decay of sinusoidal profiles observed in earlier work, we find that the decay rate increases with decreasing amplitude in this kinetic regime. The rate of shape invariant amplitude relaxation is shown to be inversely proportional to both the square of the wavelength and the current amplitude. We have also carried out numerical simulations of the relaxation of realistic sputter ripples.
AgNO 3 were 4.6 and 0.02 mol L ±1 , respectively. The cleaned planar silicon p±n junction strips were then immediately immersed into the etching solution and treated at 50 C for 60 min. After the etching process, the obtained samples were rinsed copiously in de-ionized water, and dried at room temperature. The thick silver film wrapping the silicon wafer was detached before examination of the sample using SEM. Samples were characterized using a SEM (JEOL JSM6301F). To prepare a TEM specimen, the sample was scraped using a knife, and the scraping was collected and suspended in ethanol; then a drop was placed on a carbon copper grid and examined in a JEOL 2010F microscope equipped with a Gatan GIF 678 system. The electronic properties of the SiNWs are characterized using CSAFM (Molecular Imaging).
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