Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level

We create rapidly rotating Bose-Einstein condensates in the lowest Landau level by spinning up the condensates to rotation rates Omega > 99% of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a consequence, the chemical potential drops below the cyclotron energy 2 variant Planck's over 2pi Omega. While in this mean-field quantum-Hall regime we still observe an ordered vortex lattice, its elastic shear strength is strongly reduced, as evidenced by the observed very low frequency of Tkachenko modes. Furthermore, the gas approaches the quasi-two-dimensional limit. The associated crossover from interacting- to ideal-gas behavior along the rotation axis results in a shift of the axial breathing mode frequency.     

ω Meson photoproduction from deuterium at 3.9 GeV photon energy

Measurements are presented of the cross sections for ω meson photoproduction from deuterium at an average photon energy of 3.9 GeV. The cross section for the coherent process γd → dω is found to be 1.4 ± 0.5 μb and that for the incoherent process γd → npω is 3.3 ± 0.7 μb. The forward differential cross section for γd → dω is estimated to be (dσ/dt)_t=0 = 54 ± 20 μb/GeV². This result indicates that the value of the A₂ exchange amplitude in ω photoproduction from hydrogen is less than that predicted from the measurements of the difference between the total hadron photoproduction cross sections from neutrons and protons. We note that the world data tend to show that the A₂ exchange amplitude is more consistent with zero than with the value needed to explain these differences. Measurements are also presented of the ratio of the coupling constants of the photon to the ? and ω mesons which tend to favour the vector dominance model proposed by Das, Mathur and Okubo with exact SU(3) symmetry at infinite energies.     

Mössbauer spectral studies of the interaction between triphenyltin compounds andCeratocystis ulmi

Triphenyltin compounds have been found to inhibit the growth ofCeratocystis ulmi, the fungal agent of Dutch elm disease. To determine where the tin compounds interacted with the fungus cell, tin Mössbauer spectra of the treated cells, cell walls, and cellular organelles were measured at 80K. The compounds examined included triphenyltin bromide, chloride, hydroxide, and iodide. The spectra of the whole cells were different from the spectra of the solid tin compounds and exhibited two major lines whose parameters were the same for all cells. This suggests that the tin compounds were bound to the cell as the triphenyltin cation. The same spectrum appears with cell-wall fraction, and a weak signal is present in the spectrum of treated cellular fractions. These results suggest that the tin compounds are bound to the cell walls.     

Observations on sound propagation in rapidly rotating Bose-Einstein condensates

Repulsive laser potential pulses applied to vortex lattices of rapidly rotating Bose-Einstein condensates create propagating density waves which we have observed experimentally and modeled computationally to high accuracy. We have observed a rich variety of dynamical phenomena ranging from interference effects and shock-wave formation to anisotropic sound propagation.     

Nonequilibrium effects of anisotropic compression applied to vortex lattices in bose-einstein condensates

We have studied the dynamics of large vortex lattices in a dilute-gas Bose-Einstein condensate. While undisturbed lattices have a regular hexagonal structure, large-amplitude quadrupolar shape oscillations of the condensate are shown to induce a wealth of nonequilibrium lattice dynamics. When exciting an m=-2 mode, we observe shifting of lattice planes, changes of lattice structure, and sheetlike structures in which individual vortices appear to have merged. Excitation of an m=+2 mode dissolves the regular lattice, leading to randomly arranged but still strictly parallel vortex lines.     

Fiber-laser frequency combs with subhertz relative linewidths

We investigate the comb linewidths of self-referenced, fiber-laser-based frequency combs by measuring the heterodyne beat signal between two independent frequency combs that are phase locked to a common cw optical reference. We demonstrate that the optical comb lines can exhibit instrument-limited, subhertz relative linewidths across the comb spectra from 1200 to 1720 nm with a residual integrated optical phase jitter of approximately 1 rad in a 60 mHz to 500 kHz bandwidth. The projected relative pulse timing jitter is approximately 1 fs. This performance approaches that of Ti:sapphire frequency combs.     

Coherent multiheterodyne spectroscopy using stabilized optical frequency combs

The broadband, coherent nature of narrow-linewidth fiber frequency combs is exploited to measure the full complex spectrum of a molecular gas through multiheterodyne spectroscopy. We measure the absorption and phase shift experienced by each of 155 000 individual frequency-comb lines, spaced by 100 MHz and spanning from 1495 to 1620 nm, after passing through hydrogen cyanide gas. The measured phase spectrum agrees with the Kramers-Kronig transformation of the absorption spectrum. This technique can provide a full complex spectrum rapidly, over wide bandwidths, and with hertz-level accuracy.     

Adjoint subspaces in Banach spaces,with applications to ordinary differential subspaces

Summary Given two subspaces A₀ ⊂ A₁ ⊂ W=X ⊕ Y, where X, Y are Banach spaces, we show how to characterize, in terms of generalized boundary conditions, those adjoint pairs A, A* satisfying A₀ ⊂ A ⊂ A₁, A ₁ ^* ⊂ A∗ ⊂ A ₀ ^* ⊂ W⁺=Y* ⊕ X*, where X*, Y* are the conjugate spaces of X, Y, respectively. The characterizations of selfadjoint (normal) subspace extensions of symmetric (formally normal) subspaces appear as special cases when Y=X*. These results are then applied to ordinary differential subspaces in W=L^q(ι) ⊕ L^r(ι), 1≦q, r≦∞, where τ is a real interval, and in W=C( ) ⊕ C( ), where is a compact interval. Entrata in Redazione il 21 febbraio 1977. The work of EarlA. Coddington was supported in part by the National Science Foundation under NSF Grant No. MCS-76-05855.     

Vortex-lattice dynamics in rotating spinor Bose-Einstein condensates

We observe interlaced square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a one-component BEC in an internal atomic state |1, we coherently transfer a fraction of the superfluid to a different state |2. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. The stability of the square structure is proved by its response to applied shear perturbations. An interference technique shows the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.