Bose Gases Near Unitarity

We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e. the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length $a_s<0$), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length $a_{s}^{\ast}<0$. For $a_s<a_{s}^{\ast}$, the density consists of a core of upper branch bosons surrounded by an outer layer of equilibrium phase. The conditions of low three-body recombination requires that the particle number $N<\alpha (T/\omega)^{5/2}$ in a harmonic trap with frequency $\omega$, where $\alpha$ is a constant.Comment: 4 pages, 4 figure

Rapidly Rotating Fermi Gases

We show that the density profile of a Fermi gas in rapidly rotating potential will develop prominent features reflecting the underlying Landau level like energy spectrum. Depending on the aspect ratio of the trap, these features can be a sequence of ellipsoidal volumes or a sequence of quantized steps.Comment: 4 pages, 1 postscript fil

Recent advances in numerical simulation and control of asymmetric flows around slender bodies

The problems of asymmetric flow around slender bodies and its control are formulated using the unsteady, compressible, thin-layer or full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. The problem is numerically simulated for both locally-conical and three-dimensional flows. The numerical applications include studies of the effects of relative incidence, Mach number and Reynolds number on the flow asymmetry. For the control of flow asymmetry, the numerical simulation cover passive and active control methods. For the passive control, the effectiveness of vertical fins placed in the leeward plane of geometric symmetry and side strakes with different orientations is studied. For the active control, the effectiveness of normal and tangential flow injection and surface heating and a combination of these methods is studied

Two-component Bose-Einstein Condensates with Large Number of Vortices

We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe

Phase retrieval by hyperplanes

We show that a scalable frame does phase retrieval if and only if the hyperplanes of its orthogonal complements do phase retrieval. We then show this result fails in general by giving an example of a frame for $\mathbb R^3$ which does phase retrieval but its induced hyperplanes fail phase retrieval. Moreover, we show that such frames always exist in $\mathbb R^d$ for any dimension $d$. We also give an example of a frame in $\mathbb R^3$ which fails phase retrieval but its perps do phase retrieval. We will also see that a family of hyperplanes doing phase retrieval in $\mathbb R^d$ must contain at least $2d-2$ hyperplanes. Finally, we provide an example of six hyperplanes in $\mathbb R^4$ which do phase retrieval

Numerical simulation of steady and unsteady asymmetric vortical flow

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. The unsteady asymmetric flow solution around the circular cone has also been validated using the upwind, flux-vector splitting (FVS) scheme with the thin-layer NS equations and the upwind FDS with the full NS equations. The results are in excellent agreement with each other. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round- and sharp-edged delta winds

Fermion Superfluids of Non-Zero Orbital Angular Momentum near Resonance

We study the pairing of Fermi gases near the scattering resonance of the $\ell\neq 0$ partial wave. Using a model potential which reproduces the actual two-body low energy scattering amplitude, we have obtained an analytic solution of the gap equation. We show that the ground state of $\ell=1$ and $\ell=3$ superfluid are orbital ferromagnets with pairing wavefunctions $Y_{11}$ and $Y_{32}$ respectively. For $\ell=2$, there is a degeneracy between $Y_{22}$ and a "cyclic state". Dipole energy will orient the angular momentum axis. The gap function can be determined by the angular dependence of the momentum distribution of the fermions.Comment: 4 pages, 1 figur

Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases

The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge" symmetry. This symmetry is manifested by a superfluid velocity ${\bf u}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In ``static" traps, ${\bf u}_{s}$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\bf \Omega}_{c1}$, and can lead to {\em vortex ground states}. The inversion symmetry of ${\bf \Omega}_{c1}$, however, is not broken in ``dynamic" traps. Rotations of the atom cloud can be generated by adiabatic effects without physically rotating the entire trap.Comment: Typos in the previous version corrected, thanks to the careful reading of Daniel L. Cox. 13 pages + 2 Figures in uuencode + gzip for

First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures ($0.6<T/T_{c}<1.2$) and for systems with $10^4$ to $10^8$ particles. The second sound modes (which exist only below $T_{c}$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near $T_{c}$ recently observed at JILA in systems with $10^3$ particles match surprisingly well with those of the first and second sound modes of much larger systems.Comment: a shorten version, more discussions are given on the nature of the second sound. A long footnote on the recent work of Zaremba, Griffin, and Nikuni (cond-mat/9705134) is added, the spectrum of the (\ell=1, n_2=0) mode is included in fig.