We point out that the widely accepted condition g11g22<g122 for phase separation of a two-component Bose-Einstein condensate is insufficient if kinetic energy is taken into account, which competes against the intercomponent interaction and favors pha
se mixing. Here g11, g22, and g12 are the intra- and intercomponent interaction strengths, respectively. Taking a d-dimensional infinitely deep square well potential of width L as an example, a simple scaling analysis shows that if d=1 (d=3), phase separation will be suppressed as Lrightarrow0 (Lrightarrowinfty) whether the condition g11g22<g122 is satisfied or not. In the intermediate case of d=2, the width L is irrelevant but again phase separation can be partially or even completely suppressed even if g11g22<g122. Moreover, the miscibility-immiscibility transition is turned from a first-order one into a second-order one by the kinetic energy. All these results carry over to d-dimensional harmonic potentials, where the harmonic oscillator length {xi}ho plays the role of L. Our finding provides a scenario of controlling the miscibility-immiscibility transition of a two-component condensate by changing the confinement, instead of the conventional approach of changing the values of the gs.
We present the results of 10 micron nulling interferometric observations of 13 Herbig Ae stars using the Magellan I (Baade) and the MMT 6.5 m telescopes. A portion of the observations was completed with the adaptive secondary at the MMT. We have conc
lusively spatially resolved 3 of the 13 stars, HD 100546, AB Aur, and HD 179218, the latter two recently resolved using adaptive optics in combination with nulling interferometry. For the resolved objects we find that the 10 $mu$m emitting regions have a spatial extent of 15-30 AU in diameter. We also have some evidence for resolved emission surrounding an additional 2 stars (V892 Tau and R CrA). For those objects in our study with mid-IR SEDs classifications from Meeus et al. (2001), we find that the Group I objects (those with constant to increasing mid-IR flux) are more likely to be resolved, within our limited sample. This trend is evident in correlations in the inferred disk sizes vs. the sub-millimeter SED slope and disk size vs. fractional infrared luminosity of the systems. We explore the spatial distribution and orientation of the warm dust in the resolved systems and constrain physical models which are consistent with their observational signatures.
We present a family of exact solutions of one-dimensional nonlinear Schrodinger equation, which describe the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential
. Our results show that, under the safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.
