Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions

We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR

Bose-Einstein condensates in strong electric fields -- effective gauge potentials and rotating states

Magnetically-trapped atoms in Bose-Einstein condensates are spin polarized. Since the magnetic field is inhomogeneous, the atoms aquire Berry phases of the Aharonov-Bohm type during adiabatic motion. In the presence of an eletric field there is an additional Aharonov-Casher effect. Taking into account the limitations on the strength of the electric fields due to the polarizability of the atoms, we investigate the extent to which these effects can be used to induce rotation in a Bose-Einstein condensate.Comment: 5 pages, 2 ps figures, RevTe

Vortex nucleation in Bose-Einstein condensates in time-dependent traps

Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. It is found that this theory is able to describe the creation of vortices, but not the crystallization of a vortex lattice. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center.Comment: 22 pages, 7 figures. Changes after referee report: one new figure, new refs. No conclusions altere

Rotational Dynamics of Vortices in Confined Bose-Einstein Condensates

We derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current.Comment: 6 Pages, 6 Figure

Rotating Bose gas with hard-core repulsion in a quasi-2D harmonic trap: vortices in BEC

We consider a gas of N(=6, 10, 15) Bose particles with hard-core repulsion, contained in a quasi-2D harmonic trap and subjected to an overall angular velocity $\Omega$ about the z-axis. Exact diagonalization of the $n\times n$ many-body Hamiltonian matrix in given subspaces of the total (quantized) angular momentum L$_{z}$, with $n\sim 10^{5}$(e.g. for L$_{z}$=N=15, n =240782) was carried out using Davidson's algorithm. The many-body variational ground state wavefunction, as also the corresponding energy and the reduced one-particle density-matrix were calculated. With the usual identification of $\Omega$ as the Lagrange multiplier associated with L$_{z}$ for a rotating system, the $L_{z}-\Omega$ phase diagram (or the stability line) was determined that gave a number of critical angular velocities $\Omega_{{\bf c}i}, i=1,2,3,... ,$ at which the ground state angular momentum and the associated condensate fraction undergo abrupt jumps. A number of (total) angular momentum states were found to be stable at successively higher critical angular velocities $\Omega_{{\bf c}i}, \ i=1,2,3,...$for a given N. For$L_{z}>N$, the condensate was strongly depleted. The critical$\Omega_{{\bf c}i}$values, however, decreased with increasing interaction strength as well as the particle number, and were systematically greater than the non-variational Yrast-state values for the single vortex state with L$_{z}$=N. We have also observed that the condensate fraction for the single vortex state (as also for the higher vortex states) did not change significantly even as the 2-body interaction strength was varied over several$(\sim 4)$ orders of magnitude in the moderately to the weakly interacting regime.Comment: Revtex, 11 pages, 1 table as ps file, 4 figures as ps file

Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate

We use a variational method to investigate the ground-state phase diagram of a small, asymmetric Bose-Einstein condensate with respect to the dimensionless interparticle interaction strength $\gamma$ and the applied external rotation speed $\Omega$. For a given $\gamma$, the transition lines between no-vortex and vortex states are shifted toward higher $\Omega$ relative to those for the symmetric case. We also find a re-entrant behavior, where the number of vortex cores can decrease for large $\Omega$. In addition, stabilizing a vortex in a rotating asymmetric trap requires a minimum interaction strength. For a given asymmetry, the evolution of the variational parameters with increasing $\Omega$ shows two different types of transitions (sharp or continuous), depending on the strength of the interaction. We also investigate transitions to states with higher vorticity; the corresponding angular momentum increases continuously as a function of $\Omega$

Dynamic instability of a rotating Bose-Einstein condensate

We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.Comment: 4 pages, 3 figures, last version including comparison with experiment

A single transcription factor is sufficient to induce and maintain secretory cell architecture

We hypothesized that basic helix–loop–helix (bHLH) MIST1 (BHLHA15) is a “scaling factor” that universally establishes secretory morphology in cells that perform regulated secretion. Here, we show that targeted deletion of MIST1 caused dismantling of the secretory apparatus of diverse exocrine cells. Parietal cells (PCs), whose function is to pump acid into the stomach, normally lack MIST1 and do not perform regulated secretion. Forced expression of MIST1 in PCs caused them to expand their apical cytoplasm, rearrange mitochondrial/lysosome trafficking, and generate large secretory granules. Mist1 induced a cohort of genes regulated by MIST1 in multiple organs but did not affect PC function. MIST1 bound CATATG/CAGCTG E boxes in the first intron of genes that regulate autophagosome/lysosomal degradation, mitochondrial trafficking, and amino acid metabolism. Similar alterations in cell architecture and gene expression were also caused by ectopically inducing MIST1 in vivo in hepatocytes. Thus, MIST1 is a scaling factor necessary and sufficient by itself to induce and maintain secretory cell architecture. Our results indicate that, whereas mature cell types in each organ may have unique developmental origins, cells performing similar physiological functions throughout the body share similar transcription factor-mediated architectural “blueprints.

Stability of rotating states in a weakly-interacting Bose-Einstein condensate

We investigate the lowest state of a rotating, weakly-interacting Bose-Einstein condensate trapped in a harmonic confining potential that is driven by an infinitesimally asymmetric perturbation. Although in an axially-symmetric confining potential the gas has an axially-symmetric single-particle density distribution, we show that in the presence of the small asymmetric perturbation its lowest state is the one given by the mean-field approximation, which is a broken-symmetric state. We also estimate the rate of relaxation of angular momentum when the gas is no longer driven by the asymmetric perturbation and identify two regimes of "slow" and "fast" relaxation. States of certain symmetry are found to be more robust.Comment: 6 pages, RevTe