Dissociation and Decay of Ultra-cold Sodium Molecules

The dissociation of ultracold molecules is studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energy shows non-linear dependence on the ramp speed and directly yields the strength of the atom-molecule coupling. In addition, inelastic molecule-molecule and molecule-atom collisions are characterized

Spin textures in slowly rotating Bose-Einstein Condensates

Slowly rotating spin-1 Bose-Einstein condensates are studied through a variational approach based upon lowest Landau level calculus. The author finds that in a gas with ferromagnetic interactions, such as $^{87}$Rb, angular momentum is predominantly carried by clusters of two different types of skyrmion textures in the spin-vector order parameter. Conversely, in a gas with antiferromagnetic interactions, such as $^{23}$Na, angular momentum is carried by $\pi$-disclinations in the nematic order parameter which arises from spin fluctuations. For experimentally relevant parameters, the cores of these $\pi$-disclinations are ferromagnetic, and can be imaged with polarized light.Comment: 14 pages, 12 low resolution bitmapped figures, RevTeX4. High resolution figures available from author. Suplementary movies available from autho

Double-Layer Bose-Einstein Condensates with Large Number of Vortices

In this paper we systematically study the double layer vortex lattice model, which is proposed to illustrate the interplay between the physics of a fast rotating Bose-Einstein condensate and the macroscopic quantum tunnelling. The phase diagram of the system is obtained. We find that under certain conditions the system will exhibit one novel phase transition, which is consequence of competition between inter-layer coherent hopping and inter-layer density-density interaction. In one phase the vortices in one layer coincide with those in the other layer. And in another phase two sets of vortex lattices are staggered, and as a result the quantum tunnelling between two layers is suppressed. To obtain the phase diagram we use two kinds of mean field theories which are quantum Hall mean field and Thomas-Fermi mean field. Two different criteria for the transition taking place are obtained respectively, which reveals some fundamental differences between these two mean field states. The sliding mode excitation is also discussed.Comment: 12 pages, 8 figure

An asymptotic bound for secant varieties of Segre varieties

This paper studies the defectivity of secant varieties of Segre varieties. We prove that there exists an asymptotic lower estimate for the greater non-defective secant variety (without filling the ambient space) of any given Segre variety. In particular, we prove that the ratio between the greater non-defective secant variety of a Segre variety and its expected rank is lower bounded by a value depending just on the number of factors of the Segre variety. Moreover, in the final section, we present some results obtained by explicit computation, proving the non-defectivity of all the secant varieties of Segre varieties of the shape (P^n)^4, with 1 < n < 11, except at most \sigma_199((P^8)^4) and \sigma_357((P^10)^4).Comment: 14 page

Quantum theory of a vortex line in an optical lattice

We investigate the quantum theory of a vortex line in a stack of weakly-coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin modes and the quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.Comment: Minor changes in response to a referee repor

A 5‑year audit of diagnostic gynaecologic laparoscopy under conscious sedation at the University College Hospital, Ibadan

Introduction: Diagnostic laparoscopy affords smaller incisions, shorter recovery time, and fewer complications. In developing countries, access is limited by cost, infrastructural deficit, and expertise. In a bid to reduce cost at our center, conscious sedation for diagnostic laparoscopy was introduced as far back as 1980. We present here a 5‑year audit of our outpatient diagnostic laparoscopy highlighting the various indications, findings, and complications observed. Methodology: A retrospective review of case files of patients who had diagnostic gynecological laparoscopy between 1st January 2011 and 31st December 2015. The retrieved case files had data extracted and analysed using the Statistical Package for Social Sciences version 20 (Chicago IL USA). Data was presented as simple percentages using tables and figures. Results: During the period, 1,329 outpatient gynecological procedures were performed with 207 diagnostic gynecologic laparoscopies (15.6%). Only 187 case notes were retrieved (retrieval rate of 90%). The mean age was 33.04 (±5.2) years, 84.5% (158) had post‑secondary education, and 69.0% (129) were nulliparous. Majority, 131 (70.0%), had laparoscopy and dye test, 26 (14.0%) had laparoscopy alone, and 30 (16.0%) had a combination of laparoscopy, dye test, and hysteroscopy. The commonest indications were secondary infertility (51.9%), primary infertility (24.1%), and chronic pelvic pain (11.2%). Common findings at laparoscopy were pelvic adhesions (53.5%), uterine fibroids (35.1%), and bilateral tubal blockage (30.3%). Normal findings were reported in only 19 patients (10.3%). Conclusion: Diagnostic laparoscopy under conscious sedation is cost‑effective and safe. It has very minimal complications when performed by skilled personnel. It is thus recommended for low resource settings with the view to avail low income patients the opportunity for endoscopic evaluation.Key words: Audit; conscious sedation; diagnostic laparoscopy; low income

Formation of Quantum-Degenerate Sodium Molecules

Ultra-cold sodium molecules were produced from an atomic Bose-Einstein condensate by ramping an applied magnetic field across a Feshbach resonance. More than $10^5$ molecules were generated with a conversion efficiency of $\sim$4%. Using laser light resonant with an atomic transition, the remaining atoms could be selectively removed, preventing fast collisional relaxation of the molecules. Time-of-flight analysis of the pure molecular sample yielded an instantaneous phase-space density greater than 20.Comment: 5 pages, 4 figures (final published version

The Vortex Phase Qubit: Generating Arbitrary, Counter-Rotating, Coherent Superpositions in Bose-Einstein Condensates via Optical Angular Momentum Beams

We propose a scheme for generation of arbitrary coherent superposition of vortex states in Bose-Einstein condensates (BEC) using the orbital angular momentum (OAM) states of light. We devise a scheme to generate coherent superpositions of two counter-rotating OAM states of light using known experimental techniques. We show that a specially designed Raman scheme allows transfer of the optical vortex superposition state onto an initially non-rotating BEC. This creates an arbitrary and coherent superposition of a vortex and anti-vortex pair in the BEC. The ideas presented here could be extended to generate entangled vortex states, design memories for the OAM states of light, and perform other quantum information tasks. Applications to inertial sensing are also discussed.Comment: 4 pages, 4 figures, Revtex4, to be submitted to Phys. Rev. Let

Giant Vortex Lattice Deformations in Rapidly Rotating Bose-Einstein Condensates

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [Engels \emph{et.al.}, Phys. Rev. Lett. {\bf 90}, 170405 (2003)]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.Comment: 5 pages, 6 figures; revised description of core oscillation, new subfigur

Coherent Molecular Optics using Sodium Dimers

Coherent molecular optics is performed using two-photon Bragg scattering. Molecules were produced by sweeping an atomic Bose-Einstein condensate through a Feshbach resonance. The spectral width of the molecular Bragg resonance corresponded to an instantaneous temperature of 20 nK, indicating that atomic coherence was transferred directly to the molecules. An autocorrelating interference technique was used to observe the quadratic spatial dependence of the phase of an expanding molecular cloud. Finally, atoms initially prepared in two momentum states were observed to cross-pair with one another, forming molecules in a third momentum state. This process is analogous to sum-frequency generation in optics