Measuring atomic NOON-states and using them to make precision measurements

A scheme for creating NOON-states of the quasi-momentum of ultra-cold atoms has recently been proposed [New J. Phys. 8, 180 (2006)]. This was achieved by trapping the atoms in an optical lattice in a ring configuration and rotating the potential at a rate equal to half a quantum of angular momentum . In this paper we present a scheme for confirming that a NOON-state has indeed been created. This is achieved by spectroscopically mapping out the anti-crossing between the ground and first excited levels by modulating the rate at which the potential is rotated. Finally we show how the NOON-state can be used to make precision measurements of rotation.Comment: 14 preprint pages, 7 figure

Vortex Dynamics in Anisotropic Traps

We investigate the dynamics of linear vortex lattices in anisotropic traps in two-dimensions and show that the interplay between the rotation and the anisotropy leads to a rich but highly regular dynamics.Comment: 6 pages, 6 figure

Small Numbers of Vortices in Anisotropic Traps

We investigate the appearance of vortices and vortex lattices in two-dimensional, anisotropic and rotating Bose-Einstein condensates. Once the anisotropy reaches a critical value, the positions of the vortex cores in the ground state are no longer given by an Abrikosov lattice geometry, but by a linear arrangement. Using a variational approach, we determine the critical stirring frequency for a single vortex as well as the equilibrium positions of a small number of vortices.Comment: 7 pages, 7 figure

Entanglement enhanced atomic gyroscope

The advent of increasingly precise gyroscopes has played a key role in the technological development of navigation systems. Ring-laser and fibre-optic gyroscopes, for example, are widely used in modern inertial guidance systems and rely on the interference of unentangled photons to measure mechanical rotation. The sensitivity of these devices scales with the number of particles used as $1/ \sqrt{N}$. Here we demonstrate how, by using sources of entangled particles, it is possible to do better and even achieve the ultimate limit allowed by quantum mechanics where the precision scales as 1/N. We propose a gyroscope scheme that uses ultra-cold atoms trapped in an optical ring potential.Comment: 19 pages, 2 figure

Rotating ground states of a one-dimensional spin-polarized gas of fermionic atoms with attractive p-wave interactions on a mesoscopic ring

The major finding of this paper is that a one-dimensional spin-polarized gas comprised of an even number of fermionic atoms interacting via attractive p-wave interactions and confined to a mesoscopic ring has a degenerate pair of ground states that are oppositely rotating. In any realization the gas will thus spontaneously rotate one way or the other in spite of the fact that there is no external rotation or bias fields. Our goal is to show that this counter-intuitive finding is a natural consequence of the combined effects of quantum statistics, ring topology, and exchange interactions.Comment: 4 pages, 1 figure, revtex4; 1 incorrect phrase deleted. Submitted to Phys. Rev. Let

Macroscopic superposition states of ultracold bosons in a double-well potential

We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a new mixed Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.Comment: 15 pages, 8 figures, 1 table. Mini-review prepared for the special issue of Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and Drummon

Changing relationships between multinational companies and their host regions? A case study of Aberdeen and the international oil industry

There has been a revival of interest in recent years in the relationships between multinational corporations (hereafter MNCs) and the host regions in which they operate. The branch plant thesis which generally views inward investment by MNCs in a negative light - as reinforcing power relations between core and peripheral regions - has been challenged, with the suggestion that such developments can play a key role in linking up local economies to important flows of knowledge and information in a global economy. It has also been suggested that MNC branch plant activities are in practice often upgraded over time, leading to the development of important competitive advantage's for host regions. In this paper, such claims are investigated through a case study of the Aberdeen oil region in the north east of Scotland. The changing position of Aberdeen within the oil industry's corporate division of labour is evaluated in terms of the wider theoretical debate