Magnetic Trapping of Cold Bromine Atoms

Magnetic trapping of bromine atoms at temperatures in the milliKelvin regime is demonstrated for the first time. The atoms are produced by photodissociation of Br$_2$ molecules in a molecular beam. The lab-frame velocity of Br atoms is controlled by the wavelength and polarization of the photodissociation laser. Careful selection of the wavelength results in one of the pair of atoms having sufficient velocity to exactly cancel that of the parent molecule, and it remains stationary in the lab frame. A trap is formed at the null point between two opposing neodymium permanent magnets. Dissociation of molecules at the field minimum results in the slowest fraction of photofragments remaining trapped. After the ballistic escape of the fastest atoms, the trapped slow atoms are only lost by elastic collisions with the chamber background gas. The measured loss rate is consistent with estimates of the total cross section for only those collisions transferring sufficient kinetic energy to overcome the trapping potential

Secondary pattern computation of an arbitrarily shaped main reflector

The secondary pattern of a perfectly conducting offset main reflector being illuminated by a point feed at an arbitrary location was studied. The method of analysis is based upon the application of the Fast Fourier Transform (FFT) to the aperture fields obtained using geometrical optics (GO) and geometrical theory of diffraction (GTD). Key features of the reflector surface is completely arbitrary, the incident field from the feed is most general with arbitrary polarization and location, and the edge diffraction is calculated by either UAT or by UTD. Comparison of this technique for an offset parabolic reflector with the Jacobi-Bessel and Fourier-Bessel techniques shows good agreement. Near field, far field, and scan data of a large reflector are presented

Compensation of relector antenna surface distortion using an array feed

The dimensional stability of the surface of a large reflector antenna is important when high gain or low sidelobe performance is desired. If the surface is distorted due to thermal or structural reasons, antenna performance can be improved through the use of an array feed. The design of the array feed and its relation to the surface distortion are examined. The sensitivity of antenna performance to changing surface parameters for fixed feed array geometries is also studied. This allows determination of the limits of usefulness for feed array compensation

Biased EPR entanglement and its application to teleportation

We consider pure continuous variable entanglement with non-equal correlations between orthogonal quadratures. We introduce a simple protocol which equates these correlations and in the process transforms the entanglement onto a state with the minimum allowed number of photons. As an example we show that our protocol transforms, through unitary local operations, a single squeezed beam split on a beam splitter into the same entanglement that is produced when two squeezed beams are mixed orthogonally. We demonstrate that this technique can in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page