Claudia Eberlein

Plasma spectroscopy proposed for C60 and C70

The fullerenes C60 (quasispherical though actually icosahedral) and C70 (quasispheroidal) are very like hollow shells (graphiteroles) made from a single hexagonal layer from a graphite crystal. They should support multipolar (l≥1) plasma oscillations, closely related to the plasmons seen in graphite. We estimate their frequencies using the so‐called hydrodynamic model, with (provisionally) just one parameter calibrated on graphite. We predict π plasmons in the range between 6 and 8 eV, and σ plasmons near and above 25 eV. The best, if not the only way to observe them is by electron energy‐loss spectroscopy. Only the dipole (l=1) excitation is allowed optically; in the solid, its frequency should be shifted according to the Lorentz–Lorenz formula. If, improbably, the l=1 π plasmon is observable in solution, its frequency should be unprecedentedly sensitive to the refractive index of the solvent. On C70, the multipoles are split and shifted relative to C60, but only by surprisingly little.

Exact Hydrodynamics of a Trapped Dipolar Bose-Einstein Condensate

We present exact results in the Thomas-Fermi regime for the statics and dynamics of a harmonically trapped Bose-Einstein condensate that has dipole-dipole interactions in addition to the usual s-wave contact interactions. Remarkably, despite the nonlocal and anisotropic nature of the dipolar interactions, the density profile in a general time-dependent harmonic trap is an inverted parabola. The evolution of the condensate radii is governed by local, ordinary differential equations, and as an example we calculate the monopole and quadrupole shape oscillation frequencies.

Exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate (BEC) which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the nonlocal anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s-wave case, but with a different aspect ratio. We explain in detail the mathematical tools necessary to describe dipolar BECs with or without cylindrical symmetry. Various properties such as electrostriction and stability are discussed.

Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions

We calculate the critical rotation frequency at which a vortex state becomes energetically favorable over the vortex-free ground state in a harmonically trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as well as the usual s-wave contact interactions. In the Thomas-Fermi (hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with the dipoles aligned along the axis of symmetry of the trap) tend to have lower critical rotation frequencies than their purely s-wave contact interaction counterparts. The converse is true for dipolar condensates in prolate traps. Quadrupole excitations and center of mass motion are also briefly discussed as possible competing mechanisms to a vortex as means by which superfluids with partially attractive interactions might carry angular momentum.

Casimir-Polder interaction between an atom and a dielectric grating

Ana M. Contreras-Reyes,1 Romain Guérout,2 Paulo A. Maia Neto,1 Diego A. R. Dalvit,3 Astrid Lambrecht,2 and Serge Reynaud2 1Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, CEP 21941-972, Rio de Janeiro, RJ, Brazil 2Laboratoire Kastler Brossel, case 74, CNRS, ENS, UPMC, Campus Jussieu, F-75252 Paris Cedex 05, France 3Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA (Received 1 October 2010; published 22 November 2010)

Cold atoms probe the magnetic field near a wire

A microscopic Ioffe–Pritchard trap is formed using a straight, current-carrying wire, together with suitable auxiliary magnetic fields. By measuring the distribution of cold rubidium atoms held in this trap, we detect a weak magnetic field component ΔBz parallel to the wire. This is produced by the current in the wire and is approximately periodic along the wire with period λ = 230 µm. We have measured this field at distances in the range y = 250–350 µm from the centre of the wire. Over this range we find that the decrease of the field is well described by the Bessel function K1(2πy/λ), as one would expect for the far field of a transversely oscillating current within the wire.

Force on a neutral atom near conducting microstructures

We derive the nonretarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate numerically. For an atom close to a semi-infinite half plane we determine the exact Greens function of the Laplace equation and use it to derive the exact energy shift for an arbitrary position of the atom. These results can be used to estimate the energy shift of an atom close to etched microstructures that protrude from substrates.

Fluctuations of Casimir forces on finite objects. I. Spheres and hemispheres

The mean-square forces that result from the zero-point fluctuations of quantized fields are calculated when acting on spheres and hemispheres of variable sizes. For the Maxwell field the boundary conditions of a perfectly conducting surface are imposed; the scalar field is investigated for Neumann and Dirichlet boundary conditions. The force is averaged over a finite time T; small and large objects are distinguished on the scale of cT. The results for the sphere and the hemisphere are compared with those for a piston that is embedded in an infinite plane. A small hemisphere and a small piston are found to have fluctuations of the same order of magnitude, while on a small sphere the fluctuations are by two orders of magnitude smaller because of correlations of fluctuations on the two sides of the sphere. Large spheres are shown to fit into the picture of large objects being composed of many patches each with the fluctuations impinging as on a large piston.

Quantum electrodynamics near a dielectric half-space

Radiative corrections in systems near imperfectly reflecting boundaries are investigated. As an example, the self-energy of an unbound electron close to a single surface is calculated at one-loop level. The surface is modeled by a nondispersive dielectric half-space of a constant refractive index n. In contrast to previous, perfectly reflecting models, the evanescent modes in the optically thinner medium are taken into account and are found to play a physically very important role. The Feynman propagator of the photon field is determined and given in two alternative representations, which include the evanescent modes either as a separate contribution or through analytic continuation and deformation of the integration path for the normal component of the complex wave vector k. The evaluation of the self-energy diagram encounters a number of problems that are specific to the boundary dependence and to the imperfect reflection at the boundary. These problems and methods for their resolution are discussed in depth.

Quantum electrodynamics of an atom in front of a non–dispersive dielectric half–space

The energy–level shifts and the change in the rate of spontaneous emission are calculated for an atom located at a distanceZ from a dielectric half–space. The dielectric is a non–dispersive and non–absorbing medium characterized by a constant real refractive indexn. The explicit analytic formulae derived are applicable for arbitrary values ofn. All results are analysed in the non-retarded and retarded limits, which apply to the atom being close to or far from the interface, respectively, i.e. toZ being small or large on the scale of a wavelength of a typical atomic transition. For ground-state atoms, the energy–level shift varies as 1/Z3 in the non–retarded regime and as 1/Z4 in the retarded regime, which agrees with the Casimir–Polder result for the limitn→α. For excited–state atoms, the energy–level shifts receive additional contributions that oscillate with the distanceZ from the interface.