Collective excitations in circular atomic configurations, and single-photon traps

Correlated excitations in a plane circular configuration of identical atoms with parallel dipole moments are investigated. The collective energy eigenstates, their level shifts and decay rates are computed utilizing a decomposition of the atomic state space into carrier spaces for the irreducible representations of the symmetry group \ZZ_N of the circle. It is shown that the index $p$ of these representations can be used as a quantum number analogously to the orbital angular momentum quantum number $l$ in hydrogen-like systems. Just as the hydrogen s-states are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the atoms in the circle can occupy the central atom only for vanishing \ZZ_N quantum number $p$. If a central atom is present, the $p=0$ state splits into two and shows level-crossing at certain radii; in the regions between these radii, damped Rabi oscillations between two "extreme" $p=0$ configurations occur. The physical mechanisms behind super- and subradiance at a given radius and the divergence of the level shifts at small interatomic distances are discussed. It is shown that, beyond a certain critical number of atoms in the circle, the lifetime of the maximally subradiant state increases exponentially with the number of atoms in the configuration, making the system a natural candidate for a {\it single-photon trap}.Comment: Shortened version, accepted for publication in Phys. Rev.

Topological Extensions of Noether Charge Algebras carried by D-p-branes

We derive the fully extended supersymmetry algebra carried by D-branes in a massless type IIA superspace vacuum. We find that the extended algebra contains not only topological charges that probe the presence of compact spacetime dimensions but also pieces that measure non-trivial configurations of the gauge field on the worldvolume of the brane. Furthermore there are terms that measure the coupling of the non-triviality of the worldvolume regarded as a U(1)-bundle of the gauge field to possible compact spacetime dimensions. In particular, the extended algebra carried by the D-2-brane can contain the charge of a Dirac monopole of the gauge field. In the course of this work we derive a set of generalized Gamma-matrix identities that include the ones presently known for the IIA case. In the first part of the paper we give an introduction to the basic notions of Noether current algebras and charge algebras; furthermore we find a Theorem that describes in a general context how the presence of a gauge field on the worldvolume of an embedded object transforming under the symmetry group on the target space alters the algebra of the Noether charges, which otherwise would be the same as the algebra of the symmetry group. This is a phenomenon recently found by Sorokin and Townsend in the case of the M-5-brane, but here we show that it holds quite generally, and in particular also in the case of D-branes.Comment: 45 pages, some minor misprints corrected, no modifications otherwis

Orthogonality relations for triple modes at dielectric boundary surfaces

We work out the orthogonality relations for the set of Carniglia-Mandel triple modes which provide a set of normal modes for the source-free electromagnetic field in a background consisting of a passive dielectric half-space and the vacuum, respectively. Due to the inherent computational complexity of the problem, an efficient strategy to accomplish this task is desirable, which is presented in the paper. Furthermore, we provide all main steps for the various proofs pertaining to different combinations of triple modes in the orthogonality integral.Comment: 15 page

Determination of the characteristic directions of lossless linear optical elements

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of the optical device. This formulation makes any actual computation of the characteristic directions amenable to pre-implemented numerical routines, thereby facilitating the decomposition of the transfer matrix into equivalent linear retarders and rotators according to the related Poincare equivalence theorem. The method is expected to be useful whenever the inverse problem of reconstruction of the internal state of a transparent medium from optical data obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM