We study the scattering of the probe light beam by randomly distributed strongly pumped atoms in a pencil-like medium. The density of atoms is assumed to be small (of the order of one atom per light wavelength), therefore the medium formed by the atoms cannot be treated as a continuous one. Such a configuration of atoms can be practically realized in atomic traps. We show that intensity of the scattered light increases with the third power of the probe beam intensity and with the second power of the number of atoms. We also show that under certain conditions the light is scattered into few cones.
We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for a detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives a quite accurate description of the system in the limit of weak interactions.
Localized waves in disordered left-handed materials are studied using a generalized coupled-dipole model. Resonances in an open system consisting of randomly distributed electric and magnetic dipoles are investigated. A new type of long-lived resonance modes localized at the boundary of the system is found. They resemble evanescent waves responsible for a superfocusing phenomenon by a left-handed lens.
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