As discovered by Philip Anderson in 1958, strong disorder can block propagation of waves and lead to the localization of wavelike excitations in space. Anderson localization of light is particularly exciting in view of its possible applications for random lasing or quantum information processing. We show that, surprisingly, Anderson localization of light cannot be achieved in a random three-dimensional ensemble of point scattering centers that is the simplest and widespread model to study the multiple scattering of waves. Localization is recovered if the vector character of light is neglected. This shows that, at least for point scatterers, the polarization of light plays an important role in the Anderson localization problem.

We report direct, time-resolved observations of single-photon superradiance in a highly extended, elliptical sample of cold 87 Rb atoms. The observed rapid decay rate is accompanied by its counterpart, the cooperative Lamb shift. The rate of the strongly directional decay, and the associated shift, scale linearly with the number of atoms, demonstrating the collective nature of the observed quantities.

We discover a transition from extended to localized quasi-modes for light in a gas of immobile two-level atoms in a magnetic field. The transition takes place either upon increasing the number density of atoms in a strong field or upon increasing the field at a high enough density. It has many characteristic features of a disorder-driven (Anderson) transition but is strongly influenced by near-field interactions between atoms and the anisotropy of the atomic medium induced by the magnetic field.The transition from extended to localized eigenstates upon increasing disorder in a quantum or wave system is called after Philip Anderson who was the first to predict it for electrons in disordered solids [1]. More recently, this transition was studied for various types of quantum particles (cold atoms [2], Bose-Einstein condensates [3]) as well as for classical waves (light [4-6], ultrasound [7,8]). In the most common case of time-reversal symmetric systems invariant under spin rotation Anderson transition takes place for a three-dimensional (3D) disorder only, eigenstates of low-dimensional systems being always localized [9,10]. Anderson localization of light may find applications in the design of future quantuminformation devices [11], miniature lasers [12] and solar cells [13]. However, no undisputable experimental observation of optical Anderson transition in 3D exists to date since alternative explanations were proposed for all published reports of it [14][15][16]. Moreover, we have recently shown that the simplest theoretical model in which light is scattered by point scatterers (atoms) does not predict Anderson localization of light at all [17].In the present Letter we show that an external magnetic field may induce a transition between extended and localized states for light in a gas of cold atoms. Magnetic field is an important and unique means of controlling wave propagation in disordered media. On the one hand, it breaks down the time-reversal invariance leading to a suppression of weak localization in electronic [18] and optical [19] systems and to metal-insulator transitions in topological insulators [20]. On the other hand, by profoundly modifying the scattering properties of individual scatterers the magnetic field can produce an enhancement of the coherent backscattering peak for light scattered by atoms with a degenerate ground state [21,22]. Our work adds a new element in the mosaic of magnetic-field-induced phenomena in disordered systems by demonstrating that the removal of degeneracy of the excited atomic state due to the Zeeman effect and the resulting reduction of the strength of resonant dipole-dipole * Sergey. We consider an ensemble of N 1 identical two-level atoms at random position {r i } inside a spherical volume V of radius R. The resonant frequency ω 0 of atoms defines the natural length scale 1/k 0 = c/ω 0 , where c is the vacuum speed of light. The ground state |g i of an isolated atom i is nondegenerate with the total angular momentum J g = 0, whereas the excited states |e i is three-fo...

Based on the developed quantum microscopic theory, the interaction of weak electromagnetic radiation with dense ultracold atomic clouds is described in detail. The differential and total cooperative scattering cross sections are calculated for monochromatic radiation as particular examples of application of the general theory. The angular, spectral, and polarization properties of scattered light are determined. The dependence of these quantities on the sample size and concentration of atoms is studied and the influence of collective effects is analyzed.

No abstract