A Bose-Einstein condensate in a random potential

An optical speckle potential is used to investigate the static and dynamic properties of a Bose-Einstein condensate in the presence of disorder. For strong disorder the condensate is localized in the deep wells of the potential. With smaller levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. Uncorrelated frequency shifts of the two modes are measured for a weak disorder and are explained using a sum-rules approach and by the numerical solution of the Gross-Pitaevskii equation

Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide

We investigate the one-dimensional expansion of a Bose-Einstein condensate in an optical guide in the presence of a random potential created with optical speckles. With the speckle the expansion of the condensate is strongly inhibited. A detailed investigation has been carried out varying the experimental conditions and checking the expansion when a single optical defect is present. The experimental results are in good agreement with numerical calculations based on the Gross-Pitaevskii equation.Comment: 5 pages, 5 figure

Theory for the photon statistics of random lasers

A theory for the photon statistics of a random laser is presented. Noise is described by Langevin operators, where both fluctuations of the electromagnetic field and of the medium are included. The theory is valid for all lasers with small outcoupling when the laser cavity is large compared to the wavelength of the radiation. The theory is applied to a chaotic laser cavity with a small opening. It is known that a large number of modes can be above threshold simultaneously in such a cavity. It is shown the amount of fluctuations is increased compared to the Poissonian value by an amount that depends on that number

Distributed leadership, trust and online communities

This paper analyses the role of distributed leadership and trust in online communities. The team-based informal ethos of online collaboration requires a different kind of leadership from that in formal positional hierarchies. Such leadership may be more flexible and sophisticated, capable of encompassing ambiguity and rapid change. Online leaders need to be partially invisible, delegating power and distributing tasks. Yet, simultaneously, online communities are facilitated by the high visibility and subtle control of expert leaders. This paradox: that leaders need to be both highly visible and invisible as appropriate, was derived from prior research and tested in the analysis of online community discussions using a pattern-matching process. It is argued that both leader visibility and invisibility are important for the facilitation of trusting collaboration via distributed leadership. Advanced leadership responses to complex situations in online communities foster positive group interaction and decision-making, facilitated through active distribution of specific tasks

Time Dependent Theory for Random Lasers

A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate $P_{r}^{c}$ exists for the appearance of the lasing peaks. The number of lasing modes increase with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length $\xi$ and average mode length $L_m$.Comment: 8 pages. Send to PR

Decay Rate Distributions of Disordered Slabs and Application to Random Lasers

We compute the distribution of the decay rates (also referred to as residues) of the eigenstates of a disordered slab from a numerical model. From the results of the numerical simulations, we are able to find simple analytical formulae that describe those results well. This is possible for samples both in the diffusive and in the localised regime. As example of a possible application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure

Smoothing effect and delocalization of interacting Bose-Einstein condensates in random potentials

We theoretically investigate the physics of interacting Bose-Einstein condensates at equilibrium in a weak (possibly random) potential. We develop a perturbation approach to derive the condensate wavefunction for an amplitude of the potential smaller than the chemical potential of the condensate and for an arbitrary spatial variation scale of the potential. Applying this theory to disordered potentials, we find in particular that, if the healing length is smaller than the correlation length of the disorder, the condensate assumes a delocalized Thomas-Fermi profile. In the opposite situation where the correlation length is smaller than the healing length, we show that the random potential can be significantly smoothed and, in the meanfield regime, the condensate wavefunction can remain delocalized, even for very small correlation lengths of the disorder.Comment: The word "screening" has been changed to "smoothing" to avoid confusions with other effects discussed in the literature. This does not affect the content of paper, nor the results, nor the physical discussio

Determination of the diffusion constant using phase-sensitive measurements

We apply a pulsed-light interferometer to measure both the intensity and the phase of light that is transmitted through a strongly scattering disordered material. From a single set of measurements we obtain the time-resolved intensity, frequency correlations and statistical phase information simultaneously. We compare several independent techniques of measuring the diffusion constant for diffuse propagation of light. By comparing these independent measurements, we obtain experimental proof of the consistency of the diffusion model and corroborate phase statistics theory.Comment: 9 pages, 8 figures, submitted to Phys. Rev.

Time-resolved broadband analysis of slow-light propagation and superluminal transmission of electromagnetic waves in three-dimensional photonic crystals

A time-resolved analysis of the amplitude and phase of THz pulses propagating through three-dimensional photonic crystals is presented. Single-cycle pulses of THz radiation allow measurements over a wide frequency range, spanning more than an octave below, at and above the bandgap of strongly dispersive photonic crystals. Transmission data provide evidence for slow group velocities at the photonic band edges and for superluminal transmission at frequencies in the gap. Our experimental results are in good agreement with finite-difference-time-domain simulations.Comment: 7 pages, 11 figure

Super-reflection of light from a random amplifying medium with disorder in the complex refractive index : Statistics of fluctuations

The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is derived using the method of invariant imbedding. The statistics of fluctuations have been obtained for both the correlated telegraph noise and the Gaussian white-noise models for the disorder. In both cases, an enhanced backscattering (super-reflection with reflection coefficient greater than unity) results because of coherent feedback due to Anderson localization and coherent amplification in the medium. The results show that the effect of randomness in the imaginary part of the refractive index on localization and super-reflection is qualitatively different.Comment: RevTex 6 pages, 3 figures in ps file