Matter wave switching in Bose-Einstein condensates via intensity redistribution soliton interactions

Using time dependent nonlinear (s-wave scattering length) coupling between the components of a weakly interacting two component Bose-Einstein condensate (BEC), we show the possibility of matter wave switching (fraction of atoms transfer) between the components via shape changing/intensity redistribution (matter redistribution) soliton interactions. We investigate the exact bright-bright N-soliton solution of an effective one-dimensional (1D) two component BEC by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. In particular, we show that the effective 1D coupled Gross-Pitaevskii (GP) equations with time dependent parameters can be transformed into the well known completely integrable Manakov model described by coupled nonlinear Schr\"odinger (CNLS) equations by effecting a change of variables of the coordinates and the wave functions under certain conditions related to the time dependent parameters. We obtain the one-soliton solution and demonstrate the shape changing/matter redistribution interactions of two and three soliton solutions for the time independent expulsive harmonic trap potential, periodically modulated harmonic trap potential and kink-like modulated harmonic trap potential. The standard elastic collision of solitons occur only for a specific choice of soliton parameters.Comment: 11 pages, 14 figures, 1 tabl

Bright gap solitons of atoms with repulsive interaction

We report on the first experimental observation of bright matter-wave solitons for 87Rb atoms with repulsive atom-atom interaction. This counter intuitive situation arises inside a weak periodic potential, where anomalous dispersion can be realized at the Brillouin zone boundary. If the coherent atomic wavepacket is prepared at the corresponding band edge a bright soliton is formed inside the gap. The strength of our system is the precise control of preparation and real time manipulation, allowing the systematic investigation of gap solitons.Comment: 4 pages, 4 figure

Asymmetric partially coherent solitons in saturable nonlinear media

We investigate theoretically properties of partially coherent solitons in optical nonlinear media with slow saturable nonlinearity. We have found numerically that such a medium can support spatial solitons which are asymmetric in shape and are composed of only a finite number of modes associated with the self-induced waveguide. It is shown that these asymmetric spatial solitons can propagate many diffraction lengths without changes, but that collisions change their shape and may split them apart. [S1063-651X(99)12808-3

Verifying proofs in constant depth

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's

What is Holding Back Convnets for Detection?

Convolutional neural networks have recently shown excellent results in general object detection and many other tasks. Albeit very effective, they involve many user-defined design choices. In this paper we want to better understand these choices by inspecting two key aspects "what did the network learn?", and "what can the network learn?". We exploit new annotations (Pascal3D+), to enable a new empirical analysis of the R-CNN detector. Despite common belief, our results indicate that existing state-of-the-art convnet architectures are not invariant to various appearance factors. In fact, all considered networks have similar weak points which cannot be mitigated by simply increasing the training data (architectural changes are needed). We show that overall performance can improve when using image renderings for data augmentation. We report the best known results on the Pascal3D+ detection and view-point estimation tasks

What can be learned about molecular reorientation from single molecule polarization microscopy?

We have developed a general approach for the calculation of the single molecule polarization correlation function C(t), which delivers a correlation of the emission dichroisms at time 0 and t. The approach is model independent and valid for general asymmetric top molecules. The key dynamic quantities of our analysis are the even-rank orientational correlation functions, the weighted sum of which yields C(t). We have demonstrated that the use of non-orthogonal schemes for the detection of the single molecule polarization responses makes it possible to manipulate the weighting coefficients in the expansion of C(t). Thus valuable information about the orientational correlation functions of the rank higher than second can be extracted from C(t)

Spontaneous soliton formation and modulational instability in Bose-Einstein condensates

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Strecker {\it et al.} Nature {\bf 417} 150 (2002)] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton--soliton interactions, produce bursts of hot atoms at different time scales.Comment: 4 pages, 3 figures. Phys. Rev. Lett. in pres

Ultra-broadband mid-infrared supercontinuum generation through dispersion engineering of chalcogenide microstructured fibers

We demonstrate numerically that the use of dispersion-engineered microstrucured fibers made with chalcogenide glasses allows one to generate ultrabroadband supercontinuum spectra in the mid-infrared region by launching optical pulses at a suitable wavelength. As a specific example, numerical simulations show that such a 1 cm long fiber, made with Ge11.5As24Se64.5 glass and pumped at a wavelength of 3.1 μm using short pulses with a relatively modest peak power of 3 kW, can produce a spectrum extending from 1.3 μm to beyond 11 μm (more than 3 octaves). We consider three fiber structures with microstrucured air holes in their cladding and find their optimum designs through dispersion engineering. Among these, equiangular spiral microstrucured fiber is found to be the most promising candidate for generating an ultrawide supercontinuum in the mid-infrared region

Chaos, Determinacy and Fractals in Active-Sterile Neutrino Oscillations in the Early Universe

The possibility of light sterile neutrinos allows for the resonant production of lepton number in the early universe through matter-affected neutrino mixing. For a given a mixing of the active and sterile neutrino states it has been found that the lepton number generation process is chaotic and strongly oscillatory. We undertake a new study of this process' sensitivity to initial conditions through the quantum rate equations. We confirm the chaoticity of the process in this solution, and moreover find that the resultant lepton number and the sign of the asymmetry produces a fractal in the parameter space of mass, mixing angle and initial baryon number. This has implications for future searches for sterile neutrinos, where arbitrary high sensitivity could not be determinate in forecasting the lepton number of the universe.Comment: 6 pages, 3 figure

Dynamical instability and domain formation in a spin-1 Bose condensate

We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.Comment: RevTex4, 4 pages with 3 color eps figure, to appear in Phys. Rev. Let