Stochastic resonance in periodic potentials: realization in a dissipative optical lattice

We have observed the phenomenon of stochastic resonance on the Brillouin propagation modes of a dissipative optical lattice. Such a mode has been excited by applying a moving potential modulation with phase velocity equal to the velocity of the mode. Its amplitude has been characterized by the center-of-mass (CM) velocity of the atomic cloud. At Brillouin resonance, we studied the CM-velocity as a function of the optical pumping rate at a given depth of the potential wells. We have observed a resonant dependence of the CM velocity on the optical pumping rate, corresponding to the noise strength. This corresponds to the experimental observation of stochastic resonance in a periodic potential in the low-damping regime

Localization of solitons: linear response of the mean-field ground state to weak external potentials

Two aspects of bright matter-wave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials [Sacha et al. PRL 103, 210402 (2009)], as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary external potential, with a detailed application to lattice potentials.Comment: Selected paper presented at the 2010 Spring Meeting of the Quantum Optics and Photonics Section of the German Physical Society. V2: minor changes, published versio

New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric permittivities show a contrast compared to the electric permittivity of the electrolyte phase. Our main result is the derivation of convenient low-dimensional equations, that is, of effective macroscopic porous media Poisson-Nernst-Planck equations, which reliably describe ionic transport. The contrast in the electric permittivities between liquid and solid phase and the heterogeneity of the porous medium induce strongly oscillating electric potentials (fields). In order to account for this special physical scenario, we introduce a modified asymptotic multiple-scale expansion which takes advantage of the nonlinearly coupled structure of the ionic transport equations. This allows for a systematic upscaling resulting in a new effective porous medium formulation which shows a new transport term on the macroscale. Solvability of all arising equations is rigorously verified. This emergence of a new transport term indicates promising physical insights into the influence of the microscale material properties on the macroscale. Hence, systematic upscaling strategies provide a source and a prospective tool to capitalize intrinsic scale effects for scientific, engineering, and industrial applications

Bose-Einstein Condensates in Optical Quasicrystal Lattices

We analyze the physics of Bose-Einstein condensates confined in 2D quasi-periodic optical lattices, which offer an intermediate situation between ordered and disordered systems. First, we analyze the time-of-flight interference pattern that reveals quasi-periodic long-range order. Second, we demonstrate localization effects associated with quasi-disorder as well as quasiperiodic Bloch oscillations associated with the extended nature of the wavefunction of a Bose-Einstein condensate in an optical quasicrystal. In addition, we discuss in detail the crossover between diffusive and localized regimes when the quasi-periodic potential is switched on, as well as the effects of interactions

Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization

Demonstration of a controllable three-dimensional Brownian motor in symmetric potentials

We demonstrate a Brownian motor, based on cold atoms in optical lattices, where isotropic random fluctuations are rectified in order to induce controlled atomic motion in arbitrary directions. In contrast to earlier demonstrations of ratchet effects, our Brownian motor operates in potentials that are spatially and temporally symmetric, but where spatiotemporal symmetry is broken by a phase shift between the potentials and asymmetric transfer rates between them. The Brownian motor is demonstrated in three dimensions and the noise-induced drift is controllable in our system.Comment: 5 pages, 4 figure

Characterisation of a three-dimensional Brownian motor in optical lattices

We present here a detailed study of the behaviour of a three dimensional Brownian motor based on cold atoms in a double optical lattice [P. Sjolund et al., Phys. Rev. Lett. 96, 190602 (2006)]. This includes both experiments and numerical simulations of a Brownian particle. The potentials used are spatially and temporally symmetric, but combined spatiotemporal symmetry is broken by phase shifts and asymmetric transfer rates between potentials. The diffusion of atoms in the optical lattices is rectified and controlled both in direction and speed along three dimensions. We explore a large range of experimental parameters, where irradiances and detunings of the optical lattice lights are varied within the dissipative regime. Induced drift velocities in the order of one atomic recoil velocity have been achieved.Comment: 8 pages, 14 figure

Synchronization of Hamiltonian motion and dissipative effects in optical lattices: Evidence for a stochastic resonance

We theoretically study the influence of the noise strength on the excitation of the Brillouin propagation modes in a dissipative optical lattice. We show that the excitation has a resonant behavior for a specific amount of noise corresponding to the precise synchronization of the Hamiltonian motion on the optical potential surfaces and the dissipative effects associated with optical pumping in the lattice. This corresponds to the phenomenon of stochastic resonance. Our results are obtained by numerical simulations and correspond to the analysis of microscopic quantities (atomic spatial distributions) as well as macroscopic quantities (enhancement of spatial diffusion and pump-probe spectra). We also present a simple analytical model in excellent agreement with the simulations

Spatiotemporal Dynamics in Public Transport Personal Security Perceptions: Digital Evidence from Mexico City's Periphery

The potential for information and communication technologies (ICTs) to revolutionise transportation is of long-standing interest. Just as the telegraph, trans-oceanic cable communications, the telephone, and the fax surely influenced travel behaviours and supply of transportation infrastructures and services, related developments, especially in computing, have changed the way we analyse and plan systems. The most recent wave of ICT-related technological advances – epitomised by high-powered sensing and realtime computing capabilities – promises a new era of seamless services, autonomous vehicles, and high resolution system micro-simulation, to name a few emerging opportunities.Singapore. National Research FoundationSingapore-MIT Alliance for Research and Technology Center. Future Urban Mobilit

Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle

We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose-Einstein condensate) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions