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. Sj?lund 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.     

Temperature and spatial diffusion of atoms cooled in a 3D lin ⊥lin bright optical lattice

We present a detailed experimental study of a three-dimensional lin⊥lin bright optical lattice. Measurements of the atomic temperature and spatial diffusion coefficients are reported for different angles between the lattice beams, i.e. for different lattice constants. The experimental findings are interpreted with the help of numerical simulations. In particular we show, both experimentally and theoretically, that the temperature is independent of the lattice constant. Received 5 July 2001 and Received in final form 13 August 2001     

Quantum Brownian motion on potential surfaces coupled via tunneling in an external electric field[-2mm]

The present paper deals with the motion of a Brownian particle on two identical but shifted potential surfaces, coupled via a tunneling matrix element in an external electric field. Dissipation is induced by a heat bath represented by an infinite set of harmonic oscillators with a continuum range of frequencies. We derive a perturbative solution for the quantum coherence term of the particle system after performing a small-polaron-like transformation. This is subsequently necessary for the extraction of an equation that describes the reduced dynamics and the minimal action path of the Brownian particle. Finally we extract expressions for the population relaxation rate and the pure quantum-dephasing rate of the two-level system. Received 4 January 2001 and Received in final form 12 March 2001     

Fragmentation of CO+ molecular ion through dissociative excited states produced by swift multicharged heavy ion impact on CO molecules

We report the observation of resonances in the intensity correlation spectra of a 3D rubidium optical lattice, which we attribute to light scattering from propagating atomic density fluctuations in the lattice. This process is the spontaneous analog of the stimulated scattering mechanism recently described by Courtois et al.. We investigate the dependence of the new resonances on the lattice angle and show that they disappear for large angles, thus resolving previous discrepancies on the subject. Received: 30 January 1997 / Accepted: 9 October 1997     

Light scattering with swollen hexagonal phases

We investigate, using quasi-elastic light scattering, some features of the long-wavelength, low-frequency modes of the hexagonal phase often encountered in the study of lyotropic (surfactant-solvent) systems. The hexagonal phase is swollen by an oil-based ferrofluid, allowing magnetically aligned samples to be prepared. We show experimentally the anisotropy of the two lowest-frequency modes. We develop a model which predicts that these slow modes are associated to particle diffusion and tube motion. With the help of microscopic as well as phenomenological analyses, we suggest that the latter presumably corresponds to a peristaltic mode. Confinement effects on the one-dimensional, Brownian diffusion of the colloids along the tube axis together with the coupling between the two modes are studied experimentally, varying the tube diameter to particle size ratio. Received 7 July 1999     

Bright optical lattices in a longitudinal magnetic field. Experimental study of the oscillating and jumping regimes

All the bright optical lattices studied so far have been designed to obtain a circularly polarized light at the bottom of the optical potential wells. This condition minimizes the departure rate of the atoms from the fundamental adiabatic surface and permits an oscillating regime in a large range of parameters. We present here an experimental study of cesium atoms in a three-dimensional optical lattice, where the light is linearly polarized at the bottom of the potential wells. Temperature measurements and pump-probe spectroscopy give similar results for this lattice and for the conventional lin lin lattice (which have circular polarizations at the bottom of the wells) despite the fact that one lattice operates in the jumping regime and the other in the oscillating regime. We study the behaviour of the two types of lattices in a longitudinal magnetic field, with particular emphasis on the zero field and strong field regimes. The strong field situation is very simple because the eigenstates are then almost pure Zeeman substates and the adiabatic and diabatic potential surfaces are identical. The comparison between the zero-field and the high-field situations shows that the diabatic potentials are more appropriate to account for experimental observations in the novel lattice. Received: 9 October 1997 / Accepted: 6 November 1997     

Anomalous viscosity exponent in a discretized model for a chain diffusion in one dimension

We present a one-dimensional Monte Carlo simulation for the diffusion motion of a chain of N beads. We found that the scaling exponent for the viscosity can be smaller or greater than 3. This anomalous behavior cannot be attributed to the diffusivity scaling or the length fluctuations but is due to the chain dynamics details during diffusion in which the end beads play the key role. The viscosity exponent 3 and its expected relation with the diffusivity exponent are recovered in the asymptotic regime (N ↦∞). Received 24 September 2001 and Received in final form 28 January 2002     

Brownian particles in random and quasicrystalline potentials: How they approach the equilibrium

We study the Brownian motion of an ensemble of single colloidal particles in a random square and a quasicrystalline potential when they start from non-equlibrium. For both potentials, Brownian dynamics simulations reveal a widespread subdiffusive regime before the diffusive long-time limit is reached in thermal equilibrium. We develop a random trap model based on a distribution for the depths of trapping sites that reproduces the results of the simulations in detail. Especially, it gives analytic formulas for the long-time diffusion constant and the relaxation time into the diffusive regime. Aside from detailed differences, our work demonstrates that quasicrystalline potentials can be used to mimic aspects of random potentials.     

Exact propagator of the Fokker-Planck equation with a space-dependent diffusion coefficient and a time-dependent mean-reverting force

We have investigated the algebraic structure of the Fokker-Planck equation with a variable diffusion coefficient and a time-dependent mean-reverting force. Such a model could be useful to study the general problem of a Brownian walker with a space-dependent diffusion coefficient. We also show that this model is related to the Fokker-Planck equation with a constant diffusion coefficient and a time-dependent anharmonic potential of the form V(x, t) = ?a(t)x ² + b ln x, which has been widely applied to model different physical and biological phenomena, e.g. the study of neuron models and stochastic resonance in monostable nonlinear oscillators. Using the Lie algebraic approach we have derived the exact diffusion propagators for the Fokker-Planck equations associated with different boundary conditions, namely (i) the case of a single absorbing barrier, and (ii) the case of two absorbing barriers. These exact diffusion propagators enable us to study the time evolution of the corresponding stochastic systems. Received 23 October 2001 and Received in final form 24 December 2001     

Delay, feedback and quenching in financial markets

An asset whose price exhibits geometric Brownian motion is analysed. The basic Brownian motion model is modified to account for the effects of market delay and investor feedback. A Langevin equation model is appropriate. When the feedback coupling is sufficiently strong, the market dynamics switches from a slow random walk behaviour to a rapid unstable behaviour with a fast time scale characteristic of the market delay. The unstable runaway behaviour is subsequently quenched by investors deserting a collapsing market or saturating a booming one. This quenching effect is sufficient to ensure long term bounding of the asset price. A form of market sabotage is demonstrated in which investors can push the market from a stable to an unstable regime. Received 24 February 2000     

Optical phase-space reconstruction of mirror motion at the attometer level

We describe an experiment in which the quadratures of the position of an harmonically-bound mirror are observed at the attometer level. We have studied the Brownian motion of the mirror, both in the free regime and in the cold-damped regime when an external viscous force is applied by radiation pressure. We have also studied the thermal-noise squeezing when the external force is parametrically modulated. We have observed both the % theoretical limit of squeezing at low gain and the parametric oscillation of the mirror for a large gain. Received 9 July 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: heidmann@spectro.jussieu.fr RID="b" ID="b"Unité mixte de recherche du Centre National de la Recherche Scientifique, de l'école Normale Supérieure et de l'Université Pierre et Marie Curie. Website: www.spectro.jussieu.fr/Mesure     

Single-beam optical bottle for cold atoms using a conical lens

We report a new method to generate an optical dipole potential with a null intensity region surrounded in all directions by light walls. This is achieved with a simple scheme based on a conical lens. Applications to optical trapping of neutral atoms are discussed. Received 4 September 2000 and Received in final form 21 January 2001     

Trapping and cooling cesium atoms in a speckle field

We present the results of two experiments where cold cesium atoms are trapped in a speckle field. In the first experiment, a YAG laser creates the speckle pattern and induces a far-detuned dipole potential which is a nearly-conservative potential. Localization of atoms near the intensity maxima of the speckle field is observed. In a second experiment we use two counterpropagating laser beams tuned close to a resonance line of cesium and in the linlin configuration, one of them being modulated by a holographic diffuser that creates the speckle field. Three-dimensional cooling is observed. Variations of the temperature and of the spatial diffusion coefficient with the size of a speckle grain are presented. Received 16 December 1998 and Received in final form 16 April 1999     

Transport in a ratchet with spatial disorder and time-delayed feedback

A Brownian motor with Gaussian short-range correlated spatial disorder and time-delayed feedback is investigated. The effects of disorder intensity, correlation strength and delay time on the transport properties of an overdamped periodic ratchet are discussed for different driving force. For small driving force, the disorder intensity can induce a peak in the drift motion and a linear increasing function in diffusion motion. For large driving force, the disorder intensity can suppress the drift motion but enhance the diffusion motion. For both small and large driving forces, the correlation strength of the spatial disorder can enhance the drift motion but suppress the diffusion motion. While the delay time can reduce the drift motion to a small value and enhance the diffusion motion to a large value. The drift motion increases as the driving force increases. However, the diffusion motion is either decreases or only increases slightly when the driving force increases.     

Laplace operator and random walk on one-dimensional nonhomogeneous lattice

A classical result of probability theory states that under suitable space and time renormalization, a random walk converges to Brownian motion. We prove an analogous result in the case of nonhomogeneous random walk on onedimensional lattice. Under suitable conditions on the nonhomogeneous medium, we prove convergence to Brownian motion and explicitly compute the diffusion coefficient. The proofs are based on the study of the spectrum of random matrices of increasing dimension.     

Random walks with imperfect trapping in the decoupled-ring approximation

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics. Received 23 July 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Time of avalanche mixing of granular materials in a half filled drum

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference δ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time τ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when δ is an integer part of π. Introduction of fluctuations of δ suppresses the singularities of τ(δ) and smoothes the dependence τ(δ). Received 27 October 2000 and Received in final form 13 March 2001     

Nonlinear diffusion under a time dependent external force: q-maximum entropy solutions

Nonlinear diffusion equations provide useful models for a number of interesting phenomena, such as diffusion processes in porous media. We study here a family of nonlinear Fokker-Planck equations endowed both with a power-law nonlinear diffusion term and a drift term with a time dependent force linear in the spatial variable. We show that these partial differential equations exhibit exact time dependent particular solutions of the Tsallis maximum entropy (q-MaxEnt) form. These results constitute generalizations of previous ones recently discussed in the literature [C. Tsallis, D.J. Bukman, Phys. Rev. E 54, R2197 (1996)], concerning q-MaxEnt solutions to nonlinear Fokker-Planck equations with linear, time independent drift forces. We also show that the present formalism can be used to generate approximate q-MaxEnt solutions for nonlinear Fokker-Planck equations with time independent drift forces characterized by a general spatial dependence. Received 25 April 2001 and Received in final form 6 June 2001     

Application of the ratchet effect to improve material quality (reducing vortex density in superconductors and smoothing surfaces)

Although Brownian ratchets have been conceived to describe the operation of molecular motor proteins, their basic principles are also applicable to a wide range of different physical systems. In this paper I line up two such possible applications in condensed-matter physics. The first one is the removal of vortices from superconductors. Magnetic fields frequently penetrate superconducting materials in the form of vortices, and once present, they dissipate energy and generate internal noise, limiting the operation of numerous superconducting devices. We demonstrate theoretically that the application of an alternating current to a superconductor patterned with an appropriate ratchet-like pinning potential induces an outward vortex motion. The second application is based on the fact that the Schwoebel barrier induces an asymmetry in the lattice potential of nearly flat solid surfaces. During epitaxial growth this asymmetry leads to a fast and unwanted increase in the surface roughness. We show, however, that one can take advantage of the asymmetry by applying an alternating electric field parallel to the surface, which induces a net electromigrational flow of the surface atoms from the peaks towards the wells, and thus results in a smoother surface. Received: 20 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002