Dynamics stabilization and transport coherency in a rocking ratchet for cold atoms

Cold atoms in optical lattices have emerged as an ideal system to investigate the ratchet effect, as demonstrated by several recent experiments. In this work we analyze theoretically two aspects of ac driven transport in cold atoms ratchets. We first address the issue of whether, and to which extent, an ac driven ratchet for cold atoms can operate as a motor. We thus study theoretically a dissipative motor for cold atoms, as obtained by adding a load to a 1D non-adiabatically driven rocking ratchet. We demonstrate that a current can be generated also in the presence of a load, e.g. the ratchet device can operate as a motor. Correspondingly, we determine the stall force for the motor, which characterizes the range of loads over which the device can operate as a motor, and the differential mobility, which characterizes the response to a change in the magnitude of the load. Second, we compare our results for the transport in an ac driven ratchet device with the transport in a dc driven system. We observe a peculiar phenomenon: the bi-harmonic ac force stabilizes the dynamics, allowing the generation of uniform directed motion over a range of momentum much larger than what is possible with a dc bias. We explain such a stabilization of the dynamics by observing that a non-adiabatic ac drive broadens the effective cooling momentum range, and forces the atom trajectories to cover such a region. Thus the system can dissipate energy and maintain a steady-state energy balance. Our results show that in the case of a finite-range velocity-dependent friction, a ratchet device may offer the possibility of controlling the particle motion over a broader range of momentum with respect to a purely biased system, although this is at the cost of a reduced coherency

Transverse rectification of disorder-induced fluctuations in a driven system

We study numerically the overdamped motion of particles driven in a two dimensional ratchet potential. In the proposed design, of the so-called geometrical-ratchet type, the mean velocity of a single particle in response to a constant force has a transverse component that can be induced by the presence of thermal or other unbiased fluctuations. We find that additional quenched disorder can strongly enhance the transverse drift at low temperatures, in spite of reducing the transverse mobility. We show that, under general conditions, the rectified transverse velocity of a driven particle fluid is equivalent to the response of a one dimensional flashing ratchet working at a drive-dependent effective temperature, defined through generalized Einstein relations.Comment: 4.5 pages, 3 fig

Non-equilibrium relaxation of an elastic string in random media

We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We find that, in the long time limit, $L(t)$ has a non--algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, $U(L) \sim L^\theta$.Comment: 2 pages, 1 figure, Proceedings of ECRYS-2005 International Workshop on Electronic Crysta

Uniqueness of the thermodynamic limit for driven disordered elastic interfaces

We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size $L$ displacing in a disordered medium of transverse size $M=k L^\zeta$ with periodic boundary conditions, where $\zeta$ is the depinning roughness exponent and $k$ is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow ($k\to 0$) to the infinitely wide ($k\to \infty$) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behavior of the velocity-force characteristics are {\it unique} and $k$-independent. We also show that the finite size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of $k$. Our results are relevant for understanding anisotropic size-effects in force-driven and velocity-driven interfaces.Comment: 10 pages, 12 figure

Random-Manifold to Random-Periodic Depinning of an Elastic Interface

We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence of several characteristic lengths separating different length-scale regimes of roughness. We determine the scaling behavior of these lengths as a function of the velocity, temperature, driving force, and transverse periodicity. A dynamical roughness diagram is thus obtained which contains, at small length scales, the critical and fast-flow regimes typical of the random-manifold (or domain wall) depinning, and at large length-scales, the critical and fast-flow regimes typical of the random-periodic (or charge-density wave) depinning. From the study of the equilibrium geometry we are also able to infer the roughness diagram in the creep regime, extending the depinning roughness diagram below threshold. Our results are relevant for understanding the geometry at depinning of arrays of elastically coupled thin manifolds in a disordered medium such as driven particle chains or vortex-line planar arrays. They also allow to properly control the effect of transverse periodic boundary conditions in large-scale simulations of driven disordered interfaces.Comment: 19 pages, 10 figure

Thermal rounding exponent of the depinning transition of an elastic string in a random medium

We study numerically thermal effects at the depinning transition of an elastic string driven in a two-dimensional uncorrelated disorder potential. The velocity of the string exactly at the sample critical force is shown to behave as $V \sim T^\psi$, with $\psi$ the thermal rounding exponent. We show that the computed value of the thermal rounding exponent, $\psi = 0.15$, is robust and accounts for the different scaling properties of several observables both in the steady-state and in the transient relaxation to the steady-state. In particular, we show the compatibility of the thermal rounding exponent with the scaling properties of the steady-state structure factor, the universal short-time dynamics of the transient velocity at the sample critical force, and the velocity scaling function describing the joint dependence of the steady-state velocity on the external drive and temperature

Thermal rounding of the depinning transition

We study thermal effects at the depinning transition by numerical simulations of driven one-dimensional elastic interfaces in a disordered medium. We find that the velocity of the interface, evaluated at the critical depinning force, can be correctly described with the power law $v\sim T^\psi$, where $\psi$ is the thermal exponent. Using the sample-dependent value of the critical force, we precisely evaluate the value of $\psi$ directly from the temperature dependence of the velocity, obtaining the value $\psi = 0.15 \pm 0.01$. By measuring the structure factor of the interface we show that both the thermally-rounded and the T=0 depinning, display the same large-scale geometry, described by an identical divergence of a characteristic length with the velocity $\xi \propto v^{-\nu/\beta}$, where $\nu$ and $\beta$ are respectively the T=0 correlation and depinning exponents. We discuss the comparison of our results with previous estimates of the thermal exponent and the direct consequences for recent experiments on magnetic domain wall motion in ferromagnetic thin films.Comment: 6 pages, 3 figure

Thermal Effects in the dynamics of disordered elastic systems

Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of view of fundamental physics and of practical applications. Despite important progress many questions remain open. In particular the temperature has drastic effects on the way these systems respond to an external force. We address here the important question of the thermal effect close to depinning, and whether these effects can be understood in the analogy with standard critical phenomena, analogy so useful to understand the zero temperature case. We show that close to the depinning force temperature leads to a rounding of the depinning transition and compute the corresponding exponent. In addition, using a novel algorithm it is possible to study precisely the behavior close to depinning, and to show that the commonly accepted analogy of the depinning with a critical phenomenon does not fully hold, since no divergent lengthscale exists in the steady state properties of the line below the depinning threshold.Comment: Proceedings of the International Workshop on Electronic Crystals, Cargese(2008