Ratchet Current Research Articles

Active Particles with Soft and Curved Walls: Equation of State, Ratchets, and Instabilities.

We study, from first principles, the pressure exerted by an active fluid of spherical particles on general boundaries in two dimensions. We show that, despite the nonuniform pressure along curved walls, an equation of state is recovered upon a proper spatial averaging. This holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by spontaneous shear stresses on the walls. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semiflexible filaments. Finally, we relate the force exerted on objects immersed in active baths to the particle flux they generate around them.

Helicity-Driven Ratchet Effect Enhanced by Plasmons.

We demonstrate that the ratchet effect-a radiation-induced direct current in periodically modulated structures with built-in asymmetry-is dramatically enhanced in the vicinity of the plasmonic resonances and has a nontrivial polarization dependence. For a circular polarization, the current component, perpendicular to the modulation direction, changes sign with the inversion of the radiation helicity. In the high-mobility structures, this component might increase by several orders of magnitude due to the plasmonic effects and exceed the current component in the modulation direction. Our theory also predicts that in the dirty systems, where the plasma resonances are suppressed, the ratchet current is controlled by the Maxwell relaxation.

Quantum-classical transition and quantum activation of ratchet currents in the parameter space.

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero-temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed based on quantum, semiclassical, and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

Ratchet Effect in a Triple Delta-Kicked Model

We investigate the quantum ratchet effect in a triple delta-kicked model. Three symmetric flashing potentials alternately act on a particle with a symmetric and homogeneous initial state of zero momentum. Ratchet currents emerge when quantum resonances are excited. Ratchet currents in the triple model may be stronger than those in the previous model. Our work expands upon the quantum delta-kicked model and may contribute to experimental investigation of the quantum transport of cold atoms.

Multi-Frequency Delta-Kicked Models for the Quantum Ratchet Effect

We investigate two multi-frequency delta-kicked models for the quantum ratchet effect, in which a flashing multi-frequency potential periodically acts on a particle. Ratchet currents emerge when quantum resonances are excited. Currents in multi-frequency models may be stronger than those in the previous two-frequency model. Our work expands upon the quantum delta-kicked model and may contribute to experimental investigation of the quantum transport of cold atoms.

Orbital magnetic ratchet effect

Magnetic ratchets---two-dimensional systems with superimposed noncentrosymmetric ferromagnetic gratings---are considered theoretically. It is demonstrated that excitation by radiation results in a directed motion of two-dimensional carriers due to the pure orbital effect of the periodic magnetic field. Magnetic ratchets based on various two-dimensional systems such as topological insulators, graphene, and semiconductor heterostructures are investigated. The mechanisms of the electric current generation caused by both radiation-induced heating of carriers and by acceleration in the radiation electric field in the presence of a space-oscillating Lorentz force are studied in detail. The electric currents sensitive to the linear polarization plane orientation as well as to the radiation helicity are calculated. It is demonstrated that the frequency dependence of the magnetic ratchet currents is determined by the dominant elastic-scattering mechanism of two-dimensional carriers and differs for the systems with linear and parabolic energy dispersions.

A time-asymmetric delta-kicked model for the quantum ratchet effect

We investigate a time-asymmetric delta-kicked model for the quantum ratchet effect, in which a flashing potential acts on a particle at unequal time intervals. Ratchet currents emerge when quantum resonances are excited. The currents in time-asymmetric models may be stronger than those found in the previous time-symmetric model. Our work expands upon the quantum delta-kicked model and may contribute to experimental investigation of the quantum transport of cold atoms.

Josephson junction ratchet: The impact of finite capacitances

We study transport in an asymmetric SQUID which is composed of a loop with three capacitively and resistively shunted Josephson junctions: two in series in one arm and the remaining one in the other arm. The loop is threaded by an external magnetic flux and the system is subjected to both a time-periodic and a constant current. We formulate the deterministic and, as well, the stochastic dynamics of the SQUID in terms of the Stewart-McCumber model and derive an equation for the phase difference across one arm, in which an effective periodic potential is of the ratchet type, i.e. its reflection symmetry is broken. In doing so, we extend and generalize earlier study by Zapata et al. [Phys. Rev. Lett. 77, 2292 (1996)] and analyze directed transport in wide parameter regimes: covering the over-damped to moderate damping regime up to its fully under-damped regime. As a result we detect the intriguing features of a negative (differential) conductance, repeated voltage reversals, noise induced voltage reversals and solely thermal noise-induced ratchet currents. We identify a set of parameters for which the ratchet effect is most pronounced and show how the direction of transport can be controlled by tailoring the external magnetic flux.

Pratique de neuroradiologie interventionnelle au Caire

We study the directed motion of a Brownian particle moving in a two-dimensional coupled flashing ratchet driven by Gaussian white noise. The temperature dependence of the current is evaluated numerically in terms of Langevin simulation and discussed by means of a heuristic analytical ad hoc approximation. The current can be enhanced or reversed due to the coupling effects between two degrees of freedom. Our results show that the noise is rectified even in the absence of a true activation energy barrier and the two-dimensional ratchet current does not vanish as the temperature approaches infinity.

Excluded Volume Causes Integer and Fractional Plateaus in Colloidal Ratchet Currents

We study the collective transport of paramagnetic colloids driven above a magnetic bubble lattice by an external rotating magnetic field. We measure a direct ratchet current which rises in integer and fractional steps with the field amplitude. The stepwise increase is caused by excluded volume interactions between the particles, which form composite clusters above the bubbles with mobile and immobile occupation sites. Transient energy minima located at the interstitials between the bubbles cause the colloids to hop from one composite cluster to the next with synchronous and period doubled modes of transport. The colloidal current may be polarized to make selective use of type up or type down interstitials.

A delta-kicked model for the quantum ratchet effect

We construct a delta-kicked model for the quantum ratchet effect. Two symmetric flashing potentials alternately act on a particle with a symmetric and homogeneous initial state of zero momentum. Ratchet currents emerge when quantum resonances are excited. We give some results and compare our model and a previous model. Our work provides a way to control the quantum transport of cold atoms experimentally.

Time-Shift Invariance Determines the Functional Shape of the Current in Dissipative Rocking Ratchets

Ratchets are devices able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids, show a set of universal features. A satisfactory explanation for them has challenged theorist for decades, and so far we still lack a general theory of this phenomenon. Here we provide such a theory by exploring ---through functional analysis--- the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions, and allows to make predictions of phenomena not yet observed in any experiment or simulation.

Stable structures in parameter space and optimal ratchet transport

Optimal ratchet currents are shown to be directly connected, for all parameters combinations of the ratchet model, to Isoperiodic Stable Structures (ISSs), which are believed to be generic in the parameter spaces of nonlinear dynamical systems. As the ratchet current is more efficient inside the ISSs, which usually are located in preferred direction in the parameter space, it allows us to make crucial statements about the relevant parameters combination to obtain an optimal transport. This is important from the theoretical point of view and for possible experimental realization of efficient currents. We provide an extensive numerical description of the ratchet current throughout the parameters and indicate a trio of ISSs (cusp, non-cusp and shrimp-like), which exist in all pairwise combinations of ratchet parameters. This suggests the general behavior of the ISSs in the context of ratchet transport.

Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force

We rigorously investigate the quantum dissipative dynamics of a ratchet system described by a periodic potential model based on the Caldeira-Leggett Hamiltonian with a biharmonic force. In this model, we use the reduced hierarchy equations of motion in the Wigner space representation. These equations represent a generalization of the Gaussian-Markovian quantum Fokker-Planck equation introduced by Tanimura and Wolynes (1991), which was formulated to study non-Markovian and nonperturbative thermal effects at finite temperature. This formalism allows us to treat both the classical limit and the tunneling regimes, and it is helpful for identifying purely quantum mechanical effects through the time evolution of the Wigner distribution. We carried out extensive calculations of the classical and quantum currents for various temperatures, coupling strengths, and barrier heights. Our results reveal that at low temperature, while the quantum current is larger than the classical current in the case of a high barrier, the opposite is true in the case of a low barrier. We find that this behavior results from the fact that the tunneling enhances the current in the case of a high barrier, while it suppresses the current in the case of a low barrier. This is because the effect of the ratchet potential is weak in the case of a low barrier due to the large dispersion of the distribution introduced by tunneling. This causes the spatiotemporal asymmetry, which is necessary for ratchet current, to be weak, and as a result, the net current is suppressed.

Computing With Nonequilibrium Ratchets

Electronic ratchets transduce local spatial asymmetries into directed currents in the absence of a global drain bias by rectifying temporal signals that reside far from the thermal equilibrium. We show that the absence of a drain bias can provide distinct energy advantages for computation, specifically, reducing static dissipation in a logic circuit. Since the ratchet functions as a gate voltage-controlled current source, it also potentially reduces the dynamic dissipation associated with charging/discharging capacitors. In addition, the unique charging mechanism eliminates timing-related constraints on logic inputs, in principle allowing for adiabatic charging. We calculate the ratchet currents in classical and quantum limits, and show how a sequence of ratchets can be cascaded to realize universal Boolean logic.

Symmetry breaking for ratchet transport in the presence of interactions and a magnetic field

We study the microwave induced ratchet transport of two-dimensional electrons on an oriented semidisk Galton board. The magnetic field symmetries of ratchet transport are analyzed in the presence of electron-electron interactions. Our results show that a magnetic field asymmetric ratchet current can appear due to two contributions, a Hall drift of the rectified current that depends only weakly on electron-electron interactions and a breaking of the time reversal symmetry due to the combined effects of interactions and magnetic field. In the latter case, the asymmetry between positive and negative magnetic fields vanishes in the weak interaction limit. We also discuss the recent experimental results on ratchet transport in asymmetric nanostructures.

Controlling the momentum current of an off-resonant ratchet

We experimentally investigate the phenomenon of a quantum ratchet created by exposing a Bose-Einstein Condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm a recent theoretical prediction [M. Sadgrove and S. Wimberger, New J. Phys. \textbf{11}, 083027 (2009)] that the current direction can be controlled by experimental parameters which leave the underlying symmetries of the system unchanged. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.

Coherent quantum ratchets driven by tunnel oscillations: Fluctuations and correlations

We study two capacitively coupled double quantum dots focusing on the regime in which one double dot is strongly biased, while no voltage is applied to the other. Then the latter experiences an effective driving force which induces a ratchet current, i.e., a dc current in the absence of a bias voltage. Its current noise is investigated with a quantum master equation in terms of the full-counting statistics. This reveals, that whenever the ratchet current is large, it also exhibits some features of a Poissonian process. By eliminating the drive circuit, we obtain a reduced master equation which provides analytical results for the Fano factor.

Ratchet effects in two-dimensional systems with a lateral periodic potential

Radiation-induced ratchet electric currents have been studied theoretically in graphene with a periodic noncentrosymmetric lateral potential. The ratchet current generated under normal incidence is shown to consist of two contributions, one of them being polarization-independent and proportional to the energy relaxation time, and another controlled solely by elastic scattering processes and sensitive to both the linear and circular polarization of radiation. Two realistic mechanisms of electron scattering in graphene are considered. For short-range defects, the ratchet current is helicity-dependent but independent of the direction of linear polarization. For the Coulomb impurity scattering, the ratchet current is forbidden for the radiation linearly polarized in the plane perpendicular to the lateral-potential modulation direction. For comparison, the ratchet currents in a quantum well with a lateral superlattice are calculated at low temperatures with allowance for the dependence of the momentum relaxation time on the electron energy.

Orbital Josephson effect and interactions in driven atom condensates on a ring

In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long-time dynamics of a driven interacting many-body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self-trapping and chaotic behavior. In the latter case, a full many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number.