Gating ratchet for cold atoms

Hamiltonian Ratchet for Matter-Wave Transport

We report on the design of a Hamiltonian ratchet exploiting periodically at rest integrable trajectories in the phase space of a modulated periodic potential, leading to the linear nondiffusive transport of particles. Using Bose-Einstein condensates in a modulated one-dimensional optical lattice, we make the first observations of this spatial ratchet, which provides way to coherently transport matter waves with possible applications in quantum technologies. In the semiclassical regime, the quantum transport strongly depends on the effective Planck constant due to Floquet state mixing. We also demonstrate the interest of quantum optimal control for efficient initial state preparation into the transporting Floquet states to enhance the transport periodicity.

Phase diffusion and fluctuations in a dissipative Bose-Josephson junction

We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and π-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the π-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and π-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.

Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view

This paper discusses two retrodictions of the theory of ratchet universality which explain previous experimental results concerning directed ratchet transport of cold atoms in dissipative optical lattices in one case and of fluxons in uniform annular Josephson junctions in the other, both driven by biharmonic fields. It has to be emphasized that these retrodictions are in sharp contrast with the current standard explanation of such experimental results, and they offer optimal control of the ratchetlike motion of such entities. New experimental proposals with cold atoms and fluxons are discussed, providing additional tests for novel predictions from ratchet universality.

Phase Dependent Vectorial Current Control in Symmetric Noisy Optical Ratchets

In this work, we demonstrate single microparticle transport in a symmetric noisy optical ratchet made with a linear array of 20 optical potentials, where each potential is a spatially symmetric low power (<2.5  mW) three-dimensional trap. Both the external force F(t) and the depth V_{0i}(t) of the optical potentials are dynamic and change at the same frequency ν=2  Hz. The depths of the individual optical potentials are random (uncorrelated noise) distributed around a mean value V_{0}, ⟨V_{0i}(t)⟩=V_{0}, while the external force is periodic and unbiased ⟨F(t)⟩=0. The system is completely symmetric for times t≫1/ν. Directed transport is possible as a result of the symmetry being broken at times on the order of 1/ν. We find that the direction and speed of motion (current) are coupled to the phase difference between the noise in the optical potentials and the external periodic force.

Controlling the preferential motion of chiral molecular walkers on a surface

Molecular walkers standing on two or more "feet" on an anisotropic periodic potential of a crystal surface may perform a one-dimensional Brownian motion at the surface-vacuum interface along a particular direction in which their mobility is the largest. In thermal equilibrium the molecules move with equal probabilities both ways along this direction, as expected from the detailed balance principle, well-known in chemical reactivity and in the theory of molecular motors. For molecules that possess an asymmetric potential energy surface (PES), we propose a generic method based on the application of a time-periodic external stimulus that would enable the molecules to move preferentially in a single direction thereby acting as Brownian ratchets. To illustrate this method, we consider a prototypical synthetic chiral molecular walker, 1,3-bis(imidazol-1-ylmethyl)-5(1-phenylethyl)benzene, diffusing on the anisotropic Cu(110) surface along the Cu rows. As unveiled by our kinetic Monte Carlo simulations based on the rates calculated using ab initio density functional theory, this molecule moves to the nearest equivalent lattice site via the so-called inchworm mechanism in which it steps first with the rear foot and then with the front foot. As a result, the molecule diffuses via a two-step mechanism, and due to its inherent asymmetry, the corresponding PES is also spatially asymmetric. Taking advantage of this fact, we show how the external stimulus can be tuned to separate molecules of different chirality, orientation and conformation. The consequences of these findings for molecular machines and the separation of enantiomers are also discussed.

Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on axis, perpendicular, and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.

Noise-enabled optical ratchets

In this contribution, we report on the implementation of a novel noise-enabled optical ratchet system. We demonstrate that, unlike commonly-used ratchet schemes-where complex asymmetric optical potentials are needed-efficient transport of microparticles across a one-dimensional optical lattice can be produced by introducing controllable noise in the system. This work might open interesting routes towards the development of new technologies aimed at enhancing the efficiency of transport occurring at the micro- and nanoscale, from novel particle-sorting tools to efficient molecular motors.

Multiple absolute negative mobilities

In this paper, we investigate transport of an inertial particle in a spatially symmetric potential and subjected to two harmonic signals with different frequencies in both deterministic and stochastic cases. Numerical results indicate that: (i) In the deterministic case, the two harmonic signals can induce many (up to six) segments of negative slopes in the curve of mean velocity vs. external constant force, i.e., a multiple absolute negative mobilities (ANMs) effect. But the occurrence of the effect depends on their frequencies and amplitudes. (ii) For the stochastic case, the multiple ANMs relay on stable index and symmetry parameter of the Lévy noise. In the case of symmetric noise, appropriate stable index makes the multiple ANMs be the strongest. Our further investigations indicate that an indispensable condition for the multiple ANMs to occur in the system is the temporal symmetry breaking by one multiplicative periodic signal and one additive periodic signal.

Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.

Nonsinusoidal current and current reversals in a gating ratchet

In this work, the ratchet dynamics of Brownian particles driven by an external sinusoidal (harmonic) force is investigated. The gating ratchet effect is observed when another harmonic is used to modulate the spatially symmetric potential in which the particles move. For small amplitudes of the harmonics, it is shown that the current (average velocity) of particles exhibits a sinusoidal shape as a function of a precise combination of the phases of both harmonics. By increasing the amplitudes of the harmonics beyond the small-limit regime, departures from the sinusoidal behavior are observed and current reversals can also be induced. These current reversals persist even for the overdamped dynamics of the particles.

Disorder induced regular dynamics in oscillating lattices

We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion; i.e., we observe the counterintuitive phenomenon that disorder leads to regular behavior. If the disorder is localized in a finite-sized part of the lattice, the described hopping causes initially diffusive particles to even accumulate in regular structures of the corresponding phase space. A hallmark of this accumulation is the emergence of pronounced peaks in the velocity distribution of particles that should be detectable in state of the art experiments, e.g., with cold atoms in optical lattices.

Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing

We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a nonperturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the output variable which describes the response of the system. We identify several universal features of the asymptotic response of the system, which are independent of the details of the model. In particular, we determine an asymptotic expression for the width of the resonance observed by keeping one frequency fixed and varying the other one. We show that this width is smaller than the usually assumed Fourier width by a factor determined by the two driving frequencies, and independent of the model system parameters. Additional general features can also be identified depending on the specific symmetry properties of the system. Our results find direct application in the study of sub-Fourier signal processing with nonlinear systems.

Dynamical analysis of an optical rocking ratchet: theory and experiment

A thorough analysis of the dynamics in a deterministic optical rocking ratchet [introduced in A. V. Arzola et al., Phys. Rev. Lett. 106, 168104 (2011)] and a comparison with experimental results are presented. The studied system consists of a microscopic particle interacting with a periodic and asymmetric light pattern, which is driven away from equilibrium by means of an unbiased time-periodic external force. It is shown that the asymmetry of the effective optical potential depends on the relative size of the particle with respect to the spatial period, and this is analyzed as an effective mechanism for particle fractionation. The necessary conditions to obtain current reversals in the deterministic regime are discussed in detail.

Feedback-induced oscillations in one-dimensional colloidal transport

We investigate a driven, one-dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on dynamical density functional theory.

Swallowtail band structure of the superfluid Fermi gas in an optical lattice

We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.

Quantum phase diffusion in a small underdamped Josephson junction

Quantum phase diffusion in a small underdamped Nb/AlO(x)/Nb junction (∼0.4 μm(2)) is demonstrated in a wide temperature range of 25-140 mK where macroscopic quantum tunneling (MQT) is the dominant escape mechanism. We propose a two-step transition model to describe the switching process in which the escape rate out of the potential well and the transition rate from phase diffusion to the running state are considered. The transition rate extracted from the experimental switching current distribution follows the predicted Arrhenius law in the thermal regime but is greatly enhanced when MQT becomes dominant.

Brownian motor in a granular medium

In this work we experimentally study the behavior of a freely rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation depends not only on the RMS acceleration Γ, but also on the amount of energy provided to two separate frequency bands, which are revealed to be important for the dynamics of the granular medium: The first band governs the transfer of energy from the grains to the probe, and the second affects the dynamics by altering the viscosity of the vibro-fluidized material.

Noise-induced multi-decrease and multi-increase of net voltage in Josephson junctions

In this paper, we investigate the net voltage in the Josephson junction subject to a thermal noise, a dc constant bias electric current and an ac time-periodic electric drive for the overdamped case and underdamped case simultaneously. It is shown that, by increasing the thermal noise strength, the net voltage can be decreased and increased several times as a function of the driving frequency. In addition, noise-enhanced stability is found for the net voltage of the junction.

Symmetries shape the current in ratchets induced by a biharmonic driving force

Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The biharmonic force f(t)=1 cos(qomegat+phi1)+2 cospomegat+phi2) does it for almost any choice of vphi1 and phi2, provided p and q are two coprime integers such that p+q is odd. It has been widely observed, in experiments in semiconductors, in Josephson junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape v proportional, variant1p2q cos(pphi1-qphi2+theta0) for small amplitudes, where theta0 depends on the damping ( theta0=pi/2 if there is no damping, and theta0=0 for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.

Enhancement of the longitudinal transport by a weakly transversal drive

Transport of Brownian particles in a two-dimensional asymmetric tube is investigated by applying a polarized field. From the Brownian dynamics simulations, we find that the longitudinal current can be enhanced remarkably by applying a weakly transversal drive. Multiple current reversals can be realized by altering the driving frequency of the polarized field. By coupling the longitudinal and transversal forces together, one can control the particle transport flexibly.

Deterministic ratchet from stationary light fields

Ratchets are dynamic systems where particle transport is induced by zero-average forces due to the interplay between nonlinearity and asymmetry. Generally, they rely on the effect of a strong external driving. We show that stationary optical lattices can be designed to generate particle flow in one direction while requiring neither noise nor driving. Such optical fields must be arranged to yield a combination of conservative (dipole) and nonconservative (radiation pressure) forces. Under strong friction all paths converge to a discrete set of limit periodic trajectories flowing in the same direction.

Suppression of thermally activated escape by heating

The problem of thermally activated escape over a potential barrier is solved by means of path integrals for one-dimensional reaction dynamics with very general time dependences. For a suitably chosen but still quite simple static potential landscape, the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed constant level.

Weak disorder strongly improves the selective enhancement of diffusion in a tilted periodic potential

The diffusion of an overdamped Brownian particle in a tilted periodic potential is known to exhibit a pronounced enhancement over the free thermal diffusion within a small interval of tilt values. Here we show that weak disorder in the form of small, time-independent deviations from a strictly spatially periodic potential may further boost this diffusion peak by orders of magnitude. Our general theoretical predictions are in excellent agreement with experimental observations.