Nonsinusoidal current and current reversals in a gating ratchet

Multiple Current Reversals Using Superimposed Driven Lattices

We demonstrate that directed transport of particles in a two dimensional driven lattice can be dynamically reversed multiple times by superimposing additional spatially localized lattices on top of a background lattice. The timescales of such current reversals can be flexibly controlled by adjusting the spatial locations of the superimposed lattices. The key principle behind the current reversals is the conversion of the particle dynamics from chaotic to ballistic, which allow the particles to explore regions of the underlying phase space which are inaccessible otherwise. Our results can be experimentally realized using cold atoms in driven optical lattices and allow for the control of transport of atomic ensembles in such setups.

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.

Exact stationary solutions of the parametrically driven and damped nonlinear Dirac equation

Two exact stationary soliton solutions are found in the parametrically driven and damped nonlinear Dirac equation. The parametric force considered is a complex ac force. The solutions appear when their frequencies are locked to half the frequency of the parametric force, and their phases satisfy certain conditions depending on the force amplitude and on the damping coefficient. Explicit expressions for the charge, the energy, and the momentum of these solutions are provided. Their stability is studied via a variational method using an ansatz with only two collective coordinates. Numerical simulations confirm that one of the solutions is stable, while the other is an unstable saddle point. Consequently, the stabilization of damped Dirac solitons can be achieved via time-periodic parametric excitations.

Symmetry breaking: Abnormal transport induced by mass modulation

Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.

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.