Three-Dimensional Localized-Delocalized Anderson Transition in the Time Domain.

Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modeled with the help of space periodic potentials, crystalline phenomena in time can be modeled by periodically driven systems. Disorder in the periodic driving can lead to Anderson localization in time: the probability for detecting a system at a fixed point of configuration space becomes exponentially localized around a certain moment in time. We here show that a three-dimensional system exposed to a properly disordered pseudoperiodic driving may display a localized-delocalized Anderson transition in the time domain, in strong analogy with the usual three-dimensional Anderson transition in disordered systems. Such a transition could be experimentally observed with ultracold atomic gases.

Directed transport of atoms in a Hamiltonian quantum ratchet.

Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.

Many-body coherent destruction of tunneling.

A new route to coherent destruction of tunneling is established by considering a monochromatic fast modulation of the self-interaction strength of a many-boson system. The modulation can be tuned such that only an arbitrarily, a priori prescribed number of particles are allowed to tunnel. The associated tunneling dynamics is sensitive to the odd or even nature of the number of bosons.

Inhomogeneous soliton ratchets under two ac forces.

We extend our previous work on soliton ratchet devices [L. Morales-Molina, Eur. Phys. J. B 37, 79 (2004)] to consider the joint effect of two ac forces including nonharmonic drivings, as proposed for particle ratchets by Savele'v [Europhys. Lett. 67, 179 (2004); Phys. Rev. E 70, 066109 (2004)]. Current reversals due to the interplay between the phases, frequencies, and amplitudes of the harmonics are obtained. An analysis of the effect of the damping coefficient on the dynamics is presented. We show that solitons give rise to nontrivial differences in the phenomenology reported for particle systems that arise from their extended character. A comparison with soliton ratchets in homogeneous systems with biharmonic forces is also presented. This ratchet device may be an ideal candidate for Josephson junction ratchets with intrinsic large damping.

Trapping of discrete solitons by defects in nonlinear waveguide arrays.

We study the trapping process of moving discrete solitons by linear and nonlinear impurities embedded in a one-dimensional nonlinear cubic array. We show that there exist specific values for the strength of the impurity and for the angle where a strong trapping is obtained. We introduce a criterion for studying the scattering dynamics of localized waves in nonlinear extended systems where the trapping of energy takes place.

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems.

We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a biharmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, X(t), and its width, l(t), we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width l(t) oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necessary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and phi4 systems, which are seen to exhibit the same qualitative behavior. Our results show features similar to those obtained in recent experimental work on dissipation induced symmetry breaking.

Ratchet behavior in nonlinear Klein-Gordon systems with pointlike inhomogeneities.

We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic, asymmetric lattice of pointlike inhomogeneities. We explain the underlying rectification mechanism within a collective coordinate framework, which shows that such a system behaves as a rocking ratchet for point particles. Careful attention is given to the kink width dynamics and its role in the transport. We also analyze the robustness of our kink rocking ratchet in the presence of noise. We show that the noise activates unidirectional motion in a parameter range where such motion is not observed in the noiseless case. This is subsequently corroborated by the collective variable theory. An explanation for this phenomenon is given.

Internal mode mechanism for collective energy transport in extended systems.

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explain earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.