Directed transport of atoms in a Hamiltonian quantum ratchet

Quantum ratchet with Lindblad rate equations

A quantum random-walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equations that incorporate the transition rates between the two lattice states. Leveraging the system's symmetries, the particle velocity can be described using a finite set of equations, even though the state space is of infinite dimension. These equations yield an analytical expression for the velocity in the long-time limit, which is employed to analyze the characteristics of directed motion. Notably, the velocity can exhibit multiple inversions, and to achieve directed motion, distinct, nonzero transition rates between lattice states are required.

Interaction-induced directed transport in quantum chaotic subsystems

Quantum directed transport can be realized in noninteracting, deterministic, chaotic systems by appropriately breaking the spatiotemporal symmetries in the potential. In this work, the focus is on the class of interacting two-body quantum systems whose classical limit is chaotic. It is shown that one subsystem effectively acts as a source of "noise" to the other leading to intrinsic temporal symmetry breaking. Then, the quantum directed currents, even if prohibited by symmetries in the composite system, can be realized in the subsystems. This current is of quantum origin and does not arise from semiclassical effects. This protocol provides a minimal framework-broken spatial symmetry in the potential and presence of interactions-for realizing directed transport in interacting chaotic systems. It is also shown that the magnitude of directed current undergoes multiple current reversals upon varying the interaction strength and this allows for controlling the currents. It is explicitly demonstrated in the two-body interacting kicked rotor model. The interaction-induced mechanism for subsystem directed currents would be applicable to other interacting quantum systems as well.

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.

Roughness induced current reversal in fractional hydrodynamic memory

The existence of a corrugated surface is of great importance and ubiquity in biological systems, exhibiting diverse dynamic behaviors. However, it has remained unclear whether such rough surface leads to the current reversal in fractional hydrodynamic memory. We investigate the transport of a particle within a rough potential under external forces in a subdiffusive media with fractional hydrodynamic memory. The results demonstrate that roughness induces current reversal and a transition from no transport to transport. These phenomena are analyzed through the subdiffusion, Peclet number, useful work, input power, and thermodynamic efficiency. The analysis reveals that transport results from energy conversion, wherein time-dependent periodic force is partially converted into mechanical energy to drive transport against load, and partially dissipated through environmental absorption. In addition, the findings indicate that the size and shape of ratchet tune the occurrence and disappearance of the current reversal, and control the number of times of the current reversal occurring. Furthermore, we find that temperature, friction, and load tune transport, resonant-like activity, and enhanced stability of the system, as evidenced by thermodynamic efficiency. These findings may have implications for understanding dynamics in biological systems and may be relevant for applications involving molecular devices for particle separation at the mesoscopic scale.

Brillouin propagation modes of cold atoms undergoing Sisyphus cooling

An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. The calculations are for a J_{g}=1/2→J_{e}=3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.

Laser-Driven Petahertz Electron Ratchet Nanobubbles

A laser-driven quantum electron ratchet nanodevice is proposed. The ratchet consists of a series of disconnected bubble-shaped nanodiode structures with a sharp tip to induce a large field enhancement. A laser pulse is used to create a plasmon oscillation in the vertical direction, and the shape of the bubble funnels the electrons toward the sharp tip leading to net electron transport in the horizontal direction. The electron current carries the fingerprint of the driving laser field. The system is modeled by using the time-dependent orbital free density functional theory with nanostructures containing thousands of atoms.

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.

Collective transient ratchet transport induced by many elastically interacting particles

Several dynamical systems in nature can be maintained out-of-equilibrium, either through mutual interaction of particles or by external fields. The particle’s transport and the transient dynamics are landmarking of such systems. While single ratchet systems are genuine candidates to describe unbiased transport, we demonstrate here that coupled ratchets exhibit collective transient ratchet transport. Extensive numerical simulations for up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=1024$$\end{document}N=1024 elastically interacting ratchets establish the generation of large transient ratchet currents (RCs). The lifetimes of the transient RCs increase with N and decrease with the coupling strength between the ratchets. We demonstrate one peculiar case having a coupling-induced transient RC through the asymmetric destruction of attractors. Results suggest that physical devices built with coupled ratchet systems should present large collective transient transport of particles, whose technological applications are undoubtedly appealing and feasible.

Ratchet universality in coupled dissipative oscillators without external bias

Directed ratchet transport is generally observed in nonautonomous systems as a result of the interplay of nonlinearity, symmetry breaking, and nonequilibrium fluctuations. Here we demonstrate that ratchet dynamics can appear in significant transporting degrees of freedom of dissipative coupled systems without external bias due to unidirectional coupling of oscillatory degrees of freedom (which are also nonbiasing in any direction), while optimal enhancement of directed ratchet transport occurs when the initial conditions and parameters of such ratcheting degrees of freedom are suitably chosen as predicted by the theory of ratchet universality. The simple case of linear oscillatory degrees of freedom is discussed in detail, and numerical experiments are described which confirm all the theoretical predictions, including the dependence of current (velocity) reversals on the initial conditions and the ratcheting degrees-of-freedom parameters. This autonomous ratchet scenario could be exploited technologically, for instance, in the context of noncontact, rack-and-pinion type, nanoscale setups with coupling from the lateral Casimir force, and is relevant for studies of molecular motors in the biological realm.

Ratchet universality in the bidirectional escape from a symmetric potential well

The present work discusses symmetry-breaking-induced bidirectional escape from a symmetric metastable potential well by the application of zero-average periodic forces in the presence of dissipation. We characterized the interplay between heteroclinic instabilities leading to chaotic escape and breaking of a generalized parity symmetry leading to directed ratchet escape to an attractor either at ∞ or at -∞. Optimal enhancement of directed ratchet escape is found to occur when the wave form of the zero-average periodic force acting on the damped driven oscillator matches as closely as possible to a universal wave form, as predicted by the theory of ratchet universality. Specifically, the optimal approximation to the universal force triggers the almost complete destruction of the nonescaping basin for driving amplitudes which are systematically lower than those corresponding to a symmetric periodic force having the same period. We expect that this work could be potentially useful in the control of elementary dynamic processes characterized by multidirectional escape from a potential well, such as forced chaotic scattering and laser-induced dissociation of molecular systems, among others.

Strong-chaos-caused negative mobility in a periodic substrate potential

We numerically investigate negative mobility of an inertial Brownian particle moving in a periodic double-well substrate potential in the presence of a time-periodic force and a constant bias. For the deterministic case, we find from the average velocity that the varying shape parameter and driving forces can cause negative mobility, differential negative mobility, and giant positive mobility. We analyze these findings via the bifurcation diagram and maximal Lyapunov exponent and find that certain chaos can give rise to negative mobility. For the presence of a Gaussian color noise, the results suggest that the noise intensity can enhance or result in negative and positive mobilities, whereas correlation time can enhance, weaken, or even eliminate them. On the basis of the time series, phase-space map, and power spectrum of various attractors, we unveil how these mobilities connect to strong chaotic attractors (SCAs), including both stable attractor and unstable attractors, and propose an underlying mechanism that SCAs can result in the negative mobility, whereas other attractors do not. Our findings may be potentially useful for research on anomalous transports of the particles and on designs of various devices, such as atomic chains, crystals with dislocations, and superconducting nanowires, etc.

Thouless pumping in disordered photonic systems

Thouless charge pumping protocols provide a route for one-dimensional systems to realize topological transport. Here, using arrays of evanescently coupled optical waveguides, we experimentally demonstrate bulk Thouless pumping in the presence of disorder. The degree of pumping is quite tolerant to significant deviations from adiabaticity as well as the addition of system disorder until the disorder is sufficiently strong to reduce the bulk mobility gap of the system to be on the scale of the modulation frequency of the system. Moreover, we show that this approach realizes near-full-unit-cell transport per pump cycle for a physically relevant class of localized initial system excitations. Thus, temporally pumped systems can potentially be used as a design principle for a new class of modulated slow-light devices that are resistant to system disorder.

Negative friction and mobilities induced by friction fluctuation

We study the transport phenomena of an inertial Brownian particle in a symmetric potential with periodicity, which is driven by an external time-periodic force and an external constant bias for both cases of the deterministic dynamics and the existence of friction coefficient fluctuations. For the deterministic case, it is shown that for suitable parameters, the existence of certain appropriate friction coefficients can enhance the transport of the particle, which may be interpreted as the negative friction coefficient; additionally, there coexist absolute, differential negative, and giant positive mobilities with increasing friction coefficients in the system. We analyze physical mechanisms hinted behind these findings via basins of attraction. For the existence of friction coefficient fluctuations, it is shown that the fluctuation can enhance or weaken, even eliminate these phenomena. We present the probability distribution of the particle's velocity to interpret these mobilities and the suitable parameters' regimes of these phenomena. In order to further understand the physical mechanism, we also study diffusions corresponding to these mobilities and find that for the small fluctuation, the negative friction appears, and there coexists absolute negative mobility, superdiffusion, and ballistic diffusion, whereas all of them vanish for the large fluctuation. Our findings may extensively exist in materials, including different defects, strains, the number of interfacial hydrogen bonds, the arrangements of ions, or graphite concentrations, which hints at the existence of different friction coefficients.

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.

Avoided Crossing and sub-Fourier-sensitivity in Driven Quantum Systems

The response of a linear system to an external perturbation is governed by the Fourier limit, with the inverse of the interaction time constituting a lower limit for the system bandwidth. This does not hold for nonlinear systems, which can thus exhibit sub-Fourier-behavior. The present Letter identifies a mechanism for sub-Fourier-sensitivity in driven quantum systems, which relies on avoided crossing between Floquet states. Features up to three orders of magnitude finer than the Fourier limit are presented.

Current reversals of active particles in time-oscillating potentials

Rectification of interacting active particles is numerically investigated in a two-dimensional time-oscillating potential. It is found that the oscillation of the potential and the self-propulsion of active particles are two different types of nonequilibrium driving, which can induce net currents with opposite directions. For a given asymmetry of the potential, the direction of the transport is determined by the competition of the self-propulsion and the oscillation of the potential. There exists an optimal oscillating angular frequency (or self-propulsion speed) at which the average velocity takes its maximal positive or negative value. Remarkably, when the oscillation of the potential competes with the self-propulsion, the average velocity can change direction several times due to the change in the oscillating frequency. Especially, particles with different self-propulsion velocities will move in opposite directions and can be separated. Our results provide a novel and convenient method for controlling and manipulating the transport (or separation) of active particles.

Asymptotic theory of quasiperiodically driven quantum systems

The theoretical treatment of quasiperiodically driven quantum systems is complicated by the inapplicability of the Floquet theorem, which requires strict periodicity. In this work we consider a quantum system driven by a biharmonic driving and examine its asymptotic long-time limit, the limit in which features distinguishing systems with periodic and quasiperiodic driving occur. Also, in the classical case this limit is known to exhibit universal scaling, independent of the system details, with the system's reponse under quasiperiodic driving being described in terms of nearby periodically driven system results. We introduce a theoretical framework appropriate for the treatment of the quasiperiodically driven quantum system in the long-time limit and derive an expression, based on Floquet states for a periodically driven system approximating the different steps of the time evolution, for the asymptotic scaling of relevant quantities for the system at hand. These expressions are tested numerically, finding excellent agreement for the finite-time average velocity in a prototypical quantum ratchet consisting of a space-symmetric potential and a time-asymmetric oscillating force.

Environmental rocking ratchet: Environmental rectification by a harmonically driven avoided crossing

We propose a rocking ratchet designed as a symmetric quantum two-state system driven by a single periodic harmonic force and influenced symmetrically by thermal fluctuations. We show that the necessary broken symmetry can dynamically be achieved by a thermal environment that couples to the energy difference between the two states and the tunnel coupling between them. The quantum two-state system is driven by the harmonic periodic drive through its avoided crossing. The correspondingly driven dissipative quantum dynamics results on average in a finite population difference between both states. This then causes directed particle transport.

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.

Signatures of classical structures in the leading eigenstates of quantum dissipative systems

By analyzing a paradigmatic example of the theory of dissipative systems-the classical and quantum dissipative standard map-we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kinds of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.

Light-responsive organic flashing electron ratchet

Ratchets are nonequilibrium devices that produce directional motion of particles from nondirectional forces without using a bias, and are responsible for many types of biological transport, which occur with high yield despite strongly damped and noisy environments. Ratchets operate by breaking time-reversal and spatial symmetries in the direction of transport through application of a time-dependent potential with repeating, asymmetric features. This work demonstrates the ratcheting of electrons within a highly scattering organic bulk-heterojunction layer, and within a device architecture that enables the application of arbitrarily shaped oscillating electric potentials. Light is used to modulate the carrier density, which modifies the current with a nonmonotonic response predicted by theory. This system is driven with a single unbiased sine wave source, enabling the future use of natural oscillation sources such as electromagnetic radiation.

Mechanisms of Symmetry Breaking in a Multidimensional Flashing Particle Ratchet

Ratcheting is a mechanism that produces directional transport of particles by rectifying nondirectional energy using local asymmetries rather than a net bias in the direction of transport. In a flashing ratchet, an oscillating force (here, an AC field) is applied perpendicular to the direction of transport. In an effort to explore the properties of current experimentally realizable ratchet systems, and to design new ones, this paper describes classical simulations of a damped flashing ratchet that transports charged nanoparticles within a transport layer of finite, non-zero thickness. The thickness of the layer, and the decay of the applied field in the z-direction throughout that thickness, provide a mechanism of symmetry breaking in the system that allows the ratchet to produce directional transport using a temporally unbiased oscillation of the AC driving field, a sine wave. Sine waves are conveniently produced experimentally or harvested from natural sources but cannot produce transport in a 1D or pseudo-1D system. The sine wave drive produces transport velocities an order of magnitude higher than those produced by the common on/off drive, but lower than those produced by a temporally biased square wave drive (unequal durations of the positive and negative states). The dependence of the particle velocity on the thickness of the transport layer, and on the homogeneity of the oscillating field within the layer, is presented for all three driving schemes.

Classical counterparts of quantum attractors in generic dissipative systems

In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.

Transport and diffusion properties of Brownian particles powered by a rotating wheel

Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium and induce the directed transport in an asymmetric potential. It is found that the direction of the transport along the potential is determined by the asymmetry of the potential and the position of the wheel. The average velocity is a peaked function of the angular speed (or the diffusion coefficient) and the position of the peak shifts to large angular speed (or diffusion coefficient) when the diffusion coefficient (or the angular speed) increases. There exists an optimal angular speed (or diffusion coefficient) at which the effective diffusion coefficient takes its maximal value. Remarkably, the giant acceleration of diffusion is observed by suitably adjusting the system parameters. The parameters corresponding to the maximum effective diffusion coefficient are not the same as the parameters at which average velocity is maximum.

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.

Non-Markovian linear response theory for quantum open systems and its applications

The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.

Quantum coherent tractor beam effect for atoms trapped near a nanowaveguide

We propose several schemes to realize a tractor beam effect for ultracold atoms in the vicinity of a few-mode nanowaveguide. Atoms trapped near the waveguide are transported in a direction opposite to the guided mode propagation direction. We analyse three specific examples for ultracold (23)Na atoms trapped near a specific nanowaveguide (i.e. an optical nanofibre): (i) a conveyor belt-type tractor beam effect, (ii) an accelerator tractor beam effect, and (iii) a quantum coherent tractor beam effect, all of which can effectively pull atoms along the nanofibre toward the light source. This technique provides a new tool for controlling the motion of particles near nanowaveguides with potential applications in the study of particle transport and binding as well as atom interferometry.

Exposing local symmetries in distorted driven lattices via time-averaged invariants

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a valuable tool for detecting deformations of a spatial symmetry in static and driven lattices. In the static case the invariance of the two-point currents is related to the presence of time-reversal invariance and/or probability current conservation. The obtained insights into the wave functions are further exploited for a symmetry-based convergence check which is applicable for globally broken but locally retained potential symmetries.

Identification of two mechanisms for current production in a biharmonic flashing electron ratchet

Ratchets rectify the motion of randomly moving particles, which are driven by isotropic sources of energy such as thermal and chemical energy, without applying a net, time-averaged force between source and drain. This paper describes the behavior of a damped electron, modeled by a quantum Lindblad master equation, within a flashing ratchet (a one-dimensional potential that oscillates between a flat surface and a periodic asymmetric surface). By examining the complete space of all biharmonic potential shapes and a large range of oscillation frequencies, two modes of ratchet operation, differentiated by their oscillation frequencies (relative to the rate of electron relaxation), are identified. Slow-oscillating, strong friction ratchets operate by a classical, overdamped mechanism. In fast-oscillating, weak friction ratchets, current is primarily produced when the frequency of the oscillating potential is resonant with the beating of the electron wave function in the potential well. The shape of the ratchet potential determines the direction of the current (and, in some cases, straightforwardly accounts for current reversals), but the maximum achievable current at any shape is controlled by the degree of friction applied to the electron.

Controlling chaos-assisted directed transport via quantum resonance

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏ_{eff} values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏ_{eff} and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.

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.

Experimental control of transport resonances in a coherent quantum rocking ratchet

The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose–Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport.

The ratchet effect can be used as a tool to control coherent quantum transport of ultra-cold atoms. Here, the authors demonstrate a rocking quantum ratchet with a rubidium BEC, and reveal the existence of quantum transport resonances.

Hidden Symmetries, Instabilities, and Current Suppression in Brownian Ratchets

The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of hidden symmetries, which escape identification by the standard symmetry analysis, and which require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.

General response formula and application to topological insulator in quantum open system

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

Classical to quantum correspondence in dissipative directed transport

We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏ(eff) values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results-obtained for the mean currents and asymptotic distributions only-and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.

Quantum ratchet in two-dimensional semiconductors with Rashba spin-orbit interaction

Ratchet is a device that produces direct current of particles when driven by an unbiased force. We demonstrate a simple scattering quantum ratchet based on an asymmetrical quantum tunneling effect in two-dimensional electron gas with Rashba spin-orbit interaction (R2DEG). We consider the tunneling of electrons across a square potential barrier sandwiched by interface scattering potentials of unequal strengths on its either sides. It is found that while the intra-spin tunneling probabilities remain unchanged, the inter-spin-subband tunneling probabilities of electrons crossing the barrier in one direction is unequal to that of the opposite direction. Hence, when the system is driven by an unbiased periodic force, a directional flow of electron current is generated. The scattering quantum ratchet in R2DEG is conceptually simple and is capable of converting a.c. driving force into a rectified current without the need of additional symmetry breaking mechanism or external magnetic field.

Quantum parameter space of dissipative directed transport

Quantum manifestations of isoperiodic stable structures (QISSs) have a crucial role in the current behavior of quantum dissipative ratchets. In this context, the simple shape of the ISSs has been conjectured to be an almost exclusive feature of the classical system. This has drastic consequences for many properties of the directed currents, the most important one being that it imposes a significant reduction in their maximum values, thus affecting the attainable efficiency at the quantum level. In this work we prove this conjecture by means of comprehensive numerical explorations and statistical analysis of the quantum states. We are able to describe the quantum parameter space of a paradigmatic system for different values of ℏ(eff) in great detail. Moreover, thanks to this we provide evidence on a mechanism that we call parametric tunneling by which the sharp classical borders of the regions in parameter space become blurred in the quantum counterpart. We expect this to be a common property of generic dissipative quantum systems.

Asymmetric frequency conversion in nonlinear systems driven by a biharmonic pump

A novel mechanism of asymmetric frequency conversion is investigated in nonlinear dispersive devices driven parametrically with a biharmonic pump. When the relative phase between the first and second harmonics combined in a two-tone pump is appropriately tuned, nonreciprocal frequency conversion, either upward or downward, can occur. Full directionality and efficiency of the conversion process is possible, provided that the distribution of pump power over the harmonics is set correctly. While this asymmetric conversion effect is generic, we describe its practical realization in a model system consisting of a current-biased, resistively shunted Josephson junction. Here, the multiharmonic Josephson oscillations, generated internally from the static current bias, provide the pump drive.

Symmetries and transport in site-dependent driven quantum lattices

We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum. Specifically, we show how exact crossings can be converted into avoided ones, while the widths of these resulting avoided crossings can be engineered by adjusting parameters of the local driving. Asymptotic currents are shown to be controllable over a certain parameter range.

Backaction-driven transport of Bloch oscillating atoms in ring cavities

We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counterpropagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.

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.

Adiabatic quantum motors

When parameters are varied periodically, charge can be pumped through a mesoscopic conductor without applied bias. Here, we consider the inverse effect in which a transport current drives a periodic variation of an adiabatic degree of freedom. This provides a general operating principle for adiabatic quantum motors which we discuss here in general terms. We relate the work performed per cycle on the motor degree of freedom to characteristics of the underlying quantum pump and discuss the motors' efficiency. Quantum motors based on chaotic quantum dots operate solely due to quantum interference, and motors based on Thouless pumps have ideal efficiency.

Engineering novel optical lattices

Optical lattices have developed into a widely used and highly recognized tool to study many-body quantum physics with special relevance for solid state type systems. One of the most prominent reasons for this success is the high degree of tunability in the experimental setups. While at the beginning quasi-static, cubic geometries were mainly explored, the focus of the field has now shifted toward new lattice topologies and the dynamical control of lattice structures. In this review we intend to give an overview of the progress recently achieved in this field on the experimental side. In addition, we discuss theoretical proposals exploiting specifically these novel lattice geometries.

Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands

We study the response of ultracold atoms to a weak force in the presence of a temporally strongly modulated optical lattice potential. It is experimentally demonstrated that the strong ac driving allows for a tailoring of the mobility of a dilute atomic Bose-Einstein condensate with the atoms moving ballistically either along or against the direction of the applied force. Our results are in agreement with a theoretical analysis of the Floquet spectrum of a model system, thus revealing the existence of diabatic Floquet bands in the atoms' band spectra and highlighting their role in the nonequilibrium transport of the atoms.

Magnetic quantum ratchet effect in graphene

A periodically driven system with spatial asymmetry can exhibit a directed motion facilitated by thermal or quantum fluctuations. This so-called ratchet effect has fascinating ramifications in engineering and natural sciences. Graphene is nominally a symmetric system. Driven by a periodic electric field, no directed electric current should flow. However, if the graphene has lost its spatial symmetry due to its substrate or adatoms, an electronic ratchet motion can arise. We report an experimental demonstration of such an electronic ratchet in graphene layers, proving the underlying spatial asymmetry. The orbital asymmetry of the Dirac fermions is induced by an in-plane magnetic field, whereas the periodic driving comes from terahertz radiation. The resulting magnetic quantum ratchet transforms the a.c. power into a d.c. current, extracting work from the out-of-equilibrium electrons driven by undirected periodic forces. The observation of ratchet transport in this purest possible two-dimensional system indicates that the orbital effects may appear and be substantial in other two-dimensional crystals such as boron nitride, molybdenum dichalcogenides and related heterostructures. The measurable orbital effects in the presence of an in-plane magnetic field provide strong evidence for the existence of structure inversion asymmetry in graphene.