It has been recently found that the so called isoperiodic stable structures (ISSs) have a fundamental role in the classical current behavior of dissipative ratchets [Phys. Rev. Lett. {\bf 106}, 234101 (2011)]. Here I analyze their quantum counterparts, the quantum ISSs (QISSs), which have a fundamental role in the quantum current behavior. QISSs have the simple attractor shape of those ISSs which settle down in short times. However, in the majority of the cases they are strongly different from the ISSs, looking approximately the same as the quantum chaotic attractors that are at their vicinity in parameter space. By adding thermal fluctuations of the size of $\hbar_{\rm eff}$ to the ISSs I am able to obtain very good approximations to the QISSs. I conjecture that in general, quantum chaotic attractors could be well approximated by means of just the classical information of a neighboring ISS plus thermal fluctuations. I expect to find this behavior in quantum dissipative systems in general.
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 statistic…
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 $\hbar_{\rm eff}$ 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 dis…
Quantum directed transport can be realized in non-interacting, deterministic, chaotic systems by appropriately breaking the spatio-temporal symmetries in the potential. In this work, the focus is on the class of interacting quantum systems whose classical limit is chaotic. In this limit, one subsystem effectively acts as a source of "noise" to the other leading to temporal symmetry breaking. Thus, the quantum directed currents can be generated with two ingredients -- broken spatial symmetry in the potential and presence of interactions. This is demonstrated in two-body interacting kicked rotor…
Using matter waves that are trapped in a deep optical lattice, dissipationless directed transport is demonstrated to occur if the single-band quantum dynamics is periodically tilted on one half of the lattice by a monochromatic field. Most importantly, the directed transport can exist for almost all system parameters, even after averaged over a broad range of single-band initial states. The directed transport is theoretically explained within ac-scattering theory. Total reflection phenomena associated with the matter waves travelling from a tilting-free region to a tilted region are emphasized…
We explore the dynamics of non-interacting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner. We find superdiffusion in position space for all parameters regimes. A directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time-driven potential. Magnitude and direction of the current are tunable. Several mechanisms for tra…
We investigate theoretically the transfer of excitation along a one dimensional chain of monomers for a situation in which initially the excitation is shared coherently by two monomers. We show that depending on the relative phase between the two monomers strong directionality of the energy transfer is possible. It is also investigated how dephasing, induced by an environment, influences this directed transport.
We obtained analytical expressions considering a directed continuous-time quantum walk on a directed infinite line using Bessel functions, expanding previous results in the literature, for a general initial condition. We derive the equation for the probability distribution, and show how to recover normal and enhanced decay rates for the survival probability by adjusting the phase factor of the direction of the graph. Our result shows that the mean and standard deviation for a specific non-local initial condition does not depend on the direction.
We investigate coherent control of single particles held in a bipartite optical lattice via a combined high-frequency modulation. Our analytical results show that for the photon resonance case the quantum tunneling and dynamical localization depend on the phase difference between the modulation components, which leads to a different route of the coherent destruction of tunneling and a simple method for stabilizing the system to implement the directed transport. The results could be referable for manipulating the transport characterization of the similar tilted and shaken optical or solid-state…
We study the coherent dynamics of excitations on vibrating chains. By applying an external field and matching the field strength with the oscillation frequency of the chain it is possible to obtain an (average) transport of an initial Gaussian wave packet. We distinguish between a uniform oscillation of all nodes of the chain and the chain being in its lowest eigenmode. Both cases can lead to directed transport.
We give the first example of faster transport with a quantum walk on an inherently directed graph, on the directed line with a variable number of self-loops at each vertex. These self-loops can be thought of as adding a number of small dimensions. This is a discrete time quantum walk using the Fourier transform coin, where the walk proceeds a distance $Θ(1)$ in constant time compared to $Θ(1/n)$ classically, independent of the number of these small dimensions. The analysis proceeds by reducing this walk to a walk with a two dimensional coin.
We study the quantum dynamics of Gaussian wave packets on star graphs whose arms feature each a periodic potential and an external time-dependent field. Assuming that the potentials and the field can be manipulated separately for each arm of the star, we show that it is possible to manipulate the direction of the motion of a Gaussian wave packet through the bifurcation point by a suitable choice of the parameters of the external fields. In doing so, one can achieve a transmission of the wave packet into the desired arm with nearly 70\% while also keeping the shape of the wave packet approximat…
We study experimentally and theoretically discrete solitons in crystalline structures consisting of several tens of laser-cooled ions confined in a radiofrequency trap. Resonantly exciting localized, spectrally gapped vibrational modes of the soliton, a nonlinear mechanism leads to a nonequilibrium steady state of the continuously cooled crystal. We find that the propagation and the escape of the soliton out of its a quasi-one-dimensional channel can be described as a thermal activation mechanism. We control the effective temperature of the soliton's collective coordinate by the amplitude of t…
We introduce a fully coherent way for directed transport of localized atoms in optical lattices by regularly performing phase shifts on the lattice potential during the free evolution of the system. This paves the way for realizing a possible cold atom quantum computer in which entangling gates operate by bringing two individual atoms in the proximity of each other and letting them to interact. The speed of our protocol is determined by the tunneling amplitudes of the atoms and thus is much faster than the speed of the dynamics resulted from superexchange interaction in spin chains. Our scheme…
We point out that in higher dimensions, in contrast to the one dimensional case considered usually, Bloch oscillation driven by a static force can induce transport of the wave packet. The wave packet oscillates constantly, but on a larger time scale it drifts at a constant velocity permanently. As a noteworthy feature, the net transport in the long run is always normal to the external force and thus controlled by it. We verify this prediction numerically and discuss its experimental realization both with cold atoms in optical lattices and with two dimensional photonic lattices.
We present a self-contained engine, which is made of one or more two-level systems, each of which is coupled to a single bath, as well as to a common load composed of a particle on a tilted lattice. We show that the energy and the entropy absorbed by the spins are transferred to the particle thus setting it into upward motion at an average constant speed, even when driven by a single spin connected to a single bath. When considering an ensemble of different spins, the velocity of the particle is larger when the tilt is on resonance with any of the spins' energy splitting. Interestingly, we fin…
We study a chaotic ratchet system under the influence of a thermal environment. By direct integration of the Lindblad equation we are able to analyze its behavior for a wide range of couplings with the environment, and for different finite temperatures. We observe that the enhancement of the classical and quantum currents due to temperature depend strongly on the specific properties of the system. This makes difficult to extract universal behaviors. We have also found that there is an analogy between the effects of the classical thermal noise and those of the finite $\hbar$ size. These results…
We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localised initial conditions, associated with a polaron solution, in conjunction with a nonreversion symmetric static electron on-site potential constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localised initial conditions, violation of parity prevents the existence of pairs of counter-propagating trajectories, thus allowing for a directed current despite the time-rev…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by tuning a model parameter $α$. We provide analytic solutions to the quantum walks for the star and circulant graph classes that are valid for an arbitrary value of the number of nodes $N$, time $t$ and the model parameter $α$. We discuss quantitative and qualitative aspects of quantum walks based on directed graphs and their undirected counterparts. Numerica…
A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from $N$ to $\sqrt{N}$, where $N$ is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment impleme…
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 $\hbar_{\rm eff}$ values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing uctuations of size $\hbar_{\rm eff}$ 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 …
We study motion of a quantum wavepacket in a one-dimensional potential with correlated disorder. Presence of long-range potential correlations allows for existence of both localized and extended states. Weak time-dependent perturbation in the form of a fluctuating plane wave is superimposed onto the potential. This model can be realized in experiments with optically trapped cold atoms. Time-dependent perturbation causes transitions between localized and extended states. Owing to violation of space-time symmetries, there arises atomic current which is codirectional with the wave-like perturbati…
We present a very simple model for realizing directed transport with cold atoms in a pair of periodically flashed optical lattices. The origin of this ratchet effect is explained and its robustness demonstrated under imperfections typical of cold atom experiments. We conclude that our model offers a clear-cut way to implement directed transport in an atom optical experiment.
We numerically investigate the quantum transport in a coupled kicked rotors with the $\mathcal{PT}$-symmetric potential. We find that the spontaneous $\mathcal{PT}$-symmetry breaking of wavefunctions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of the $\mathcal{PT}$-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strengt…
We analyze the performance of quantum ratchets by considering the dynamics of an initially localized wave packet loaded into a flashing periodic potential. The directed center-of-mass motion can be initiated by the uniform modulation of the potential height, provided that the modulation protocol breaks all relevant time- and spatial reflection symmetries. A poor performance of quantum ratchet transport is characterized by a slow net motion and a fast diffusive spreading of the wave packet, while the desirable optimal performance is the contrary. By invoking a quantum analog of the classical Pé…
By studying a modified (unbiased) quantum multibaker map, we were able to obtain a {\em finite} asymptotic quantum current without a classical analogue. This result suggests a general method for the design of {\em purely} quantum ratchets, and sheds light on the investigation of the mechanisms leading to net transport generation by breaking symmetries of quantum systems. Moreover, we propose the multibaker map as a resource to study directed transport phenomena in chaotic systems without bias. In fact, this is a paradigmatic model in classical and quantum chaos, but also in statistical mechani…
We present theoretical and numerical results on the dynamics of ultracold atoms in an accelerated single- and double-periodic optical lattice. In the single-periodic potential Bloch oscillations can be used to generate fast directed transport with very little dispersion. The dynamics in the double-periodic system is dominated by Bloch-Zener oscillations, i.e. the interplay of Bloch oscillations and Zener tunneling between the subbands. Apart from directed transport, the latter system permits various interesting applications, such as widely tunable matter wave beam splitters and Mach-Zehnder in…
We raise the question whether there is a way to characterize the quantum information transport properties of a medium or material. For this analysis the special features of quantum information have to be taken into account. We find that quantum communication over an isotropic medium, as opposed to classical information transfer, requires the transmitter to direct the signal towards the receiver. Furthermore, for large classes of media there is a threshold, in the sense that `sufficiently much' of the signal has to be collected. Therefore, the medium's capacity for quantum communication can be …
