In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of ``Brownian motors.'' In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

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Artificial Brownian motors: Controlling transport on the nanoscale

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

We develop the Floquet scattering theory for quantum-mechanical pumping in mesoscopic conductors. The nonequilibrium distribution function, the dc charge, and heat currents are investigated at arbitrary pumping amplitude and frequency. For mesoscopic samples with a discrete spectrum we predict a sign reversal of the pumped current when the pump frequency is equal to the level spacing in the sample. This effect allows us to measure the phase of the transmission coefficient through the mesoscopic sample. We discuss the necessary symmetry conditions (both spatial and temporal) for pumping.

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Floquet scattering theory of quantum pumps

The on-demand emission of coherent and indistinguishable electrons by independent synchronized sources is a challenging task of quantum electronics, in particular regarding its application for quantum information processing. Using two independent on-demand electron sources, we triggered the emission of two single-electron wave packets at different inputs of an electronic beam splitter. Whereas classical particles would be randomly partitioned by the splitter, we observed two-particle interference resulting from quantum exchange. Both electrons, emitted in indistinguishable wave packets with synchronized arrival time on the splitter, exited in different outputs as recorded by the low-frequency current noise. The demonstration of two-electron interference provides the possibility of manipulating coherent and indistinguishable single-electron wave packets in quantum conductors.

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Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources

Electrons strongly interact with other electrons and their environment, making it extremely difficult to isolate and detect a single moving electron in a similar way to single photons in quantum optics experiments. But now, in two unrelated reports, Hermelin et al. and McNeil et al. demonstrate that it is possible to emit a single electron from one quantum dot and detect it again with high efficiency after longevity propagation over several micrometres to another quantum dot. The single electron is isolated from other electrons as it is sent into a one-dimensional channel, where it is carried along on a surface acoustic wave induced by microwave excitation. McNeil et al. also show that the same electron can be transferred back and forth up to 60 times, a total distance of 0.25 millimetres. This work demonstrates a new way of transporting a single quantum particle over a long distance in nanostructures, and could pave the way for a range of quantum optics experiments and for quantum information circuits based on single electrons. Electrons in a metal are indistinguishable particles that interact strongly with other electrons and their environment. Isolating and detecting a single flying electron after propagation, in a similar manner to quantum optics experiments with single photons1,2, is therefore a challenging task. So far only a few experiments have been performed in a high-mobility two-dimensional electron gas in which the electron propagates almost ballistically3,4,5. In these previous works, flying electrons were detected by means of the current generated by an ensemble of electrons, and electron correlations were encrypted in the current noise. Here we demonstrate the experimental realization of high-efficiency single-electron source and detector for a single electron propagating isolated from the other electrons through a one-dimensional channel. The moving potential is excited by a surface acoustic wave, which carries the single electron along the one-dimensional channel at a speed of 3 μm ns−1. When this quantum channel is placed between two quantum dots several micrometres apart, a single electron can be transported from one quantum dot to the other with quantum efficiencies of emission and detection of 96% and 92%, respectively. Furthermore, the transfer of the electron can be triggered on a timescale shorter than the coherence time T2* of GaAs spin qubits6. Our work opens new avenues with which to study the teleportation of a single electron spin and the distant interaction between spatially separated qubits in a condensed-matter system.

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Electrons surfing on a sound wave as a platform for quantum optics with flying electrons

We analyze the time-dependent energy and heat flows in a resonant level coupled to a fermionic continuum. The level is periodically forced with an external power source that supplies energy into the system. Based on the tunneling Hamiltonian approach and scattering theory, we discuss the different contributions to the total energy flux. We then derive the appropriate expression for the dynamical dissipation, in accordance with the fundamental principles of thermodynamics. Remarkably, we find that the dissipated heat can be expressed as a Joule law with a universal resistance that is constant at all times.

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Dynamical energy transfer in ac-driven quantum systems

Fil: Arrachea, Liliana del Carmen. Universidad de Zaragoza; Espana. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisica de Buenos Aires; Argentina

Relation between scattering-matrix and Keldysh formalisms for quantum transport driven by time-periodic fields

Landauer - Buttiker Formalism Current Noise Non-Stationary Scattering Theory DC Current Generation AC Current Generation Noise of a Dynamical Scatterer Energetics of a Dynamical Scatterer Dynamical Mesoscopic Capacitor Quantum Circuits with Mesoscopic Capacitor as a Particle Emitter

Scattering Matrix Approach to Non-Stationary Quantum Transport

We investigate the shot noise generated by particle emission from a mesoscopic capacitor into an edge state coupled to another edge state at a quantum point contact (QPC). For a capacitor subject to a periodic voltage the resulting shot noise is proportional to the number of particles (both electrons and holes) emitted during a period. The shot noise is proportional to the driving frequency, however it is independent of the applied voltage. If two capacitors are coupled to a QPC at different sides then the resulting shot noise is maximally the sum of noises produced by each of the capacitors. However, the noise is suppressed if particles of the same kind are emitted simultaneously.

Shot noise of a mesoscopic two-particle collider.

A quantum coherent capacitor subject to large amplitude pulse cycles can be made to emit or reabsorb an electron in each half cycle. Quantized currents with pulse cycles in the GHz range have been demonstrated experimentally. We develop a nonlinear dynamical scattering theory for arbitrary pulses to describe the properties of this very fast single electron source. Using our theory we analyze the accuracy of the current quantization and investigate the noise of such a source. Our results are important for future scientific and possible metrological applications of this source.

Michael Moskalets

Papers

Dynamical energy transfer in ac-driven quantum systems

Relation between scattering-matrix and Keldysh formalisms for quantum transport driven by time-periodic fields

Scattering Matrix Approach to Non-Stationary Quantum Transport

Shot noise of a mesoscopic two-particle collider.

Quantized dynamics of a coherent capacitor.