Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps. Received: 8 February 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Three-junction SQUID rocking ratchet

We investigate three-junction SQUIDs which show voltage rectification if biased with an ac current drive with zero mean value. The Josephson phase across the SQUID experiences an effective ratchet potential, and the device acts as an efficient rocking ratchet, as demonstrated experimentally for adiabatic and nonadiabatic drive frequencies. For high-frequency drives the rectified voltage is quantized due to synchronization of the phase dynamics with the external drive. The experimental data are in excellent agreement with numerical simulations including thermal fluctuations.     

A Brownian-ratchet DNA pump with applications to single-nucleotide polymorphism genotyping

We have fabricated a micron-scale device capable of transporting DNA oligomers using Brownian ratchets. The ratchet potential is generated by applying a voltage difference to interdigitated electrodes. Cycling between the charged state and a discharged, free-diffusion state rectifies the Brownian motion of charged particles. The observed macroscopic transport properties agree with the transport rate predicted from microscopic parameters including the DNA diffusivity, the dimensions of the ratchet potential, and the cycling time. Applications to human genetics, primarily genotyping of single-nucleotide polymorphisms (SNPs), are discussed. Received: 7 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

d-wave induced zero-field resonances in dc pi-superconducting quantum interference devices

A dc pi SQUID consists of a superconducting ring interrupted by two Josephson junctions, one of which carries in equilibrium a pi phase difference, caused, for example, by the d-wave pairing symmetry of the high- T(c) cuprates. If this phase shift is maintained in the voltage state, anomalous resonance currents are expected in the SQUIDs transport characteristics. Here we report the observation of such resonances for high- T(c) dc pi SQUIDs, providing evidence for the influence of the d-wave symmetry on the voltage state of a Josephson junction for frequencies of several tens of GHz.     

Coulomb blockade and coherent single-cooper-pair tunneling in single Josephson junctions

We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.     

Charging ratchets: Coulomb blockade and rectification

Discrete ratchets describe directed motion of a ‘reaction coordinate’ through a cycle of states in response to some varying external parameter. Such systems, in the simple, history-independent case, are described by a Markov process which in turn leads to a master equation with a transition matrix. Thus the ratchet property is reduced to a characteristic of the parameter-dependent symmetry of matrices. In the standard model of tunneling through a set of quantum dots in the Coulomb-blockade regime, a master equation is also used to describe the evolution through states in ‘dot-occupancy space’, leading to transport of electrons from a source to a drain. The symmetry of the transition matrix in this case is also a function of external parameters, notably the applied gate voltages and source–drain voltage, as well as depending on the configuration of dots and their tunnel couplings. We show that rectification and other ratchet behavior is a common feature of tunneling transport in the Coulomb-blockade regime. We also show that specific arrangements of dots and their tunnel couplings can be designed to enhance the ratchet effect. Finally, we show that the strong rectification of Coulomb-blockaded systems results from the reduction in phase space accessible to the system as it traverses the states in the reaction cycle. Received: 16 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Wide-band tuneability,nonlinear transmission,and dynamic multistability in SQUID metamaterials

Superconducting metamaterials comprising rf Superconducting QUantum Interference Devices (SQUIDs) have been recently realized and investigated with respect to their tuneability, permeability, and dynamic multistability properties. These properties are a consequence of intrinsic nonlinearities due to the sensitivity of the superconducting state to external stimuli. SQUIDs, made of a superconducting ring interrupted by a Josephson junction, possess yet another source of nonlinearity, which makes them widely tuneable with an applied dc dlux. A model SQUID metamaterial, based on electric equivalent circuits, is used in the weak coupling approximation to demonstrate the dc flux tuneability, dynamic multistability, and nonlinear transmission in SQUID metamaterials comprising non-hysteretic SQUIDs. The model equations reproduce the experimentally observed tuneability patterns and predict tuneability with the power of an applied ac magnetic field. Moreover, the results indicate the opening of nonlinear frequency bands for energy transmission through SQUID metamaterials, for sufficiently strong ac fields.     

Rectifying effect in a Josephson junction ratchet array

We have studied numerically a rectifying effect in an underdamped Josephson junction ratchet array driven by dc and ac current. The array consists of both alternating potential barriers and alternating inter-capacitances along the direction of vortex flow. The guide banks of high critical currents are assigned for all the longitudinal junctions to prevent the percolative pattern of vortex motion. In some junction parameters, we see a rectifying effect which indicates a finite value of the time-averaged voltage at zero dc bias. The directional dependence of the vortex motion becomes fairly large when the junction parameters lie in an optimal range which gives rise to a Shapiro step at zero dc bias. Such a rectifying effect survives for small thermal fluctuation, but eventually disappear beyond a certain critical temperature.     

Soliton ratchets out of point-like inhomogeneities

We introduce and study a novel design for a ratchet potential for soliton excitations. The potential is implemented by means of an array of point-like (delta) inhomogeneities in an otherwise homogeneous potential. We use collective coordinates which predict that the effective potential acting on the soliton is periodic but asymmetric and gives rise to the ratchet effect. Numerical simulations fully confirm this prediction; quantitative agreement is reached by an improved version of the theory. Although we specifically show that it is most interesting for building Josephson junction ratchets capable to rectify time-symmetric ac forces, the proposed mechanism is very general and can appear in many contexts, including biological systems.Received: 25 November 2003, Published online: 19 February 2004PACS: 05.45.Yv Solitons - 05.60.-k Transport processes - 63.20.Pw Localized modes     

Peculiarities of rf SQUID response in finite magnetic fields

Single-layer washer-type high-T_c YBa₂Cu₃O_7−x rf SQUIDs with grain-boundary Josephson junctions, as well as low-T_c Nb rf SQUIDs with Nb–Al₂O₃–Nb tunnel junctions, have been investigated in finite magnetic fields. It was shown experimentally that the suppression of the critical current of the Josephson junction due to the magnetic field leads to a modulation of the amplitude of the SQUID output signal. The role of the “unwanted” junction in high-T_c rf SQUIDs, which is formed by the grain boundary running through the washer of the SQUIDs on bicrystal substrates, has also been clarified. The drop of the SQUID signal at a finite magnetic field is originated by the penetration of the magnetic field into the unwanted junction. Based on these results, a direct radio-frequency method for the determination of the first critical field H_c1 for long Josephson junctions has been developed.     

Functional fractionation-ratchets

Electrophoretic ratchets have been developed for both analytical and preparative electrophoresis. These ratchets use a new type of pulsed field. The quality of the fractionations meets the usual standards for biochemistry-based electrophoresis. The supporting medium is either an agarose gel or a capillary-contained polymer solution. The electrophoretic ratchets are effective with a particle that has an electrophoretic mobility (μ=velocity/electrical field) that varies as the electrical field varies. A ratchet developed for DNA molecules is effective because μ increases in magnitude as the electrical field increases in magnitude. Ratchets developed for both DNA–protein complexes and spheres are effective because of the opposite dependence of μ on the electrical field. Ratchet-based gel electrophoresis can be performed in a continuous, preparative mode. Ratchet-based capillary electrophoresis provides a necessary component for cyclic capillary electrophoresis. Cyclic capillary electrophoresis of DNA is a procedure for analyzing a DNA profile in several segments. These segments are separated by electrophoretic enhancements of the DNA profile. Cyclic capillary electrophoresis is being developed for increasing both the length and the accuracy of the analysis of a DNA-sequencing ladder. Received: 16 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Vortex-rectification effects in films with periodic asymmetric pinning

We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field, and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very different from standard overdamped models. Rather, the repinning force, necessary to stop vortex motion, is considerably smaller than the depinning force, resembling the behavior of the so-called inertia ratchets. Calculations based on an underdamped ratchet model provide a very good fit to the experimental data.     

Ratchets, power strokes, and molecular motors

We present a method for determining the effective driving potential for a molecular motor from measurements of its stochastic position versus time. In developing the method we can make precise the previously vague notions of ‘Brownian ratchet’ and ‘power stroke’, and suggest means to experimentally distinguish between the two. In particular, we distinguish between two kinds of ratchets: ratchets that rectify large fluctuations and ratchets that bias small fluctuations. Received: 24 October 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Energetics of Brownian motors: a review

We review the literature on the energetics of Brownian motors, distinguishing between forced ratchets, chemical motors – driven out of equilibrium by differences of chemical potential, and thermal motors – driven by temperature differences. The discussion is focused on the definition of efficiency and the compatibility between the models and the laws of thermodynamics. Received: 13 November 2001 / Accepted: 10 January 2002 / Published online: 22 April 2002     

YBCO step-edge SQUIDs by magnetron sputtering technique

Summary YBCO step-edge junction d.c. SQUIDs have been realized by using the Inverted Cylindrical Magnetron Sputtering (ICMS) technique. This last represents a novel technology for high-T _c Josephson junctions (HTSC). Steps are obtained by standard ion milling procedure on LaAlO₃ (100) substrates using Nb-masks patterned by reactive ion etching. Measurements of currentvs. voltage, maximum d.c. Josephson currentvs. magnetic field and SQUID voltage response measurements have been performed, also as a function of the temperature. Operating temperature as high as 77K has been achieved. At 4.2K the SQUIDs show a maximum voltage of flux transfer function (∂V/∂ϕ)_max=870 μV/Ф₀ and a good periodicity of theV-ϕ modulation up to 20Ф₀ without any sign of hysteresis. The ratio between the step height (h) and the film thickness (d) seems to play a fundamental role in determining Josephson properties of the bridges, these conditions being more severe with respect to most of the data available in literature. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Current-driven dynamics in Josephson junction networks with an asymmetric potential

Current-driven dynamics of Josephson junction networks (JJNs) is studied using numerical simulations. We consider a JJN with an asymmetric and periodic potential of vortices, which is realized by saw-tooth modulation of junction critical currents. When external ac currents are applied to the JJN in a magnetic field, there appears a ratchet effect, and then directed motion of vortices is induced in certain system parameter regimes. A ratchet behavior is observed even for JJNs with weak structural disorder. We clarify the vortex pinning and dynamics in the JJN as a ratchet system.     

Strategies for the separation of polyelectrolytes based on non-linear dynamics and entropic ratchets in a simple microfluidic device

We perform Monte Carlo simulations of an existing electrophoretic microchannel device used for the size separation of large DNA fragments. This device is normally operated with a constant (dc) driving field. In contrast, we consider the case of a varying (ac) driving field, in the zero-frequency limit. We find that a time-asymmetric pulse can yield interesting migration regimes, in particular bidirectional transport for different molecular sizes. We also study a spatially asymmetric version of the device and show that it can rectify unbiased but non-equilibrium molecular motion, in agreement with previous predictions for entropic ratchets. Finally, at finite frequency we uncover a resonance for the molecular velocity in the channel which could lead to improved performance. Received: 16 November 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Vortex motion rectification in Josephson junction arrays with a ratchet potential

By means of electrical transport measurements we have studied the rectified motion of vortices in ratchet potentials engineered on overdamped Josephson junction arrays. The rectified voltage as a function of the vortex density shows a maximum efficiency close a matching condition to the period of the ratchet potential indicating a collective vortex motion. Vortex current reversals were detected varying the driving force and vortex density revealing the influence of vortex-vortex interaction in the ratchet effect.     

YBaCuO BICRYSTAL JUNCTIONS AND DC SUPERCONDUCTING QUANTUM INTERFERENCE DEVICES

We have prepared yttria-stabilized-zirconia bicrystal substrates using a simple hot-pressing method. The grain-boundary junctions have been fabricated with YBa₂Cu₃O₇ thin films grown epitaxially on the bicrystals. The patterns are defined by conventional photolithography, The dc and microwave characteristics of the junctiorts and the dc superconducting quantum interference devices (SQUIDs) have been intensively studied. The current-voltage curves are bridge-typed with noise rounding near the critical current. Resistive tail has been observed in the resistance versus temperature curves. The results are compared with the theoretical prediction for classical Josephson junctions. It is found that the behavior of bicrystal junctions can be described in the frame of classical theory. The deviations are attributed to the nonuniformity of the junctions. The small loop dc SQUIDs demonstrate diffraction and interference effects with regard to the applied magnetic field. A large square-washer with a new configuration has been designed to enhance the effective area of dc SQUID as a magnetometer. It has achieved a magnetic field resolution down to 1 pT/(Hz)^1/2(at 10Hz) at 77K.