Quantum Memristors

Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems

Cascade of Quantum Phase Transitions in Tunnel-Coupled Edge States

We report on the cascade of quantum phase transitions exhibited by tunnel-coupled edge states across a quantum Hall line junction. We identify a series of quantum critical points between successive strong and weak tunneling regimes in the zero-bias conductance. Scaling analysis shows that the conductance near the critical magnetic fields $B_{c}$ is a function of a single scaling argument $|B-B_{c}|T^{-\kappa}$, where the exponent $\kappa = 0.42$. This puzzling resemblance to a quantum Hall-insulator transition points to importance of interedge correlation between the coupled edge states.Comment: 4 pages, 3 figure

Magnetoresistance Oscillations in Two-dimensional Electron Systems Induced by AC and DC Fields

We report on magnetotransport measurements in a high-mobility two-dimentional electron system subject simultaneously to AC (microwave) and DC (Hall) fields. We find that DC excitation affects microwave photoresistance in a nontrivial way. Photoresistance maxima (minima) evolve into minima (maxima) and back, reflecting strong coupling and interplay of AC- and DC-induced effects. Most of our observations can be explained in terms of indirect electron transitions using a new, ``combined'' resonant condition. Observed quenching of microwave-induced zero resistance by a DC field cannot be unambiguously linked to a domain model, at least until a systematic theory treating both excitation types within a single framework is developed

Resonant Phonon Scattering in Quantum Hall Systems Driven by dc Electric Fields

Using dc excitation to spatially tilt Landau levels, we study resonant acoustic phonon scattering in two-dimensional electron systems. We observe that dc electric field strongly modifies phonon resonances, transforming resistance maxima into minima and back into maxima. Further, phonon resonances are enhanced dramatically in the non-linear dc response and can be detected even at low temperatures. Most of our observations can be explained in terms of dc-induced (de)tuning of the resonant acoustic phonon scattering and its interplay with intra-Landau level impurity scattering. Finally, we observe a dc-induced zero-differential resistance state and a resistance maximum which occurs when the electron drift velocity approaches the speed of sound.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Giant microwave photoresistivity in a high-mobility quantum Hall system

We report the observation of a remarkably strong microwave photoresistivity effect in a high-mobility two-dimensional electron system subject to a weak magnetic field and low temperature. The effect manifests itself as a giant microwave-induced resistivity peak which, in contrast to microwave-induced resistance oscillations, appears only near the second harmonic of the cyclotron resonance and only at sufficiently high microwave frequencies. Appearing in the regime linear in microwave intensity, the peak can be more than an order of magnitude stronger than the microwave-induced resistance oscillations and cannot be explained by existing theories.Comment: 4 pages, 4 figure

Anomalous spin-resolved point-contact transmission of holes due to cubic Rashba spin-orbit coupling

Evidence is presented for the finite wave vector crossing of the two lowest one-dimensional spin-split subbands in quantum point contacts fabricated from two-dimensional hole gases with strong spin-orbit interaction. This phenomenon offers an elegant explanation for the anomalous sign of the spin polarization filtered by a point contact, as observed in magnetic focusing experiments. Anticrossing is introduced by a magnetic field parallel to the channel or an asymmetric potential transverse to it. Controlling the magnitude of the spin-splitting affords a novel mechanism for inverting the sign of the spin polarization.Comment: 4 pages, 3 figure

Quantum and classical surface acoustic wave induced magnetoresistance oscillations in a 2D electron gas

We study theoretically the geometrical and temporal commensurability oscillations induced in the resistivity of 2D electrons in a perpendicular magnetic field by surface acoustic waves (SAWs). We show that there is a positive anisotropic dynamical classical contribution and an isotropic non-equilibrium quantum contribution to the resistivity. We describe how the commensurability oscillations modulate the resonances in the SAW-induced resistivity at multiples of the cyclotron frequency. We study the effects of both short-range and long-range disorder on the resistivity corrections for both the classical and quantum non-equilibrium cases. We predict that the quantum correction will give rise to zero-resistance states with associated geometrical commensurability oscillations at large SAW amplitude for sufficiently large inelastic scattering times. These zero resistance states are qualitatively similar to those observed under microwave illumination, and their nature depends crucially on whether the disorder is short- or long-range. Finally, we discuss the implications of our results for current and future experiments on two dimensional electron gases.Comment: 16 pages, 8 figure