<title>Low-frequency excitation of double quantum dots</title>

We address theoretically adiabatic regime of charge transport for a model of two tunnel-coupled quantum dots connected in series. The energy levels of the two dots are harmonically modulated by an external potential with a constant phase shift between the two. Motivated by recent experiments with surface-acoustic-wave excitation, we consider two situations: (a) pure pumping in the absence of external voltage (also at finite temperature), and (b) adiabatic modulation of the current driven by large external bias. In both cases we derive results consistent with published experimental data. For the case (b) we explicitly derive the adiabatic limit of Tien-Gordon formula for photon-assisted tunn…

Quantum dot state initialization by control of tunneling rates

We study the loading of electrons into a quantum dot with dynamically controlled tunnel barriers. We introduce a method to measure tunneling rates for individual discrete states and to identify their relaxation paths. Exponential selectivity of the tunnel coupling enables loading into specific quantum dot states by tuning independently energy and rates. While for the single-electron case orbital relaxation leads to fast transition into the ground state, for electron pairs triplet-to-singlet relaxation is suppressed by long spin-flip times. This enables the fast gate-controlled initialization of either a singlet or a triplet electron pair state in a quantum dot with broad potential applicati…

Electronic charge redistribution in LaAlO$_3$(001) thin films deposited at SrTiO$_3$(001) substrate: First principles analysis and the role of stoichiometry

We present a comprehensive first-principles study of the electronic charge redistribution in atomically sharp LaAlO$_3$/SrTiO$_3$(001) heterointerfaces of both n- and p-types allowing for non-stoichiometric composition. Using two different computational methods within the framework of the density functional theory (linear combination of atomic orbitals and plane waves) we demonstrate that conducting properties of LaAlO$_3$/SrTiO$_3$(001) heterointerfaces strongly depend on termination of LaAlO$_3$ (001) surface. We argue that both the polar "catastrophe" and the polar distortion scenarios may be realized depending on the interface stoichiometry. Our calculations predict that heterointerface…

Derivation of the universal decay cascade distribution

A detailed derivation of the decay cascade probability distribution stated in Eqs. (4)-(6) and (11) of Phys. Rev. Lett. 104, 186805 (2010) [arXiv:0901.4102] by Kashcheyevs and Kaestner is provided. Recurrence relations are solved explicitly and connections between solutions in different limits are demonstrated.

Universal decay cascade model for dynamic quantum dot initialization.

Dynamic quantum dots can be formed by time-dependent electrostatic potentials in nanoelectronic devices, such as gate- or surface-acoustic-wave-driven electron pumps. Ability to control the number of captured electrons with high precision is required for applications in fundamental metrology and quantum information processing. In this work we propose and quantify a scheme to initialize quantum dots with a controllable number of electrons. It is based on the stochastic decrease in the electron number of a shrinking dynamic quantum dot and is described by a nuclear decay cascade model with "isotopes" being different charge states of the dot. Unlike the natural nuclei, the artificial confineme…

Partitioning of on-demand electron pairs

The on-demand generation and separation of entangled photon pairs are key components of quantum information processing in quantum optics. In an electronic analogue, the decomposition of electron pairs represents an essential building block for using the quantum state of ballistic electrons in electron quantum optics. The scattering of electrons has been used to probe the particle statistics of stochastic sources in Hanbury Brown and Twiss experiments and the recent advent of on-demand sources further offers the possibility to achieve indistinguishability between multiple sources in Hong-Ou-Mandel experiments. Cooper pairs impinging stochastically at a mesoscopic beamsplitter have been succe…

Modeling of a tunable-barrier non-adiabatic electron pump beyond the decay cascade model

We generalize the decay cascade model of charge capture statistics for a tunable-barrier non-adiabatic electron pump dominated by the backtunneling error at the quantum dot decoupling stage. The energy scales controlling the competition between the thermal and the dynamical mechanisms for accurate trapped charge quantization are discussed. Empirical fitting formula incorporating quantum dot re-population errors due to particle-hole fluctuations in the source lead is suggested and tested against an exactly solvable rate equation model.

Adiabatic charge pumping in carbon nanotube quantum dots.

We investigate charge pumping in carbon nanotube quantum dots driven by the electric field of a surface acoustic wave. We find that, at small driving amplitudes, the pumped current reverses polarity as the conductance is tuned through a Coulomb blockade peak using a gate electrode. We study the behavior as a function of wave amplitude, frequency, and direction and develop a model in which our results can be understood as resulting from adiabatic charge redistribution between the leads and quantum dots on the nanotube.

Gigahertz Single-Electron Pumping Mediated by Parasitic States

In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz, the accuracy typically decreases. Recently, hybrid pumps based on QDs coupled to trap states have led to increased transfer rates due to tighter electrostatic confinement. Here, we operate a hybrid electron pump in silicon obtained by coupling a QD to multiple parasitic states, and achi…

Quantum fluctuations and coherence in high-precision single-electron capture.

The phase of a single quantum state is undefined unless the history of its creation provides a reference point. Thus quantum interference may seem hardly relevant for the design of deterministic single-electron sources which strive to isolate individual charge carriers quickly and completely. We provide a counterexample by analyzing the non-adiabatic separation of a localized quantum state from a Fermi sea due to a closing tunnel barrier. We identify the relevant energy scales and suggest ways to separate the contributions of quantum non-adiabatic excitation and backtunneling to the rare non-capture events. In the optimal regime of balanced decay and non-adiabaticity, our simple electron tr…

Generation of energy selective excitations in quantum hall edge states

We operate an on-demand source of single electrons in high perpendicular magnetic fields up to 30T, corresponding to a filling factor below 1/3. The device extracts and emits single charges at a tunable energy from and to a two-dimensional electron gas, brought into well defined integer and fractional quantum Hall (QH) states. It can therefore be used for sensitive electrical transport studies, e.g. of excitations and relaxation processes in QH edge states.

A random-walk benchmark for single-electron circuits

Mesoscopic integrated circuits aim for precise control over elementary quantum systems. However, as fidelities improve, the increasingly rare errors and component crosstalk pose a challenge for validating error models and quantifying accuracy of circuit performance. Here we propose and implement a circuit-level benchmark that models fidelity as a random walk of an error syndrome, detected by an accumulating probe. Additionally, contributions of correlated noise, induced environmentally or by memory, are revealed as limits of achievable fidelity by statistical consistency analysis of the full distribution of error counts. Applying this methodology to a high-fidelity implementation of on-dema…

Nonlinear thermovoltage and thermocurrent in quantum dots

Quantum dots are model systems for quantum thermoelectric behavior because of their ability to control and measure the effects of electron-energy filtering and quantum confinement on thermoelectric properties. Interestingly, nonlinear thermoelectric properties of such small systems can modify the efficiency of thermoelectric power conversion. Using quantum dots embedded in semiconductor nanowires, we measure thermovoltage and thermocurrent that are strongly nonlinear in the applied thermal bias. We show that most of the observed nonlinear effects can be understood in terms of a renormalization of the quantum-dot energy levels as a function of applied thermal bias and provide a theoretical m…

Quantized current source with mesoscopic feedback

We study a mesoscopic circuit of two quantized current sources, realized by nonadiabatic single-electron pumps connected in series with a small micron-sized island in between. We find that quantum transport through the second pump can be locked onto the quantized current of the first one by a feedback due to charging of the mesoscopic island. This is confirmed by a measurement of the charge variation on the island using a nearby charge detector. Finally, the charge feedback signal clearly evidences loading into excited states of the dynamic quantum dot during single-electron pump operation. © 2011 American Physical Society.

Robust single-parameter quantized charge pumping

This paper investigates a scheme for quantized charge pumping based on single-parameter modulation. The device was realized in an AlGaAs-GaAs gated nanowire. We find a remarkable robustness of the quantized regime against variations in the driving signal, which increases with applied rf power. This feature together with its simple configuration makes this device a potential module for a scalable source of quantized current.

Low-frequency excitation of double quantum dots

We address theoretically adiabatic regime of charge transport for a model of two tunnel-coupled quantum dots connected in series. The energy levels of the two dots are harmonically modulated by an external potential with a constant phase shift between the two. Motivated by recent experiments with surface-acoustic-wave excitation, we consider two situations: (a) pure pumping in the absence of external voltage (also at finite temperature), and (b) adiabatic modulation of the current driven by large external bias. In both cases we derive results consistent with published experimental data. For the case (b) we explicitly derive the adiabatic limit of Tien-Gordon formula for photon-assisted tunn…

Single-parameter quantized charge pumping in high magnetic fields

We study single-parameter quantized charge pumping via a semiconductor quantum dot in high magnetic fields. The quantum dot is defined between two top gates in an AlGaAs/GaAs heterostructure. Application of an oscillating voltage to one of the gates leads to pumped current plateaus in the gate characteristic, corresponding to controlled transfer of integer multiples of electrons per cycle. In a perpendicular-to-plane magnetic field the plateaus become more pronounced indicating an improved current quantization. Current quantization is sustained up to magnetic fields where full spin polarization of the device can be expected.

Global oscillation mechanism in the stochastic Lotka model.

The microscopic one-parameter kinetic model of the oscillatory $A+\stackrel{\ensuremath{\rightarrow}}{B}2B$ reaction (Lotka model) is studied using direct Monte Carlo simulations and analytical methods. Percolation is proposed as the mechanism of global oscillations that are not limited to any finite size of a system. An analytical estimate of the oscillation frequency is derived and compared to computer simulations. We also observe the transition from synchronized oscillations to specific ${f}^{\ensuremath{-}2}$ noise in two dimensions which was previously reported for self-organized critical models.

Magnetic field enhanced robustness of quantized current plateaus in single and double quantum dot non-adiabatic single charge pumps

We compare the robustness of the quantized current plateaus of semiconductor non-adiabatic quantized charge pumps consisting of a single quantum dot (SQD) and two QDs connected in series (DQD). For the SQD application of a perpendicular magnetic field leads to an enhanced robustness of the first current plateau I = ef, with f the pumping frequency and e the elementary charge. In contrast for the DQD a comparably enhanced robustness of the plateau I = 2ef is found. These findings might allow generation of higher currents without compromising quantization accuracy by optimizing the device geometry.

Non-adiabatic pumping of single electrons affected by magnetic fields

Non-adiabatic pumping of discrete charges, realized by a dynamical quantum dot in an AlGaAs/GaAs heterostructure, is studied under influence of a perpendicular magnetic field. Application of an oscillating voltage in the GHz-range to one of two top gates, crossing a narrow wire and confining a quantum dot, leads to quantized pumped current plateaus in the gate characteristics. The regime of pumping one single electron is traced back to the diverse tunneling processes into and out-of the dot. Extending the theory to multiple electrons allows to investigate conveniently the pumping characteristics in an applied magnetic field. In this way, a qualitatively different behavior between pumping ev…

Time-energy filtering of single electrons in ballistic waveguides

Characterizing distinct electron wave packets is a basic task for solid-state electron quantum optics with applications in quantum metrology and sensing. A important circuit element for this task is a non-stationary potential barrier than enables backscattering of chiral particles depending on their energy and time of arrival. Here we solve the quantum mechanical problem of single-particle scattering by a ballistic constriction in an fully depleted quantum Hall system under spatially uniform but time-dependent electrostatic potential modulation. The result describes electrons distributed in time-energy space according to a modified Wigner quasiprobability distribution and scattered with an …

Enhancing the sensitivity of nano-FTIR spectroscopy.

Synchrotron radiation-based nano-FTIR spectroscopy utilizes the highly brilliant and ultra-broadband infrared (IR) radiation provided by electron storage rings for the infrared spectroscopic characterization of samples at the nanoscale. In order to exploit the full potential of this approach we investigated the influence of the properties of the radiation source, such as the electron bunch shape and spectral bandwidth of the emitted radiation, on near-field infrared spectra of silicon-carbide (SiC). The adapted configuration of the storage ring optics enables a modification of the transverse electron bunch profile allowing an increase of the measured near-field signal amplitude. Additionall…

Design and operation of CMOS-compatible electron pumps fabricated with optical lithography

We report CMOS-compatible quantized current sources (electron pumps) fabricated with nanowires (NWs) on 300mm SOI wafers. Unlike other Al, GaAs or Si based metallic or semiconductor pumps, the fabrication does not rely on electron-beam lithography. The structure consists of two gates in series on the nanowire and the only difference with the SOI nanowire process lies in long (40nm) nitride spacers. As a result a single, silicide island gets isolated between the gates and transport is dominated by Coulomb blockade at cryogenic temperatures thanks to the small size and therefore capacitance of this island. Operation and performances comparable to devices fabricated using e-beam lithography is…

Classical-to-quantum crossover in electron on-demand emission

Emergence of a classical particle trajectory concept from the full quantum description is a key feature of quantum mechanics. Recent progress of solid state on-demand sources has brought single-electron manipulation into the quantum regime, however, the quantum-to-classical crossover remains unprobed. Here we describe theoretically a mechanism for generating single-electron wave packets by tunneling from a driven localized state, and show how to tune the degree of quantumness. Applying our theory to existing on-demand sources, we demonstrate the feasibility of an experimental investigation of quantum-to-classical crossover for single electrons, and open up yet unexplored potential for few-e…

Quantum criticality perspective on the charging of narrow quantum-dot levels.

Understanding the charging of exceptionally narrow levels in quantum dots in the presence of interactions remains a challenge within mesoscopic physics. We address this fundamental question in the generic model of a narrow level capacitively coupled to a broad one. Using bosonization we show that for arbitrary capacitive coupling charging can be described by an analogy to the magnetization in the anisotropic Kondo model, featuring a low-energy crossover scale that depends in a power-law fashion on the tunneling amplitude to the level. Explicit analytical expressions for the exponent are derived and confirmed by detailed numerical and functional renormalization-group calculations.

NATIONAL PHYSICS OLYMPIADS FROM THE POINT OF VIEW OF PARTICIPANTS AND PHYSICS TEACHERS

The development of student's interests and skills is strategically important to foster their career choice in the field of science, technology and engineering, which is one of the goals of Latvia's National Development Plan for 2021-2027. Physics Olympiads can be used as one of the enrichment measures to supplement formal school teaching in raising student motivation and developing their skills and talents. We explore directions in which the existing system of Physics Olympiads can be improved, with the goals of reaching a wider audience of teachers and students and achieving further integration with the learning processes in schools. We have conducted a survey of physics teachers (NT=188),…

Realization of a robust single-parameter quantized charge pump

This paper describes a novel scheme for quantized charge pumping based on single-parameter modulation. The device is realized in an AlGaAs-GaAs gated nanowire. A particular advantage of this realization is that operation in the quantized regime can be achieved in a potentially large range of amplitude and dc off-set of the driving signal. This feature together with the simple configuration might enable large scale parallel operation of many such devices.

Non-adiabatic quantized charge pumping with tunable-barrier quantum dots: a review of current progress.

Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property --- the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of $q_e f$ as function of control parameters, where $q_e$ is the electron charge and $f$ is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These de…

Exact canonical occupation numbers in a Fermi gas with finite level spacing and a q-analog of Fermi-Dirac distribution

We consider equilibrium level occupation numbers in a Fermi gas with a fixed number of particles, n, and finite level spacing. Using the method of generating functions and the cumulant expansion we derive a recurrence relation for canonical partition function and an explicit formula for occupation numbers in terms of single-particle partition function at n different temperatures. We apply this result to a model with equidistant non-degenerate spectrum and obtain close-form expressions in terms of q-polynomials and Rogers-Ramanujan partial theta function. Deviations from the standard Fermi-Dirac distribution can be interpreted in terms of a gap in the chemical potential between the particle …

Dopant-controlled single-electron pumping through a metallic island

We investigate a hybrid metallic island/single dopant electron pump based on fully depleted silicon-on-insulator technology. Electron transfer between the central metallic island and the leads is controlled by resonant tunneling through single phosphorus dopants in the barriers. Top gates above the barriers are used to control the resonance conditions. Applying radio frequency signals to the gates, non-adiabatic quantized electron pumping is achieved. A simple deterministic model is presented and confirmed by comparing measurements with simulations.

Continuous-Variable Tomography of Solitary Electrons

A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wide-band tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated fro…

Computer modeling of metal colloid formation in tracks of swift heavy ions in ionic solids

Abstract We present results of computer modelling of the aggregation of primary radiation defects—F centers—in ionic crystals within tracks of swift heavy ions. We study how F-aggregate properties depend on the initial density of primary Frenkel defects in the track and its radius. The mean number of F centers in aggregates is typically very small, about five defects, which greatly complicates detection of expected metal colloids by ESR.

Modeling of primary defect aggregation in tracks of swift heavy ions in LiF

To simulate aggregation of primary F centers created along the path of swift heavy ions in LiF, Monte Carlo simulations were developed. Parameters relevant for defect aggregation as a result of their random hopping, such as the migration energy, temperature in the track, initial defect concentration, and diffusion time, were estimated from available experimental data. It is estimated that in the electronically excited state and under temperature locally increased up to 1200 K F centers are mobile enough to make several tens of hops. Most of the F aggregates formed are extremely small and consist only of two or three F centers. The fraction of larger F clusters ~with more than 10 defects! is…

Modeling of an adiabatic tunable-barrier electron pump

Quantized adiabatic quantum pumping due to interference

Recent theoretical calculations, demonstrating that quantized charge transfer due to adiabatically modulated potentials in mesoscopic devices can result purely from the interference of the electron wave functions (without invoking electron-electron interactions) are reviewed: (1) A new formula is derived for the pumped charge Q (per period); It reproduces the Brouwer formula without a bias, and also yields the effect of the modulating potential on the Landauer formula in the presence of a bias. (2) For a turnstile geometry, with time-dependent gate voltages V_L(t) and V_R(t), the magnitude and sign of Q are determined by the relative position and orientation of the closed contour traversed …

Exact non-Hookean scaling of cylindrically bent elastic sheets and the large-amplitude pendulum

A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence on the interplate distance [Siber and Buljan, arXiv:1007.4699 (2010)]. The phenomenon has been used as a basis for an experimental problem at the 41st International Physics Olympiad. We show that the corresponding variational problem for the equilibrium energy of the deformed cylinder is equivalent to a minimum action description of a simple gravitational pendulum with an amplitude of 90 degrees. We use this analogy to show that the power-law of the force…

Counting statistics for electron capture in a dynamic quantum dot

We report non-invasive single-charge detection of the full probability distribution $P_n$ of the initialization of a quantum dot with $n$ electrons for rapid decoupling from an electron reservoir. We analyze the data in the context of a model for sequential tunneling pinch-off, which has generic solutions corresponding to two opposing mechanisms. One limit considers sequential "freeze out" of an adiabatically evolving grand canonical distribution, the other one is an athermal limit equivalent to the solution of a generalized decay cascade model. We identify the athermal capturing mechanism in our sample, testifying to the high precision of our combined theoretical and experimental methods. …

Measurement and control of electron wave packets from a single-electron source

We report an experimental technique to measure and manipulate the arrival-time and energy distributions of electrons emitted from a semiconductor electron pump, operated as both a single-electron source and a two-electron source. Using an energy-selective detector whose transmission we control on picosecond time scales, we can measure directly the electron arrival-time distribution and we determine the upper bound to the distribution width to be 30 ps. We study the effects of modifying the shape of the voltage wave form that drives the electron pump, and show that our results can be explained by a tunneling model of the emission mechanism. This information was in turn used to control the em…

Quantum Transport and Current Distribution at Radio Frequency in Multiwall Carbon Nanotubes

Multiwall carbon nanotubes represent a low-dimensional material that could serve as building blocks for future carbon-based nanoelectronics. The understanding of the electromagnetic performances at radio frequency of these materials for use in nanointerconnects is strictly related to the analysis of their transport properties as function of the working conditions. In this paper, we present an explicit expression of the conducting channels as function of diameter, temperature, doping, and supply voltage for both metallic and semiconducting carbon nanotubes. The proposed formula is based on the Dirac cone approximation of the conducting band energy of graphene nearby the Fermi points, combine…

Dataset for Wenz et al. Phys. Rev. B 99, 201409(R) (2019), "Quantum dot state initialization by control of tunneling rates"

Collection of the datasets used to generate the figures in the following journal paper: "Quantum dot state initialization by control of tunneling rates" Tobias Wenz, Jevgeny Klochan, Frank Hohls, Thomas Gerster, Vyacheslavs Kashcheyevs, and Hans W. Schumacher PHYSICAL REVIEW B 99, 201409(R) (2019) DOI: 10.1103/PhysRevB.99.201409