Single-electron Source Research Articles

Femtosecond Laser Induced Resonant Tunneling in an Individual Quantum Dot Attached to a Nanotip

Quantized nano-objects offer a myriad of exciting possibilities for manipulating electrons and light that impact photonics, nanoelectronics, and quantum information. In this context, ultrashort laser pulses combined with nanotips and field emission have permitted renewing nano-characterization and control electron dynamics with unprecedented space and time resolution reaching femtosecond and even attosecond regimes. A crucial missing step in these experiments is that no signature of quantized energy levels has yet been observed. We combine in situ nanostructuration of nanotips and ultrashort laser pulse excitation to induce multiphoton excitation and electron emission from a single quantized nano-object attached at the apex of a metal nanotip. Femtosecond induced tunneling through well-defined localized confinement states that are tunable in energy is demonstrated. This paves the way for the development of ultrafast manipulation of electron emission from isolated nano-objects including stereographically fixed individual molecules and high brightness, ultrafast, coherent single electron sources for quantum optics experiments.

Single-electron emission from degenerate quantum levels

Single-electron sources on-demand are requisite for a promising fully electronic platform for solid-state quantum information processing. Most of the experimentally realized sources use the fact that only one electron can be taken from a singly occupied quantum level. Here I take the next step and discuss emission from orbitally degenerate quantum levels that arise, for example, in quantum dots with a nontrivial ring topology. I show that degeneracy provides additional flexibility for single- and two-electron emission. Indeed, the small Aharonov-Bohm flux, which slightly lifts the degeneracy, is a powerful tool for changing the relative width of the emitted wave packets over a wide range. In a ring with one lead, even electrons emitted from completely degenerate levels can be separated in time if the driving potential changes at the appropriate rate. In a ring with two leads, electrons can be emitted to different leads if one of the leads has a bound state with Fermi energy at its end.

Etching process of narrow wire and application to tunable-barrier electron pump.

Single electron sources have been studied as a device to establish an electric current standard for 30 years and recently as an on-demand coherent source for fermion quantum optics. In order to construct the single electron source on a GaAs/AlGaAs two-dimensional electron gas (2DEG), it is often necessary to fabricate a sub-micrometer wire by etching. We have established techniques to fabricate the wire made of the fragile 2DEG by combining photolithography and electron beam lithography with one-step photoresist coating, which enables us to etch fine and coarse structures simultaneously. It has been demonstrated that the fabricated single electron source pumps a fixed number of electrons per cycle with radio frequency. The fabrication technique improves the lithography process with lower risk of damage to the 2DEG.

Quantum teleportation of single-electron states

We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations we take into account environmental effects.

Composite two-particle sources

Multi-particle sources constitute an interesting new paradigm following the recent development of on-demand single-electron sources. Versatile devices can be designed using several single-electron sources, possibly of different types, coupled to the same quantum circuit. However, if combined \textit{non-locally} to avoid cross-talk, the resulting architecture becomes very sensitive to electronic decoherence. To circumvent this problem, we here analyse two-particle sources that operate with several single-electron (or hole) emitters attached in series to the same electronic waveguide. We demonstrate how such a device can emit exactly two electrons without exciting unwanted electron-hole pairs if the driving is adiabatic. Going beyond the adiabatic regime, perfect two-electron emission can be achieved by driving two quantum dot levels across the Fermi level of the external reservoir. If a single-electron source is combined with a source of holes, the emitted particles can annihilate each other in a process which is governed by the overlap of their wave functions. Importantly, the degree of annihilation can be controlled by tuning the emission times, and the overlap can be determined by measuring the shot noise after a beam splitter. In contrast to a Hong-Ou-Mandel experiment, the wave functions overlap close to the emitters and not after propagating to the beam splitter, making the shot noise reduction less susceptible to electronic decoherence.

A controllable and efficient method for the fabrication of a single HfC nanowire field-emission point electron source aided by low keV FIB milling.

A single hafnium carbide (HfC) nanowire field-induced electron emitter with a sharp tip apex is fabricated by Pt deposition and focused ion beam (FIB) milling. The structure of the electron emitter is characterized by scanning transmission electron microscopy (STEM) and atom probe tomography (APT). The HfC nanowire is single-crystalline with a thin oxide layer on its tip surface. The field emission properties are determined by using both in situ transmission electron microscopy (TEM) and a field-emission probe in a high-vacuum chamber. A high current of 173 nA was obtained at a low extraction voltage of 631 V with an emission gap of 5 mm. The emission current is stable at 60 nA for 100 min with a fluctuation of 0.7%. The deduced work function was 3.1 eV. It is suggested that the implanted Ga ions and the oxide layer induce more downward dipoles that are beneficial for lowering the work function and creating a stable surface. When the low keV FIB processing is applied, it takes within 30 minutes to finish a HfC nanowire emitter, establishing an efficient procedure for the preparation of nanowire emitters. These results provide a controllable and fast production method for the fabrication of single nanowire field-emission point electron sources.

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 from the Fermi sea. While we cannot resolve the pure state Wigner function of our excitations due to classical fluctuations, we can partially resolve the chirp and squeezing of the Wigner function imposed by emission conditions and quantify the quantumness of the source. This tomography scheme, when implemented with sufficient experimental resolution, will enable quantum-limited measurements, providing information on electron coherence and entanglement at the individual particle level.

Picosecond coherent electron motion in a silicon single-electron source.

An advanced understanding of ultrafast coherent electron dynamics is necessary for the application of submicrometre devices under a non-equilibrium drive to quantum technology, including on-demand single-electron sources1, electron quantum optics2-4, qubit control5-7, quantum sensing8,9 and quantum metrology10. Although electron dynamics along an extended channel has been studied extensively2-4,11, it is hard to capture the electron motion inside submicrometre devices. The frequency of the internal, coherent dynamics is typically higher than 100 GHz, beyond the state-of-the-art experimental bandwidth of less than 10 GHz (refs. 6,12,13). Although the dynamics can be detected by means of a surface-acoustic-wave quantum dot14, this method does not allow for a time-resolved detection. Here we theoretically and experimentally demonstrate how we can observe the internal dynamics in a silicon single-electron source that comprises a dynamic quantum dot in an effective time-resolved fashion with picosecond resolution using a resonant level as a detector. The experimental observations and the simulations with realistic parameters show that a non-adiabatically excited electron wave packet15 spatially oscillates quantum coherently at ~250 GHz inside the source at 4.2 K. The developed technique may, in future, enable the detection of fast dynamics in cavities, the control of non-adiabatic excitations15 or a single-electron source that emits engineered wave packets16. With such achievements, high-fidelity initialization of flying qubits5, high-resolution and high-speed electromagnetic-field sensing8 and high-accuracy current sources17 may become possible.

Measurement of the curvature and height of the potential barrier for a dynamic quantum dot

We report a method to characterize the potential barrier of a dynamic quantum dot by measuring the barrier height and determining the curvature. We show that the loading statistics and hence accuracy of electron transfer through the dynamic quantum dot depend significantly on these parameters, and hence our method provides a detailed characterization of device performance. This method takes a further step towards tunable barrier shapes, which would greatly increase the accuracy of single electron sources, allowing the single electron current to be useful for quantum sensing, quantum information, and metrology. We apply our method to the case of a tunable-barrier single-electron pump, an exemplary device that shows promise as a source of hot single electron wavepackets.

Sound-driven single-electron transfer in a circuit of coupled quantum rails

Surface acoustic waves (SAWs) strongly modulate the shallow electric potential in piezoelectric materials. In semiconductor heterostructures such as GaAs/AlGaAs, SAWs can thus be employed to transfer individual electrons between distant quantum dots. This transfer mechanism makes SAW technologies a promising candidate to convey quantum information through a circuit of quantum logic gates. Here we present two essential building blocks of such a SAW-driven quantum circuit. First, we implement a directional coupler allowing to partition a flying electron arbitrarily into two paths of transportation. Second, we demonstrate a triggered single-electron source enabling synchronisation of the SAW-driven sending process. Exceeding a single-shot transfer efficiency of 99%, we show that a SAW-driven integrated circuit is feasible with single electrons on a large scale. Our results pave the way to perform quantum logic operations with flying electron qubits.

Electron pumping in the strong coupling and non-Markovian regime: A reaction coordinate mapping approach

We study electron pumping in the strong coupling and non-Markovian regime. Our model is a single quantum dot with periodically modulated energy and tunnelling amplitudes. We identify four parameters to control the direction of the current: the driving phase, the coupling strength, the driving frequency and the location of the maxima of the spectral density. In the high-frequency regime, we use a Markovian embedding strategy to map our model to three serial quantum dots weakly coupled to the reservoirs allowing us to use a Floquet master equation. We observe a rectification effect of the pumped charge that is exclusive to the non-Markovian character of our model. In the low-frequency regime, we apply an additional transformation to see our model as three independent transport channels. With the use of full counting statistics, we study charge fluctuations and validate that our model behaves as a single electron source.

Energy relaxation in hot electron quantum optics via acoustic and optical phonon emission

We study theoretically the relaxation of hot quantum-Hall edge-channel electrons under the emission of both acoustic and optical phonons. Aiming to model recent experiments with single-electron sources, we describe simulations that provide the distribution of electron energies and arrival times at a detector a fixed distance from the source. From these simulations we extract an effective rate of emission of optical phonons that contains contributions from both a direct emission process as well as one involving inter-edge-channel transitions that are driven by the sequential emission of first an acoustic -- and then an optical -- phonon. Furthermore, we consider the mean energy loss due to acoustic phonon emission and resultant broadening of the electron energy distribution and derive an effective drift-diffusion model for this process.

Iron-Enhanced Reactivity of Radicals Enables C–H Tertiary Alkylations for Construction of Functionalized Quaternary Carbons

Iron is one of the most attractive catalysts, especially for aromatic C–H functionalizations. However, stoichiometric amounts of oxidants and strong carbanions are required, and C–H tertiary alkylation, especially with electron-deficient alkyl groups, is unexplored. In this paper, we describe the development of iron-catalyzed selective C–H tertiary alkylations with heteroaromatics, in which an iron salt acts as a single-electron source and enhances the reactivity of a tertiary alkyl radical generated from α-bromocarbonyl compounds. Our established methodology was demonstrated in the efficient synthesis of various quaternary carbon atoms under very simple conditions.

LO-Phonon Emission Rate of Hot Electrons from an On-Demand Single-Electron Source in a GaAs/AlGaAs Heterostructure.

Using a recent time-of-flight measurement technique with 1ps time resolution and electron-energy spectroscopy, we develop a method to measure the longitudinal-optical-phonon emission rate of hot electrons traveling along a depleted edge of a quantum Hall bar. Comparison to a single-particle model implies the scattering mechanism involves a two-step process via an intra-Landau-level transition. We show that this can be suppressed by control of the edge potential profile, and a scattering length >1 mm can be achieved, allowing the use of this system for scalable single-electron device applications.

Probing charge- and heat-current noise by frequency-dependent fluctuations in temperature and potential

Fluctuations are an important spectroscopic tool for characterizing the single-electron sources relevant to metrology and quantum electron optics. The authors theoretically propose an experimental method to measure mesoscopic and nanoscale transport properties through macroscopic fluctuations. This proposal puts forward the solution to the open question of how to experimentally access energy-current fluctuations. The research team explains the physical mechanism behind the proposed setup, analyzes its feasibility, and provides guidelines for its optimization.

Unveiling the bosonic nature of an ultrashort few-electron pulse

Quantum dynamics is very sensitive to dimensionality. While two-dimensional electronic systems form Fermi liquids, one-dimensional systems—Tomonaga–Luttinger liquids—are described by purely bosonic excitations, even though they are initially made of fermions. With the advent of coherent single-electron sources, the quantum dynamics of such a liquid is now accessible at the single-electron level. Here, we report on time-of-flight measurements of ultrashort few-electron charge pulses injected into a quasi one-dimensional quantum conductor. By changing the confinement potential we can tune the system from the one-dimensional Tomonaga–Luttinger liquid limit to the multi-channel Fermi liquid and show that the plasmon velocity can be varied over almost an order of magnitude. These results are in quantitative agreement with a parameter-free theory and demonstrate a powerful probe for directly investigating real-time dynamics of fractionalisation phenomena in low-dimensional conductors.

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory.

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Pseudorandom binary injection of levitons for electron quantum optics

The recent realization of single electron sources let us envision performing electron quantum optics experiments, where electrons can be viewed as flying qubits propagating in a ballistic conductor. To date, all electron sources operate in a periodic electron injection mode leading to energy spectrum singularities in various physical observables which sometimes hide the bare nature of physical effects. To go beyond this, we propose a spread-spectrum approach where electron flying qubits are injected in a non-periodic manner following a pseudorandom binary bit pattern. Extending the Floquet scattering theory approach from periodic to spread-spectrum drive, the shot noise of pseudorandom binary sequences of single electron injection can be calculated for leviton and non-leviton sources. Our new approach allows us to disentangle the physics of the manipulated excitations from that of the injection protocol. In particular, the spread spectrum approach is shown to provide a better knowledge of electronic Hong Ou Mandel correlations and to clarify the nature of the pulse train coherence and the role of the dynamical orthogonality catastrophe for non-integer charge injection.

Strong suppression of shot noise in a feedback-controlled single-electron transistor.

Feedback control of quantum mechanical systems is rapidly attracting attention not only due to fundamental questions about quantum measurements, but also because of its novel applications in many fields in physics. Quantum control has been studied intensively in quantum optics but progress has recently been made in the control of solid-state qubits as well. In quantum transport only a few active and passive feedback experiments have been realized on the level of single electrons, although theoretical proposals exist. Here we demonstrate the suppression of shot noise in a single-electron transistor using an exclusively electronic closed-loop feedback to monitor and adjust the counting statistics. With increasing feedback response we observe a stronger suppression and faster freezing of charge current fluctuations. Our technique is analogous to the generation of squeezed light with in-loop photodetection as used in quantum optics. Sub-Poisson single-electron sources will pave the way for high-precision measurements in quantum transport similar to optical or optomechanical equivalents.

Emission of entangled Kramers pairs from a helical mesoscopic capacitor

The realization of single-electron sources in integer quantum Hall systems has paved the way for exploring electronic quantum optics experiments in solid-state devices. In this work, we characterize a single Kramers pair emitter realized by a driven antidot embedded in a two-dimensional topological insulator, where spin-momentum locked edge states can be exploited for generating entanglement. Contrary to previous proposals, the antidot is coupled to both edges of a quantum spin Hall bar, thus enabling this mesoscopic capacitor to emit an entangled two-electron state. We study the concurrence $\mathcal{C}$ of the emitted state and the efficiency $\mathcal{F}$ of its emission as a function of the different spin-preserving and spin-flipping tunnel couplings of the antidot with the edges. We show that the efficiency remains very high ($\mathcal{F}\geq 50\%$) even for maximally entangled states ($\mathcal{C}=1$). We also discuss how the entanglement can be probed by means of noise measurements and violation of the Clauser-Horne-Shimony-Holt inequality.