Coherent Single-electron Research Articles

Room Temperature Quantum Control of N‐Donor Electrons at Si/SiO2 Interface

AbstractThe manuscript theoretically discusses various important aspects for donor atom based single qubit operations in silicon (Si) quantum computer architecture at room temperature using a single nitrogen (N) deep‐donor close to the Si/SiO2 interface. Quantitative investigation of room temperature single electron shuttling between a single N‐donor atom and the interface is the focus of attention under the influence of externally applied electric and magnetic field. To apprehend the realistic experimental configurations, central cell correction along with effective mass approach is adopted throughout the study. Furthermore, a detailed discussion currently explores the significant time scales implicated in the process and their suitability for experimental purposes. Theoretical estimates are also provided for all the external fields required to successfully achieve coherent single electron shuttling and their stable maintenance at the interface as required. The results presented in this work offer practical guidance for quantum electron control using N‐donor atoms in Si at room temperature.

Majorana signatures in charge transport through a topological superconducting double-island system

We investigate the dynamics of a charge qubit consisting of two Coulomb-blockaded islands hosting Majorana zero modes. The frequency of the qubit is determined by coherent single-electron tunneling between two islands originating from the hybridization of two Majorana zero modes localized at the junction. We calculate the sequential tunneling current $I$ through the double-island device coupled to normal metal leads. We demonstrate that the $I\!-\!V$ characteristics in the large-bias regime can be used as a measurement of the coherent Majorana coupling $E_M$. We propose dc and ac transport experiments for measuring $E_M$, and discuss their limitations due to intrinsic dephasing mechanisms such as excited quasiparticles.

Coulomb blockade in field electron emission from carbon nanotubes

We report the observation of Coulomb blockade in electron field emission (FE) from single-wall carbon nanotubes (SWCNTs), which is manifested as pronounced steps in the FE current–voltage curves and oscillatory variations in the energy distribution of emitted electrons. The appearance of the Coulomb blockade is explained by the formation of nanoscale protrusions at the apexes of SWCNTs due to the electric field-assisted surface diffusion of adsorbates and carbon adatoms. The proposed adsorbate-assisted FE mechanism is substantially different from the well-known resonant tunneling associated with discrete electronic states of adsorbed atoms. The simulations based on the Coulomb blockade theory are in excellent agreement with the experimental results. The SWCNT field emitters controlled by the Coulomb blockade effect are expected to be used to develop on-demand coherent single-electron sources for advanced vacuum nanoelectronic devices.

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.

Carbon single-electron point source controlled by Coulomb blockade

The Coulomb blockade effect is commonly used in solid state electronics for the control of electron flow at the single-particle level. Potentially, it allows the creation of single-electron point sources demanded for prospective electron microscopy instruments and other vacuum electronics devices. Here we realize this potential via creation of a stable point electron source composed of a carbon nanowire electrically coupled to a diamond nanotip by a tunnel junction. Using energy spectroscopy analysis, we characterize the electrons liberated from the nanometer scale carbon heterostructures in time and energy domains. Our experimental results demonstrate perfect agreement with theory prediction of Coulomb oscillations of the Fermi level in the nanowire and allow to determine the mechanisms of their suppression. Persistence of the oscillations at room temperature, high intensity field emission with currents up to 1 μA, and other characteristics of our emitters are very promising for practical realization of coherent single-electron guns.

Levitons in helical liquids with Rashba spin-orbit coupling probed by a superconducting contact

We consider transport properties of a single edge of a two-dimensional topological insulators, in presence of Rashba spin-orbit coupling, driven by two external time-dependent voltages and connected to a thin superconductor. We focus on the case of a train of Lorentzian-shaped pulses, which are known to generate coherent single-electron excitations in two-dimensional electron gas, and prove that they are minimal excitations for charge transport also in helical edge states, even in the presence of spin-orbit interaction. Importantly, these properties of Lorentzian-shaped pulses can be tested computing charge noise generated by the scattering of particles at the thin superconductor. This represents a novel setup where electron quantum optics experiments with helical states can be implemented, with the superconducting contact as an effective beamsplitter. By elaborating on this configuration, we also evaluate charge noise in a collisional Hong-Ou-Mandel configuration, showing that, due to the peculiar effects induced by Rashba interaction, a non-vanishing dip at zero delay appears.

Quantum interference capacitor based on double-passage Landau-Zener-Stückelberg-Majorana interferometry

The implementation of quantum technologies in electronics leads naturally to the concept of coherent single-electron circuits, in which a single charge is used coherently to provide enhanced performance. In this work, we propose a coherent single-electron device that operates as an electrically-tunable capacitor. This system exhibits a sinusoidal dependence of the capacitance with voltage, in which the amplitude of the capacitance changes and the voltage period can be tuned by electric means. The device concept is based on double-passage Landau-Zener-St\"uckelberg-Majorana interferometry of a coupled two-level system that is further tunnel-coupled to an electron reservoir. We test this model experimentally by performing Landau-Zener-St\"uckelberg-Majorana interferometry in a single-electron double quantum dot coupled to an electron reservoir and show that the voltage period of the capacitance oscillations is directly proportional to the excitation frequency and that the amplitude of the oscillations depends on the dynamical parameters of the system: intrinsic relaxation and coherence time, as well as the tunneling rate to the reservoir. Our work opens up an opportunity to use the non-linear capacitance of double quantum dots to obtain enhanced device functionalities.

Rapid Detection of Coherent Tunneling in an InAs Nanowire Quantum Dot through Dispersive Gate Sensing

Dispersive sensing is a powerful technique that enables scalable and high-fidelity readout of solid-state quantum bits. In particular, gate-based dispersive sensing has been proposed as the readout mechanism for future topological qubits, which can be measured by single electrons tunneling through zero-energy modes. The development of such a readout requires resolving the coherent charge tunneling amplitude from a quantum dot in a Majorana-zero-mode host system faithfully on short time scales. Here, we demonstrate rapid single-shot detection of a coherent single-electron tunneling amplitude between InAs nanowire quantum dots. We have realized a sensitive dispersive detection circuit by connecting a sub-GHz, lumped element microwave resonator to a high-lever arm gate on one of dots. The resulting large dot-resonator coupling leads to an observed dispersive shift that is of the order of the resonator linewidth at charge degeneracy. This shift enables us to differentiate between Coulomb blockade and resonance, corresponding to the scenarios expected for qubit state readout, with a signal to noise ratio exceeding 2 for an integration time of 1 microsecond. Our result paves the way for single shot measurements of fermion parity on microsecond timescales in topological qubits.

Coherent Single-Electron Transfer in Coupled Semiconductor Quantum Dots Driven by a Few-Cycle Pulse

We theoretically study the coherent transport of a single electron between the ground states of a double coupled quantum dot structure. The coherent transport is externally controlled by applying a few-cycle pulse with an adjustable carrier-envelope phase (CEP). By simulating numerically, it is shown that there exhibits a strong dependence of electron transport on the CEP and on the arrival time of few-cycle pulse. We provide a simple analytical description for this phenomenon by approximating the quantum dot structure as a three-level Λ-type system. These results also illustrate the potential of utilizing excitation in coupled quantum dots as a means of measuring the CEP of few-cycle pulses.

Electron capture imaging of two-dimensional materials

We demonstrate that electron transfer induced by fast ion impact can be used as an imaging technique of two-dimensional materials. Applied to a keV proton beam passing through a graphene surface, it is shown that coherent single-electron capture gives a sub-\aa{}ngstr\"om-scale spatial resolution image of the electronic structure of a single sheet. This imaging scheme is shown to be particularly effective, resolving missing atoms (vacancies) in the lattice, in a narrow projectile 5--10-keV energy region, where the capture probability exhibits a minimum at the center of the hexagonal cells. This geometry-dependent phenomenon is caused by the coupling dynamic between the initial state and a multi-electron entangled one-hole state and is therefore highly sample selective.

Coherent electron transfer in a coupled quantum dot nanostructure using stimulated Raman adiabatic passage

We study the potential for coherent transfer of a single electron between the ground states of two anharmonic coupled quantum dots using an adiabatic passage method. We consider the interaction of a quantum dot structure characterized by an asymmetric confining potential by two external electromagnetic fields. We use the method of stimulated Raman adiabatic passage (STIRAP) for control of the dynamics of the electron, and ultimately for succeeding the transfer of the electron from the initially occupied quantum dot to the other quantum dot. Results for several values of the parameters of the applied electromagnetic fields are presented, and we show that STIRAP can lead to efficient coherent single electron transfer for a wide range of these parameters.

4D Electron Microscopy: Principles and Applications

The transmission electron microscope (TEM) is a powerful tool enabling the visualization of atoms with length scales smaller than the Bohr radius at a factor of only 20 larger than the relativistic electron wavelength of 2.5 pm at 200 keV. The ability to visualize matter at these scales in a TEM is largely due to the efforts made in correcting for the imperfections in the lens systems which introduce aberrations and ultimately limit the achievable spatial resolution. In addition to the progress made in increasing the spatial resolution, the TEM has become an all-in-one characterization tool. Indeed, most of the properties of a material can be directly mapped in the TEM, including the composition, structure, bonding, morphology, and defects. The scope of applications spans essentially all of the physical sciences and includes biology. Until recently, however, high resolution visualization of structural changes occurring on sub-millisecond time scales was not possible. In order to reach the ultrashort temporal domain within which fundamental atomic motions take place, while simultaneously retaining high spatial resolution, an entirely new approach from that of millisecond-limited TEM cameras had to be conceived. As shown below, the approach is also different from that of nanosecond-limited TEM, whose resolution cannot offer the ultrafast regimes of dynamics. For this reason "ultrafast electron microscopy" is reserved for the field which is concerned with femtosecond to picosecond resolution capability of structural dynamics. In conventional TEMs, electrons are produced by heating a source or by applying a strong extraction field. Both methods result in the stochastic emission of electrons, with no control over temporal spacing or relative arrival time at the specimen. The timing issue can be overcome by exploiting the photoelectric effect and using pulsed lasers to generate precisely timed electron packets of ultrashort duration. The spatial and temporal resolutions achievable with short intense pulses containing a large number of electrons, however, are limited to tens of nanometers and nanoseconds, respectively. This is because Coulomb repulsion is significant in such a pulse, and the electrons spread in space and time, thus limiting the beam coherence. It is therefore not possible to image the ultrafast elementary dynamics of complex transformations. The challenge was to retain the high spatial resolution of a conventional TEM while simultaneously enabling the temporal resolution required to visualize atomic-scale motions. In this Account, we discuss the development of four-dimensional ultrafast electron microscopy (4D UEM) and summarize techniques and applications that illustrate the power of the approach. In UEM, images are obtained either stroboscopically with coherent single-electron packets or with a single electron bunch. Coulomb repulsion is absent under the single-electron condition, thus permitting imaging, diffraction, and spectroscopy, all with high spatiotemporal resolution, the atomic scale (sub-nanometer and femtosecond). The time resolution is limited only by the laser pulse duration and energy carried by the electron packets; the CCD camera has no bearing on the temporal resolution. In the regime of single pulses of electrons, the temporal resolution of picoseconds can be attained when hundreds of electrons are in the bunch. The applications given here are selected to highlight phenomena of different length and time scales, from atomic motions during structural dynamics to phase transitions and nanomechanical oscillations. We conclude with a brief discussion of emerging methods, which include scanning ultrafast electron microscopy (S-UEM), scanning transmission ultrafast electron microscopy (ST-UEM) with convergent beams, and time-resolved imaging of biological structures at ambient conditions with environmental cells.

ELECTRON QUANTUM OPTICS IN QUANTUM HALL EDGE CHANNELS

In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the usual case of photon quantum optics. In particular, it provides a natural playground to understand decoherence and relaxation effects in quantum transport.

Coherent single-electron transfer in coupled quantum dots

We theoretically investigate the coherent transfer of one electron between the ground states of a double coupled quantum dot structure. The coherent transfer of the electron is externally controlled by applied electromagnetic fields with on- or close-resonance driving frequencies and various shapes and duration. We derive the analytical expressions for the parameters of the external fields by approximating the quantum dot system as a three-level Λ-type system. The analytical solutions are compared with numerical results and good agreement is found. The control methods developed here are applicable in symmetric and asymmetric quantum dot nanostructures.

Coherent Time Evolution of a Single-Electron Wave Function

Observation of coherent single-electron dynamics is severely limited by experimental bandwidth. We present a method to overcome this using moving quantum dots defined by surface acoustic waves. Each dot holds a single electron, and travels through a static potential landscape. When the dot passes abruptly between regions of different confinement, the electron is excited into a superposition of states, and oscillates unitarily from side to side. We detect these oscillations by using a weak, repeated measurement of the current across a tunnel barrier, and find close agreement with simulations.

Resonant optical electron transfer in one-dimensional multiwell structures

We consider coherent single-electron dynamics in one-dimensional nanostructures under aresonant electromagnetic pulse. The structure is composed of two deep quantumwells positioned at the edges of the structure and separated by a sequence ofshallow internal wells. We show that complete electron transfer between the stateslocalized in the edge wells through one of the excited delocalized states can takeplace at a discrete set of times provided that the pulse frequency matches one ofresonant transition frequencies. The transfer time varies from several tens to severalhundreds of picoseconds and depends on the structure and pulse parameters. Theresults obtained in this paper can be applied to the development of quantumnetworks used in quantum communications and/or quantum information processing.

Coherent single-electron transport between coupled quantum dots

We propose a method for a fully coherent transport of single electrons between the ground states of two anharmonic coupled quantum dots. The transition is achieved as a result of an intrinsic interplay between an external applied radio-frequency field and the interdot tunnel coupling between the single dot states. We have developed a four-level model for the system, and full quantitative agreement with the exact solution of the time-dependent Schr\"odinger equation is obtained for a wide range of field parameters. The model can be solved analytically for the symmetric case and has the advantage that it can be used as guidance in the actual design of such systems.

Interacting Two-Electron Model of a Coherent Quantum-Dot Single-Electron Turnstile

We show how coherent single-electron turnstile action in a picosecond time scale can be achieved with high probability in a triple-well semiconductor structure by means of an applied time-dependent, long-wavelength electric field. We demonstrate the turnstile behavior by studying the exact temporal evolution of two electrons, including their Coulomb interaction, and considering both triplet and singlet states.