Single-electron Emitters Research Articles

Ultracoherent Single-Electron Emission of Carbon Nanotubes.

A single-electron emitter, based on a single quantized energy level, can potentially achieve ultimate temporal and spatial coherence with a large emission current, which is desirable for atomic-resolution electron probes. This is first developed by constructing a nano-object on a metal tip to form a quantized double barrier structure. However, the single-electron-emission current can only achieve a picoampere level due to the low electron tunneling rate of the heterojunction with large barrier width, which limits the practical applications. In this study, carbon nanotubes (CNTs) serve as a single-electron emitter and a current up to 1.5nA is demonstrated. The double barrier structure formed on the CNT tip enables a high tunneling rate (≈1012 s-1 ) due to the smaller barrier width. The emitter also shows high temporal coherence (energy dispersion of ≈10meV) and spatial coherence (effective source radius of ≈0.85nm). This work represents a highly coherent electron source to simplify the electron optics system of atomic-resolution electron microscopy and sub-10nm electron beam lithography.

Finite-frequency noise of interacting single-electron emitters: Spectroscopy with higher noise harmonics

We derive the symmetrized current-noise spectrum of a quantum dot, which is weakly tunnel-coupled to an electron reservoir and driven by a slow time-dependent gate voltage. This setup can be operated as an on-demand emitter of single electrons into a mesoscopic conductor. By extending a real-time diagrammatic technique which is perturbative in the tunnel coupling, we obtain the time-resolved finite-frequency noise as well as its decomposition into noise harmonics in the presence of both strong Coulomb interaction and slow time-dependent driving. We investigate the noise over a large range of frequencies and point out where the interplay of Coulomb interaction and driving leads to unique signatures in finite-frequency noise spectra, in particular in the first harmonic. Besides that, we employ the first noise harmonic as a spectroscopic tool to access individual fluctuation processes. We discuss how the inverse noise frequency sets a time scale for fluctuations, which competes with time scales of the quantum-dot relaxation dynamics as well as the driving.

Self-referenced single-electron quantized current source.

The future redefinition of the international system of units in terms of natural constants requires a robust, high-precision quantum standard for the electrical base unit ampere. However, the reliability of any single-electron current source generating a nominally quantized output current I=ef by delivering single electrons with charge e at a frequency f is eventually limited by the stochastic nature of the underlying quantum mechanical tunneling process. We experimentally explore a path to overcome this fundamental limitation by serially connecting clocked single-electron emitters with multiple insitu single-electron detectors. Correlation analysis of the detector signatures during current generation reveals erroneous pumping events and enables us to determine the deviation of the output current from the nominal quantized value ef. This demonstrates the concept of a self-referenced single-electron source for electrical quantum metrology.

Dephasing in single-electron generation due to environmental noise probed by Hong-Ou-Mandel interferometry

We consider the effect of dephasing on a quantum dot which injects single electrons on a chiral edge channel of the quantum Hall effect. Dephasing is described by the coupling of the dot to a bosonic bath which represents the electromagnetic environment. Using the input-output formalism of quantum optics, we derive the density matrix of the edge degrees of freedom. Results are illustrated by computing the zero frequency current-current correlations when two such single electron emitters achieve a collision at the location of a quantum point contact, in the same spirit as the Hong Ou Mandel experiment of quantum optics. Such correlations are directly linked to the quantum mechanical purity. We show that as observed in a recent experiment, the effect of dephasing leads to a non-vanishing of the Hong Ou Mandel dip when the time delay between the two electron wave packets is zero. Generalizations to time filtered wave packets as well as to asymmetric, detuned injection between opposite edges are obtained.

Emission of time-bin entangled particles into helical edge states

We propose a single-particle source which emits into the helical edge states of a two-dimensional quantum spin Hall insulator. Without breaking time-reversal symmetry, this source acts like a pair of noiseless single-electron emitters which each inject separately into a chiral edge state. By locally breaking time-reversal symmetry, the source becomes a proper single-particle emitter which exhibits shot noise. Due to its intrinsic helicity, this system can be used to produce time-bin entangled pairs of electrons in a controlled manner. The shot noise created by the source is related to the concurrence of the emitted state.

Electron quantum optics in ballistic chiral conductors

AbstractThe edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics‐like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on‐demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury‐Brown and Twiss geometry where two‐particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.

Noise of a single-electron emitter

I analyze the correlation function of currents generated by the periodically driven quantum capacitor emitting single electrons and holes into the chiral waveguide. I compare adiabatic and non-adiabatic, transient working regimes of a single-electron emitter and find the striking difference between the correlation functions in two regimes. Quite generally for the system driven with frequency $\Omega$ the correlation function depends on two frequencies, $\omega$ and $\ell \Omega - \omega$, where $\ell$ is an integer. For the emitter driven non-adiabatically the correlation functions for different $\ell$ are similar and almost symmetric in $\omega$. While in the case of adiabatic drive the correlation functions for $\ell \ne 0$ are highly asymmetric in $\omega$ and exceed significantly the one corresponding to $\ell = 0$. Under optimal operating conditions the correlation function for odd $\ell$ is zero.

Current noise spectrum of a single-particle emitter: Theory and experiment

The controlled and accurate emission of coherent electronic wave packets is of prime importance for future applications of nano-scale electronics. Here we present a theoretical and experimental analysis of the finite-frequency noise spectrum of a periodically driven single electron emitter. The electron source consists of a mesoscopic capacitor that emits single electrons and holes into a chiral edge state of a quantum Hall sample. We compare experimental results with two complementary theoretical descriptions: On one hand, the Floquet scattering theory which leads to accurate numerical results for the noise spectrum under all relevant operating conditions. On the other hand, a semi-classical model which enables us to develop an analytic description of the main sources of noise when the emitter is operated under optimal conditions. We find excellent agreement between experiment and theory. Importantly, the noise spectrum provides us with an accurate description and characterization of the mesoscopic capacitor when operated as a periodic single electron emitter.

Real-time simulation of finite-frequency noise from a single-electron emitter

We study the real-time emission of single electrons from a quantum dot coupled to a one dimensional conductor, using exact diagonalization on a discrete tight-binding chain. We show that from the calculation of the time-evolution of the one electron states, we have a simple access to all the relevant physical quantities in the system. In particular, we are able to compute accurately the finite frequency current autocorrelation noise. The method which we use is general and versatile, allowing to study the impact of many different parameters like the dot transparency or level position. Our results can be directly compared with existing experiments, and can also serve as a basis for future calculations including electronic interactions using the time dependent density-matrix renormalisation group and other techniques based on tight-binding models.

Distributions of Waiting Times of Dynamic Single-Electron Emitters

The distribution of waiting times between elementary tunneling events is of fundamental importance for understanding the stochastic charge transfer processes in nanoscale conductors. Here we investigate the waiting time distributions (WTDs) of periodically driven single-electron emitters and evaluate them for the specific example of a mesoscopic capacitor. We show that the WTDs provide a particularly informative characterization of periodically driven devices and we demonstrate how the WTDs allow us to reconstruct the full counting statistics (FCS) of charges that have been transferred after a large number of periods. We find that the WTDs are capable of describing short-time physics and correlations which are not accessible via the FCS alone.

Spectroscopy of electron flows with single- and two-particle emitters

To analyze the state of injected carrier streams of different electron sources, we propose to use correlation measurements at a quantum point contact with the different sources connected via chiral edge states to the two inputs. In particular we consider the case of an on-demand single-electron emitter correlated with the carriers incident from a biased normal reservoir, a contact subject to an alternating voltage and a stochastic single electron emitter. The correlation can be viewed as a spectroscopic tool to compare the states of injected particles of different sources. If at the quantum point contact the amplitude profiles of electrons overlap, the noise correlation is suppressed. In the absence of an overlap the noise is roughly the sum of the noise powers due to the electron streams in each input. We show that the electron state emitted from a (dc or ac) biased metallic contact is different from a Lorentzian amplitude electron state emitted by the single electron emitter (a quantum capacitor driven with slow harmonic potential), since with these inputs the noise correlation is not suppressed. In contrast, if quantized voltage pulses are applied to a metallic contact instead of a dc (ac) bias then the noise can be suppressed. We find a noise suppression for multi-electron pulses and for the case of stochastic electron emitters for which the appearance of an electron at the quantum point contact is probabilistic.

Current correlations of an on-demand single-electron emitter

In analogy with quantum optics, short-time correlations of the current fluctuations are measured and used to assess the quality of the single-particle emission of a recently introduced on-demand electron source. We observe, in the context of electronics, the fundamental noise limit associated with the quantum fluctuations of the emission time of single particles, or quantum jittering. In optimum operating conditions of the source, the noise reduces to the quantum jitter limit, which demonstrates single-particle emission. Combined with the coherent manipulations of single electrons in a quantum conductor, this electron quantum optics experiment opens the way to explore new problems including quantum statistics and interactions at the single-electron level.