Shintaro Takada

Coherent control of single electrons: a review of current progress

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

Electrons surfing on a sound wave as a platform for quantum optics with flying electrons

Electrons in a metal are indistinguishable particles that interact strongly with other electrons and their environment. Isolating and detecting a single flying electron after propagation, in a similar manner to quantum optics experiments with single photons, is therefore a challenging task. So far only a few experiments have been performed in a high-mobility two-dimensional electron gas in which the electron propagates almost ballistically. In these previous works, flying electrons were detected by means of the current generated by an ensemble of electrons, and electron correlations were encrypted in the current noise. Here we demonstrate the experimental realization of high-efficiency single-electron source and detector for a single electron propagating isolated from the other electrons through a one-dimensional channel. The moving potential is excited by a surface acoustic wave, which carries the single electron along the one-dimensional channel at a speed of 3 μm ns−1. When this quantum channel is placed between two quantum dots several micrometres apart, a single electron can be transported from one quantum dot to the other with quantum efficiencies of emission and detection of 96% and 92%, respectively. Furthermore, the transfer of the electron can be triggered on a timescale shorter than the coherence time T2* of GaAs spin qubits. Our work opens new avenues with which to study the teleportation of a single electron spin and the distant interaction between spatially separated qubits in a condensed-matter system.

Quantum Manipulation of Two-Electron Spin States in Isolated Double Quantum Dots.

We studied experimentally the dynamics of the exchange interaction between two antiparallel electron spins in an isolated double quantum dot where coupling to the electron reservoirs can be ignored. We demonstrate that the level of control of such a double dot is higher than in conventional double dots. In particular, it allows us to couple coherently two electron spins in an efficient manner following a scheme initially proposed by Loss and DiVincenzo [Phys. Rev. A 57, 120 (1998)]. The present study demonstrates that isolated quantum dots are a possible route to increase the number of coherently coupled quantum dots.

Transmission Phase in the Kondo Regime Revealed in a Two-Path Interferometer

We report on the direct observation of the transmission phase shift through a Kondo correlated quantum dot by employing a new type of two-path interferometer. We observed a clear π/2-phase shift, which persists up to the Kondo temperature TK. Above this temperature, the phase shifts by more than π/2 at each Coulomb peak, approaching the behavior observed for the standard Coulomb blockade regime. These observations are in remarkable agreement with two-level numerical renormalization group calculations. The unique combination of experimental and theoretical results presented here fully elucidates the phase evolution in the Kondo regime.

Injection of a single electron from static to moving quantum dots.

We study the injection mechanism of a single electron from a static quantum dot into a moving quantum dot. The moving quantum dots are created with surface acoustic waves (SAWs) in a long depleted channel. We demonstrate that the injection process is characterized by an activation law with a threshold that depends on the SAW amplitude and on the dot-channel potential gradient. By sufficiently increasing the SAW modulation amplitude, we can reach a regime where the transfer has unity probability and is potentially adiabatic. This study points to the relevant regime to use moving dots in quantum information protocols.

Aharonov–Bohm interferometry with a tunnel-coupled wire

Recent experiments (Yamamoto et al 2012 Nature Nanotechnology 7 247) used the transport of electrons through an Aharonov–Bohm (AB) interferometer and two coupled channels (at both ends of the interferometer) to demonstrate a manipulable flying qubit. Results included in-phase and anti-phase (AB) oscillations of the two outgoing currents as a function of the magnetic flux, for strong and weak inter-channel coupling, respectively. Here we present new experimental results for a three terminal interferometer, with a tunnel coupling between the two outgoing wires. We show that in some limits, this system is an even simpler realization of the ‘two-slit’ experiment. We also present a simple tight-binding theoretical model which imitates the experimental setup. For weak inter-channel coupling, the AB oscillations in the current which is reflected from the device are very small, and therefore the oscillations in the two outgoing currents must cancel each other, yielding the anti-phase behavior, independent of the length of the coupling regime. Technically, the tight binding equations within the two coupled wires have four solutions for each electronic energy. In the ‘anti-phase’ region all of these solutions are wave-like, oscillating with the distance along the wires. As the coupling between the wires increases, two of these solutions become evanescent, and their amplitudes decay as the electron moves in the wires. In this regime, the amplitudes of the two remaining ‘running’ waves are proportional to each other, with a ratio which is practically flux-independent. As a result, the two outgoing currents are proportional to each other, yielding the ‘in phase’ behavior. For larger coupling all the solutions are evanescent, and the outgoing currents become very small.

Fast and efficient single electron transfer between distant quantum dots

Lateral quantum dots are a promising system for quantum information processing devices. The required basic manipulations of a single electron spin have indeed been demonstrated. However, a stringent requirement is the ability to transfer quantum information from place to place within one sample. In this work, we explore and demonstrate the possibility to transfer a single electron between two distant quantum dots in a fast and reliable manner.

Measurement of the transmission phase of an electron in a quantum two-path interferometer

A quantum two-path interferometer allows for direct measurement of the transmission phase shift of an electron, providing useful information on coherent scattering problems. In mesoscopic systems, however, the two-path interference is easily smeared by contributions from other paths, and this makes it difficult to observe the true transmission phase shift. To eliminate this problem, multi-terminal Aharonov-Bohm (AB) interferometers have been used to derive the phase shift by assuming that the relative phase shift of the electrons between the two paths is simply obtained when a smooth shift of the AB oscillations is observed. Nevertheless, the phase shifts using such a criterion have sometimes been inconsistent with theory. On the other hand, we have used an AB ring contacted to tunnel-coupled wires and acquired the phase shift consistent with theory when the two output currents through the coupled wires oscillate with well-defined anti-phase. Here, we investigate thoroughly these two criteria used to ensu...

Mesoscopic phase behavior in a quantum dot around crossover between single-level and multilevel transport regimes

The transmission phase across a quantum dot (QD) is expected to show mesoscopic behavior, where the appearance of a phase lapse between Coulomb peaks (CPs) as a function of the gate voltage depends on the orbital parity relation between the corresponding CPs. On the other hand, such mesoscopic behavior has been observed only in a limited QD configuration (a few-electron and single-level transport regime) and universal phase lapses by

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