Electrical control of a solid-state flying qubit

Time-resolved sensing of electromagnetic fields with single-electron interferometry

Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field's time-dependent amplitude and its quantum fluctuations. So far, this has been achieved by using either homodyne detection or fast digitizers. Both methods rely on the extraction of microwave radiation through an amplification chain towards the detector placed at room temperature, thereby limiting the time resolution to the ~10-GHz bandwidth of the measurement chain. Additionally, the coupling of high-impedance samples to the 50-Ω measurement chain is very weak, setting strong limitations on the detection sensitivity. In this work, we demonstrate an on-chip quantum sensor that exploits the phase of a single-electron wavefunction, measured in an electronic Fabry-Pérot interferometer, to detect the amplitude of a classical time-dependent electric field. The interferometer is implemented in a GaAs/AlGaAs quantum Hall conductor. The time resolution, limited by the temporal width of the electronic wavepacket, is ~35 ps. The interferometry technique provides a voltage resolution of ~50 μV, corresponding to a few microwave photons. Importantly, our detector measures both phase and contrast of the interference pattern. The latter opens the way to the detection of non-classical electromagnetic fields, such as squeezed or Fock states.

Exploring the Accuracy of Interferometric Quantum Measurements under Conservation Laws

A (target) quantum system is often measured through observations performed on a second (meter) system to which the target is coupled. In the presence of global conservation laws holding on the joint meter-target system, the Wigner-Araki-Yanase theorem and its generalizations predict a lower bound on the measurement's error (Ozawa's bound). While practically negligible for macroscopic meters, it becomes relevant for microscopic ones. Here, we propose a simple interferometric setup, arguably within reach of present technology, in which a flying particle (a microscopic quantum meter) is used to measure a qubit by interacting with it in one arm of the interferometer. In this scenario, the globally conserved quantity is the total energy of particle and qubit. We show how the measurement error ϵ is linked to the nonstationary nature of the measured observable and the finite duration of the target-meter interaction while Ozawa's bound ϵ_{B} only depends on the momentum uncertainty of the meter's wave packet. When considering short wave packets with respect to the evolution time of the qubit, we show that ϵ/ϵ_{B} is strictly tied to the position-momentum uncertainty of the meter's wave packet and ϵ/ϵ_{B}→1 only when employing Gaussian wave packets. On the contrary, long wave packets of any shape lead to ϵ/ϵ_{B}→sqrt[2]. In addition to their fundamental relevance, our findings have important practical consequences for optimal resource management in quantum technologies.

High-temperature quantum valley Hall effect with quantized resistance and a topological switch

Edge states of a topological insulator can be used to explore fundamental science emerging at the interface of low dimensionality and topology. Achieving a robust conductance quantization, however, has proven challenging for helical edge states. In this work, we show wide resistance plateaus in kink states-a manifestation of the quantum valley Hall effect in Bernal bilayer graphene-quantized to the predicted value at zero magnetic field. The plateau resistance has a very weak temperature dependence up to 50 kelvin and is flat within a dc bias window of tens of millivolts. We demonstrate the electrical operation of a topology-controlled switch with an on/off ratio of 200. These results demonstrate the robustness and tunability of the kink states and its promise in constructing electron quantum optics devices.

Shaping Electronic Flows with Strongly Correlated Physics

Nonequilibrium quantum transport is of central importance in nanotechnology. Its description requires the understanding of strong electronic correlations that couple atomic-scale phenomena to the nanoscale. So far, research in correlated transport has focused predominantly on few-channel transport, precluding the investigation of cross-scale effects. Recent theoretical advances enable the solution of models that capture the interplay between quantum correlations and confinement beyond a few channels. This problem is the focus of this study. We consider an atomic impurity embedded in a metallic nanosheet spanning two leads, showing that transport is significantly altered by tuning only the phase of a single local hopping parameter. Furthermore─depending on this phase─correlations reshape the electronic flow throughout the sheet, either funneling it through the impurity or scattering it away from a much larger region. This demonstrates the potential for quantum correlations to bridge length scales in the design of nanoelectronic devices and sensors.

Scaling behavior of electron decoherence in a graphene Mach-Zehnder interferometer

Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer1,2, and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers.

Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

Phase-space studies of backscattering diffraction of defective Schrödinger cat states

The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.

Coherent Beam Splitting of Flying Electrons Driven by a Surface Acoustic Wave

We develop a coherent beam splitter for single electrons driven through two tunnel-coupled quantum wires by surface acoustic waves (SAWs). The output current through each wire oscillates with gate voltages to tune the tunnel coupling and potential difference between the wires. This oscillation is assigned to coherent electron tunneling motion that can be used to encode a flying qubit and is well reproduced by numerical calculations of time evolution of the SAW-driven single electrons. The oscillation visibility is currently limited to about 3%, but robust against decoherence, indicating that the SAW electron can serve as a novel platform for a solid-state flying qubit.

Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects

We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom—both linear and quadratic—in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.

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 optics^2-4, qubit control^5-7, quantum sensing^8,9 and quantum metrology¹⁰. Although electron dynamics along an extended channel has been studied extensively^2-4,11, 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.

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.

Quantum tomography of electrical currents

In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunctions and their emission probabilities from any electrical current. It combines two-particle interferometry with signal processing. Using our technique, we extract the wavefunctions generated by trains of Lorentzian pulses carrying one or two electrons. By demonstrating the synthesis and complete characterization of electronic wavefunctions in conductors, this work offers perspectives for quantum information processing with electrical currents and for investigating basic quantum physics in many-body systems.

Orbital-flop Induced Magnetoresistance Anisotropy in Rare Earth Monopnictide CeSb

The charge and spin of the electrons in solids have been extensively exploited in electronic devices and in the development of spintronics. Another attribute of electrons—their orbital nature—is attracting growing interest for understanding exotic phenomena and in creating the next-generation of quantum devices such as orbital qubits. Here, we report on orbital-flop induced magnetoresistance anisotropy in CeSb. In the low temperature high magnetic-field driven ferromagnetic state, a series of additional minima appear in the angle-dependent magnetoresistance. These minima arise from the anisotropic magnetization originating from orbital-flops and from the enhanced electron scattering from magnetic multidomains formed around the first-order orbital-flop transition. The measured magnetization anisotropy can be accounted for with a phenomenological model involving orbital-flops and a spin-valve-like structure is used to demonstrate the viable utilization of orbital-flop phenomenon. Our results showcase a contribution of orbital behavior in the emergence of intriguing phenomena.

The orbital degree of freedom can be as important as the charge and spin of the electron to the electronic phenomena. Here the authors show additional minimum in the angle-dependent magnetoresistance (MR) for the low temperature high magnetic field driven ferromagnetic state in CeSb which indicates the orbital flop induced MR anisotropy.

Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot

In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stückelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport.

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.

Electronic excitations in low-dimensional quantum nanoelectronic devices are collective waves that are strongly affected by the Coulomb interaction. Here, the authors demonstrate that they are able to prepare these collective excitations down to the single electron level and control their propagation.

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.

Non-universal transmission phase behaviour of a large quantum dot

The electron wave function experiences a phase modification at coherent transmission through a quantum dot. This transmission phase undergoes a characteristic shift of π when scanning through a Coulomb blockade resonance. Between successive resonances either a transmission phase lapse of π or a phase plateau is theoretically expected to occur depending on the parity of quantum dot states. Despite considerable experimental effort, this transmission phase behaviour has remained elusive for a large quantum dot. Here we report on transmission phase measurements across such a large quantum dot hosting hundreds of electrons. Scanning the transmission phase along 14 successive resonances with an original two-path interferometer, we observe both phase lapses and plateaus. We demonstrate that quantum dot deformation alters the sequence of phase lapses and plateaus via parity modifications of the involved quantum dot states. Our findings set a milestone towards an comprehensive understanding of the transmission phase of quantum dots.

Absorptive pinhole collimators for ballistic Dirac fermions in graphene

Ballistic electrons in solids can have mean free paths far larger than the smallest features patterned by lithography. This has allowed development and study of solid-state electron-optical devices such as beam splitters and quantum point contacts, which have informed our understanding of electron flow and interactions. Recently, high-mobility graphene has emerged as an ideal two-dimensional semimetal that hosts unique chiral electron-optical effects due to its honeycomb crystalline lattice. However, this chiral transport prevents the simple use of electrostatic gates to define electron-optical devices in graphene. Here we present a method of creating highly collimated electron beams in graphene based on collinear pairs of slits, with absorptive sidewalls between the slits. By this method, we achieve beams with angular width 18° or narrower, and transmission matching classical ballistic predictions.

Shaping and guiding the flow of ballistic electrons is at the core of electron optics; however in graphene this is hindered by chiral tunneling. Here, the authors experimentally demonstrate an electron collimator based on hBN-encapsulated ballistic graphene, capable of emitting narrow electron beams.

Minimal Excitations in the Fractional Quantum Hall Regime

We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown-Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.

Fractionally Charged Zero-Energy Single-Particle Excitations in a Driven Fermi Sea

A voltage pulse of a Lorentzian shape carrying half of the flux quantum excites out of a zero-temperature Fermi sea an electron in a mixed state, which looks like a quasiparticle with an effectively fractional charge e/2. A prominent feature of such an excitation is a narrow peak in the energy distribution function lying exactly at the Fermi energy μ. Another spectacular feature is that the distribution function has symmetric tails around μ, which results in a zero-energy excitation. This sounds improbable since at zero temperature all available states below μ are fully occupied. The resolution lies in the fact that such a voltage pulse also excites electron-hole pairs, which free some space below μ and thus allow a zero-energy quasiparticle to exist. I discuss also how to address separately electron-hole pairs and a fractionally charged zero-energy excitation in an experiment.

Doppler effect induced spin relaxation boom

We study an electron spin qubit confined in a moving quantum dot (QD), with our attention on both spin relaxation, and the product of spin relaxation, the emitted phonons. We find that Doppler effect leads to several interesting phenomena. In particular, spin relaxation rate peaks when the QD motion is in the transonic regime, which we term a spin relaxation boom in analogy to the classical sonic boom. This peak indicates that a moving spin qubit may have even lower relaxation rate than a static qubit, pointing at the possibility of coherence-preserving transport for a spin qubit. We also find that the emitted phonons become strongly directional and narrow in their frequency range as the qubit reaches the supersonic regime, similar to Cherenkov radiation. In other words, fast moving excited spin qubits can act as a source of non-classical phonons. Compared to classical Cherenkov radiation, we show that quantum dot confinement produces a small but important correction on the Cherenkov angle. Taking together, these results have important implications to both spin-based quantum information processing and coherent phonon dynamics in semiconductor nanostructures.

Mode Dependency of Quantum Decoherence Studied via an Aharonov-Bohm Interferometer

We investigate the dependence of decoherence on the mode number M in a multiple-mode Aharonov-Bohm (AB) interferometer. The design of the AB interferometer allows us to precisely determine M by the additivity rule of ballistic conductors; meanwhile, the decoherence rate is simultaneously deduced by the variance of the AB oscillation amplitude. The AB amplitude decreases and fluctuates with depopulating M. Moreover, the normalized amplitude exhibits a maximum at a specific M (∼9). Data analysis reveals that the charge-fluctuation-induced dephasing, which depends on the geometry and the charge relaxation resistance of the system, could play an essential role in the decoherence process. Our results suggest that the phase coherence, in principle, can be optimized using a deliberated design and pave one of the ways toward the engineering of quantum coherence.

The classical and quantum dynamics of molecular spins on graphene

Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain's threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices.

Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets

We compute the exact single-particle time-resolved dynamics of electronic Mach-Zehnder interferometers based on Landau edge-states transport, and assess the effect of the spatial localization of carriers on the interference pattern. The exact carrier dynamics is obtained by solving numerically the time-dependent Schrödinger equation with a suitable 2D potential profile reproducing the interferometer design. An external magnetic field, driving the system to the quantum Hall regime with filling factor one, is included. The injected carriers are represented by a superposition of edge states, and their interference pattern-controlled via magnetic field and/or area variation-reproduces the one of (Ji et al 2003 Nature 422 415). By tuning the system towards different regimes, we find two additional features in the transmission spectra, both related to carrier localization, namely a damping of the Aharonov-Bohm oscillations with increasing difference in the arms length, and an increased mean transmission that we trace to the energy-dependent transmittance of quantum point contacts. Finally, we present an analytical model, also accounting for the finite spatial dispersion of the carriers, able to reproduce the above effects.

Subdecoherence time generation and detection of orbital entanglement in quantum dots

Recent experiments have demonstrated subdecoherence time control of individual single-electron orbital qubits. Here we propose a quantum-dot-based scheme for generation and detection of pairs of orbitally entangled electrons on a time scale much shorter than the decoherence time. The electrons are entangled, via two-particle interference, and transferred to the detectors during a single cotunneling event, making the scheme insensitive to charge noise. For sufficiently long detector dot lifetimes, cross-correlation detection of the dot charges can be performed with real-time counting techniques, providing for an unambiguous short-time Bell inequality test of orbital entanglement.

Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization

Coulomb interaction has a striking effect on electronic propagation in one-dimensional conductors. The interaction of an elementary excitation with neighbouring conductors favours the emergence of collective modes, which eventually leads to the destruction of the Landau quasiparticle. In this process, an injected electron tends to fractionalize into separated pulses carrying a fraction of the electron charge. Here we use two-particle interferences in the electronic analogue of the Hong-Ou-Mandel experiment in a quantum Hall conductor at filling factor 2 to probe the fate of a single electron emitted in the outer edge channel and interacting with the inner one. By studying both channels, we analyse the propagation of the single electron and the generation of interaction-induced collective excitations in the inner channel. These complementary pieces of information reveal the fractionalization process in the time domain and establish its relevance for the destruction of the quasiparticle, which degrades into the collective modes.

A charge injected into the edge of a correlated one-dimensional system can split into separate charge packages. Freulon et al. now study this electron fractionalization on the picosecond timescale using Hong-Ou-Mandel interferometry.

The a.c. Josephson effect without superconductivity

Superconductivity derives its most salient features from the coherence of the associated macroscopic wave function. The related physical phenomena have now moved from exotic subjects to fundamental building blocks for quantum circuits such as qubits or single photonic modes. Here we predict that the a.c. Josephson effect—which transforms a d.c. voltage V_b into an oscillating signal cos (2eV_bt/ħ)—has a mesoscopic counterpart in normal conductors. We show that when a d.c. voltage V_b is applied to an electronic interferometer, there exists a universal transient regime where the current oscillates at frequency eV_b/h. This effect is not limited by a superconducting gap and could, in principle, be used to produce tunable a.c. signals in the elusive 0.1–10-THz ‘terahertz gap’.

Most of the peculiar effects resulting from superconductivity have counterparts in nonsuperconducting nanoelectronic devices, but not yet in the a.c. Josephson effect. Here, the authors propose how to generate a transient version of this phenomenon in a normal conductor by abruptly changing the bias voltage.

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 successfully partitioned, as verified by measuring the coincidence of arrival. Here, we demonstrate the splitting of electron pairs generated on demand. Coincidence correlation measurements allow the reconstruction of the full counting statistics, revealing regimes of statistically independent, distinguishable or correlated partitioning, and have been envisioned as a source of information on the quantum state of the electron pair. The high pair-splitting fidelity opens a path to future on-demand generation of spin-entangled electron pairs from a suitably prepared two-electron quantum-dot ground state.

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.

Aharonov-Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap

Quantum tunnelling is a common fundamental quantum mechanical phenomenon that originates from the wave-like characteristics of quantum particles. Although the quantum tunnelling effect was first observed 85 years ago, some questions regarding the dynamics of quantum tunnelling remain unresolved. Here we realize a quantum tunnelling system using two-dimensional ionic structures in a linear Paul trap. We demonstrate that the charged particles in this quantum tunnelling system are coupled to the vector potential of a magnetic field throughout the entire process, even during quantum tunnelling, as indicated by the manifestation of the Aharonov-Bohm effect in this system. The tunnelling rate of the structures periodically depends on the strength of the magnetic field, whose period is the same as the magnetic flux quantum φ0 through the rotor [(0.99 ± 0.07) × φ0].

Minimal-excitation states for electron quantum optics using levitons

The on-demand generation of pure quantum excitations is important for the operation of quantum systems, but it is particularly difficult for a system of fermions. This is because any perturbation affects all states below the Fermi energy, resulting in a complex superposition of particle and hole excitations. However, it was predicted nearly 20 years ago that a Lorentzian time-dependent potential with quantized flux generates a minimal excitation with only one particle and no hole. Here we report that such quasiparticles (hereafter termed levitons) can be generated on demand in a conductor by applying voltage pulses to a contact. Partitioning the excitations with an electronic beam splitter generates a current noise that we use to measure their number. Minimal-excitation states are observed for Lorentzian pulses, whereas for other pulse shapes there are significant contributions from holes. Further identification of levitons is provided in the energy domain with shot-noise spectroscopy, and in the time domain with electronic Hong-Ou-Mandel noise correlations. The latter, obtained by colliding synchronized levitons on a beam splitter, exemplifies the potential use of levitons for quantum information: using linear electron quantum optics in ballistic conductors, it is possible to imagine flying-qubit operation in which the Fermi statistics are exploited to entangle synchronized electrons emitted by distinct sources. Compared with electron sources based on quantum dots, the generation of levitons does not require delicate nanolithography, considerably simplifying the circuitry for scalability. Levitons are not limited to carrying a single charge, and so in a broader context n-particle levitons could find application in the study of full electron counting statistics. But they can also carry a fraction of charge if they are implemented in Luttinger liquids or in fractional quantum Hall edge channels; this allows the study of Abelian and non-Abelian quasiparticles in the time domain. Finally, the generation technique could be applied to cold atomic gases, leading to the possibility of atomic levitons.

Coherence and indistinguishability of single electrons emitted by independent sources

The on-demand emission of coherent and indistinguishable electrons by independent synchronized sources is a challenging task of quantum electronics, in particular regarding its application for quantum information processing. Using two independent on-demand electron sources, we triggered the emission of two single-electron wave packets at different inputs of an electronic beam splitter. Whereas classical particles would be randomly partitioned by the splitter, we observed two-particle interference resulting from quantum exchange. Both electrons, emitted in indistinguishable wave packets with synchronized arrival time on the splitter, exited in different outputs as recorded by the low-frequency current noise. The demonstration of two-electron interference provides the possibility of manipulating coherent and indistinguishable single-electron wave packets in quantum conductors.