Coulomb-mediated antibunching of an electron pair surfing on sound

Electron flying qubits are envisioned as potential information links within a quantum computer, but also promise-like photonic approaches-to serve as self-standing quantum processing units. In contrast to their photonic counterparts, electron-quantum-optics implementations are subject to Coulomb interactions, which provide a direct route to entangle the orbital or spin degree of freedom. However, controlled interaction of flying electrons at the single-particle level has not yet been established experimentally. Here we report antibunching of a pair of single electrons that is synchronously shuttled through a circuit of coupled quantum rails by means of a surface acoustic wave. The in-flight partitioning process exhibits a reciprocal gating effect which allows us to ascribe the observed repulsion predominantly to Coulomb interaction. Our single-shot experiment marks an important milestone on the route to realize a controlled-phase gate for in-flight quantum manipulations.

Bilinear Magnetoresistance in HgTe Topological Insulator: Opposite Signs at Opposite Surfaces Demonstrated by Gate Control

Spin-orbit effects appearing in topological insulators (TI) and at Rashba interfaces are currently revolutionizing how we can manipulate spins and have led to several newly discovered effects, from spin-charge interconversion and spin-orbit torques to novel magnetoresistance phenomena. In particular, a puzzling magnetoresistance has been evidenced as bilinear in electric and magnetic fields. Here, we report the observation of bilinear magnetoresistance (BMR) in strained HgTe, a prototypical TI. We show that both the amplitude and sign of this BMR can be tuned by controlling with an electric gate the relative proportions of the opposite contributions of opposite surfaces. At magnetic fields of 1 T, the magnetoresistance is of the order of 1% and has a larger figure of merit than previously measured TIs. We propose a theoretical model giving a quantitative account of our experimental data. This phenomenon, unique to TI, offers novel opportunities to tune their electrical response for spintronics.

A single hole spin with enhanced coherence in natural silicon

Semiconductor spin qubits based on spin-orbit states are responsive to electric field excitations, allowing for practical, fast and potentially scalable qubit control. Spin electric susceptibility, however, renders these qubits generally vulnerable to electrical noise, which limits their coherence time. Here we report on a spin-orbit qubit consisting of a single hole electrostatically confined in a natural silicon metal-oxide-semiconductor device. By varying the magnetic field orientation, we reveal the existence of operation sweet spots where the impact of charge noise is minimized while preserving an efficient electric-dipole spin control. We correspondingly observe an extension of the Hahn-echo coherence time up to 88 μs, exceeding by an order of magnitude existing values reported for hole spin qubits, and approaching the state-of-the-art for electron spin qubits with synthetic spin-orbit coupling in isotopically purified silicon. Our finding enhances the prospects of silicon-based hole spin qubits for scalable quantum information processing.

Distant spin entanglement via fast and coherent electron shuttling

In the quest for large-scale quantum computing, networked quantum computers offer a natural path towards scalability. While recent experiments have demonstrated nearest neighbour entanglement for electron spin qubits in semiconductors, on-chip long-distance entanglement could bring more versatility to connect quantum core units. Here, we employ the moving trapping potential of a surface acoustic wave to realize the controlled and coherent transfer of a pair of entangled electron spins between two distant quantum dots. The subsequent electron displacement induces coherent spin rotations, which drives spin quantum interferences. We observe high-contrast interference as a signature of the preservation of the entanglement all along the displacement procedure, which includes a separation of the two spins by a distance of 6 μm. This work opens the route towards fast on-chip deterministic interconnection of remote quantum bits in semiconductor quantum circuits.

Coherent control of individual electron spins in a two-dimensional quantum dot array

The coherent manipulation of individual quantum objects organized in arrays is a prerequisite to any scalable quantum information platform. The cumulated efforts to control electron spins in quantum dot arrays have permitted the recent realization of quantum simulators and multielectron spin-coherent manipulations. Although a natural path to resolve complex quantum-matter problems and to process quantum information, two-dimensional (2D) scaling with a high connectivity of such implementations remains undemonstrated. Here we demonstrate the 2D coherent control of individual electron spins in a 3 × 3 array of tunnel-coupled quantum dots. We focus on several key quantum functionalities: charge-deterministic loading and displacement, local spin readout and local coherent exchange manipulation between two electron spins trapped in adjacent dots. This work lays some of the foundations to exploit a 2D array of electron spins for quantum simulation and information processing.

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.

Gate-based high fidelity spin readout in a CMOS device

The engineering of a compact qubit unit cell that embeds all quantum functionalities is mandatory for large-scale integration. In addition, these functionalities should present the lowest error rate possible to successfully implement quantum error correction protocols¹. Electron spins in silicon quantum dots are particularly promising because of their high control fidelity^2-5 and their potential compatibility with complementary metal-oxide-semiconductor industrial platforms^6,7. However, an efficient and scalable spin readout scheme is still missing. Here we demonstrate a high fidelity and robust spin readout based on gate reflectometry in a complementary metal-oxide-semiconductor device that consists of a qubit dot and an ancillary dot coupled to an electron reservoir. This scalable method allows us to read out a spin in a single-shot manner with an average fidelity above 98% for a 0.5 ms integration time. To achieve such a fidelity, we combine radio-frequency gate reflectometry with a latched spin blockade mechanism that requires electron exchange between the ancillary dot and the reservoir. We show that the demonstrated high readout fidelity is fully preserved up to 0.5 K. This result holds particular relevance for the future cointegration of spin qubits and classical control electronics.

Gate-reflectometry dispersive readout and coherent control of a spin qubit in silicon

Silicon spin qubits have emerged as a promising path to large-scale quantum processors. In this prospect, the development of scalable qubit readout schemes involving a minimal device overhead is a compelling step. Here we report the implementation of gate-coupled rf reflectometry for the dispersive readout of a fully functional spin qubit device. We use a p-type double-gate transistor made using industry-standard silicon technology. The first gate confines a hole quantum dot encoding the spin qubit, the second one a helper dot enabling readout. The qubit state is measured through the phase response of a lumped-element resonator to spin-selective interdot tunneling. The demonstrated qubit readout scheme requires no coupling to a Fermi reservoir, thereby offering a compact and potentially scalable solution whose operation may be extended above 1 K.

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.

Highly Efficient Spin-to-Charge Current Conversion in Strained HgTe Surface States Protected by a HgCdTe Layer

We report the observation of spin-to-charge current conversion in strained mercury telluride at room temperature, using spin pumping experiments. We show that a HgCdTe barrier can be used to protect the HgTe from direct contact with the ferromagnet, leading to very high conversion rates, with inverse Edelstein lengths up to 2.0±0.5  nm. The influence of the HgTe layer thickness on the conversion efficiency is found to differ strongly from what is expected in spin Hall effect systems. These measurements, associated with the temperature dependence of the resistivity, suggest that these high conversion rates are due to the spin momentum locking property of HgTe surface states.

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.

Coherent long-distance displacement of individual electron spins

Controlling nanocircuits at the single electron spin level is a possible route for large-scale quantum information processing. In this context, individual electron spins have been identified as versatile quantum information carriers to interconnect different nodes of a spin-based semiconductor quantum circuit. Despite extensive experimental efforts to control the electron displacement over long distances, maintaining electron spin coherence after transfer remained elusive up to now. Here we demonstrate that individual electron spins can be displaced coherently over a distance of 5 µm. This displacement is realized on a closed path made of three tunnel-coupled lateral quantum dots at a speed approaching 100 ms⁻¹. We find that the spin coherence length is eight times longer than expected from the electron spin coherence without displacement, pointing at a process similar to motional narrowing observed in nuclear magnetic resonance experiments. The demonstrated coherent displacement will open the route towards long-range interaction between distant spin qubits.

The spin states of electrons in quantum dots have well-established potential for use as qubits but some proposed developments require the ability to move the quantum spin state across a larger device. Here, the authors experimentally demonstrate coherent shuttling of spins in a ring of three dots.

Fast spin information transfer between distant quantum dots using individual electrons

Transporting ensembles of electrons over long distances without losing their spin polarization is an important benchmark for spintronic devices. It usually requires injecting and probing spin-polarized electrons in conduction channels using ferromagnetic contacts or optical excitation. In parallel with this development, important efforts have been dedicated to achieving control of nanocircuits at the single-electron level. The detection and coherent manipulation of the spin of a single electron trapped in a quantum dot are now well established. Combined with the recently demonstrated control of the displacement of individual electrons between two distant quantum dots, these achievements allow the possibility of realizing spintronic protocols at the single-electron level. Here, we demonstrate that spin information carried by one or two electrons can be transferred between two quantum dots separated by a distance of 4 μm with a classical fidelity of 65%. We show that at present it is limited by spin flips occurring during the transfer procedure before and after electron displacement. Being able to encode and control information in the spin degree of freedom of a single electron while it is being transferred over distances of a few micrometres on nanosecond timescales will pave the way towards 'quantum spintronics' devices, which could be used to implement large-scale spin-based quantum information processing.

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.

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.

Magnetic dephasing in mesoscopic spin glasses

We have measured universal conductance fluctuations in the metallic spin glass Ag:Mn as a function of temperature and magnetic field. From this measurement, we can access the phase coherence time of the electrons in the spin glass. We show that this phase coherence time increases with both the inverse of the temperature and the magnetic field. From this, we deduce that decoherence mechanisms are still active even deep in the spin glass phase.

The diamond superconducting quantum interference device

Diamond is an electrical insulator in its natural form. However, when doped with boron above a critical level (∼0.25 atom %) it can be rendered superconducting at low temperatures with high critical fields. Here we present the realization of a micrometer-scale superconducting quantum interference device (μ-SQUID) made from nanocrystalline boron-doped diamond (BDD) films. Our results demonstrate that μ-SQUIDs made from superconducting diamond can be operated in magnetic fields as large as 4 T independent of the field direction. This is a decisive step toward the detection of quantum motion in a diamond-based nanomechanical oscillator.

Efficient radio frequency filters for space constrained cryogenic setups

Noise filtering is an essential part for measurement of quantum phenomena at extremely low temperatures. Here, we present the design of a filter which can be installed in space constrained cryogenic environment containing a large number of signal carrying lines. Our filters have a -3 db point of 65 kHz and their performance at GHz frequencies is comparable to the best available RF filters.

Nanostructures made from superconducting boron-doped diamond

We report on the transport properties of nanostructures made from boron-doped superconducting diamond. Starting from nanocrystalline superconducting boron-doped diamond thin films, grown by chemical vapour deposition, we pattern by electron-beam lithography devices with dimensions in the nanometer range. We show that even for such small devices, the superconducting properties of the material are well preserved: for wires of width less than 100 nm, we measure critical temperatures in the kelvin range and critical fields in the tesla range.

Effect of disorder on the quantum coherence in mesoscopic wires

We present phase coherence time measurements in quasi-one-dimensional mesoscopic wires made from high mobility two-dimensional electron gas. By implanting gallium ions into a GaAs/AlGaAs heterojunction we are able to vary the diffusion coefficient over 2 orders of magnitude. We show that in the diffusive limit, the decoherence time follows a power law as a function of diffusion coefficient as expected by theory. When the disorder is low enough so that the samples are semiballistic, we observe a new and unexpected regime in which the phase coherence time is independent of disorder. In addition, for all samples the temperature dependence of the phase coherence time follows a power law down to the lowest temperatures without any sign of saturation and this strongly suggests that the frequently observed low temperature saturation is not intrinsic.

Experimental signature of phonon-mediated spin relaxation in a two-electron quantum dot

We observe an experimental signature of the role of phonons in spin relaxation between triplet and singlet states in a two-electron quantum dot. Using both the external magnetic field and the electrostatic confinement potential, we change the singlet-triplet energy splitting from 1.3 meV to zero and observe that the spin relaxation time depends nonmonotonously on the energy splitting. A simple theoretical model is derived to capture the underlying physical mechanism. The present experiment confirms that spin-flip energy is dissipated in the phonon bath.

Driven coherent oscillations of a single electron spin in a quantum dot

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.

Nondestructive Rydberg atom counting with mesoscopic fields in a cavity

We present an efficient, state-selective, nondemolition atom-counting procedure based on the dispersive interaction of a sample of circular Rydberg atoms with a mesoscopic field contained in a high-quality superconducting cavity. The state-dependent atomic index of refraction, proportional to the atom number, shifts the classical field phase. A homodyne procedure translates the information from the phase to the intensity. The final field intensity is readout by a mesoscopic atomic sample. This method opens promising routes for quantum information processing and nonclassical state generation with Rydberg atoms.

Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence

Using an echo technique proposed by Morigi et al., we have time-reversed the atom-field interaction in a cavity quantum electrodynamics experiment. The collapse of the atomic Rabi oscillation in a coherent field is reversed, resulting in an induced revival signal. The amplitude of this "echo" is sensitive to nonunitary decoherence processes. Its observation demonstrates the existence of a mesoscopic quantum superposition of field states in the cavity between the collapse and the revival times.

Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity

We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large quantum state superpositions at the quantum-classical boundary.

Direct measurement of the Wigner function of a one-photon Fock state in a cavity

We have measured the complete Wigner function W of the vacuum and of a single-photon state for a field stored in a high-Q cavity. This experiment implements the direct Lutterbach and Davidovich method [L. G. Lutterbach and L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)]] and is based on the dispersive interaction of a single circular Rydberg atom with the cavity field. The nonclassical nature of the single-photon field is exhibited by a region of negative W values. Extensions to other nonclassical cavity field states are discussed.