Magnetic field compatible circuit quantum electrodynamics with graphene Josephson junctions.

Circuit quantum electrodynamics has proven to be a powerful tool to probe mesoscopic effects in hybrid systems and is used in several quantum computing (QC) proposals that require a transmon qubit able to operate in strong magnetic fields. To address this we integrate monolayer graphene Josephson junctions into microwave frequency superconducting circuits to create graphene based transmons. Using dispersive microwave spectroscopy we resolve graphene's characteristic band dispersion and observe coherent electronic interference effects confirming the ballistic nature of our graphene Josephson junctions. We show that the monoatomic thickness of graphene renders the device insensitive to an applied magnetic field, allowing us to perform energy level spectroscopy of the circuit in a parallel magnetic field of 1 T, an order of magnitude higher than previous studies. These results establish graphene based superconducting circuits as a promising platform for QC and the study of mesoscopic quantum effects that appear in strong magnetic fields.

Conductance through a helical state in an Indium antimonide nanowire.

The motion of an electron and its spin are generally not coupled. However in a one-dimensional material with strong spin-orbit interaction (SOI) a helical state may emerge at finite magnetic fields, where electrons of opposite spin will have opposite momentum. The existence of this helical state has applications for spin filtering and cooper pair splitter devices and is an essential ingredient for realizing topologically protected quantum computing using Majorana zero modes. Here, we report measurements of a quantum point contact in an indium antimonide nanowire. At magnetic fields exceeding 3 T, the 2 e 2/h conductance plateau shows a re-entrant feature toward 1 e 2/h which increases linearly in width with magnetic field. Rotating the magnetic field clearly attributes this experimental signature to SOI and by comparing our observations with a numerical model we extract a spin-orbit energy of approximately 6.5 meV, which is stronger than the spin-orbit energy obtained by other methods.Indium antimonide nanowires have large spin-orbit coupling, which can give rise to helical states that are an important part of proposals for topological quantum computing. Here the authors measure conductance through the helical states and extract a larger spin-orbit energy than obtained before.

Demonstration of an ac Josephson junction laser.

Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.

A valley-spin qubit in a carbon nanotube.

Although electron spins in III-V semiconductor quantum dots have shown great promise as qubits, hyperfine decoherence remains a major challenge in these materials. Group IV semiconductors possess dominant nuclear species that are spinless, allowing qubit coherence times up to 2 s. In carbon nanotubes, where the spin-orbit interaction allows for all-electrical qubit manipulation, theoretical predictions of the coherence time vary by at least six orders of magnitude and range up to 10 s or more. Here, we realize a qubit encoded in two nanotube valley-spin states, with coherent manipulation via electrically driven spin resonance mediated by a bend in the nanotube. Readout uses Pauli blockade leakage current through a double quantum dot. Arbitrary qubit rotations are demonstrated and the coherence time is measured for the first time via Hahn echo, allowing comparison with theoretical predictions. The coherence time is found to be ∼65 ns, probably limited by electrical noise. This shows that, even with low nuclear spin abundance, coherence can be strongly degraded if the qubit states are coupled to electric fields.

Large spin-orbit coupling in carbon nanotubes.

It has recently been recognised that the strong spin-orbit interaction present in solids can lead to new phenomena, such as materials with non-trivial topological order. Although the atomic spin-orbit coupling in carbon is weak, the spin-orbit coupling in carbon nanotubes can be significant due to their curved surface. Previous works have reported spin-orbit couplings in reasonable agreement with theory, and this coupling strength has formed the basis of a large number of theoretical proposals. Here we report a spin-orbit coupling in three carbon nanotube devices that is an order of magnitude larger than previously measured. We find a zero-field spin splitting of up to 3.4 meV, corresponding to a built-in effective magnetic field of 29 T aligned along the nanotube axis. Although the origin of the large spin-orbit coupling is not explained by existing theories, its strength is promising for applications of the spin-orbit interaction in carbon nanotubes devices.

Fast spin-orbit qubit in an indium antimonide nanowire.

Because of the strong spin-orbit interaction in indium antimonide, orbital motion and spin are no longer separated. This enables fast manipulation of qubit states by means of microwave electric fields. We report Rabi oscillation frequencies exceeding 100 MHz for spin-orbit qubits in InSb nanowires. Individual qubits can be selectively addressed due to intrinsic differences in their g factors. Based on Ramsey fringe measurements, we extract a coherence time T(2)(*)=8±1 ns at a driving frequency of 18.65 GHz. Applying a Hahn echo sequence extends this coherence time to 34 ns.

Electrical control of single hole spins in nanowire quantum dots.

The development of viable quantum computation devices will require the ability to preserve the coherence of quantum bits (qubits). Single electron spins in semiconductor quantum dots are a versatile platform for quantum information processing, but controlling decoherence remains a considerable challenge. Hole spins in III-V semiconductors have unique properties, such as a strong spin-orbit interaction and weak coupling to nuclear spins, and therefore, have the potential for enhanced spin control and longer coherence times. A weaker hyperfine interaction has previously been reported in self-assembled quantum dots using quantum optics techniques, but the development of hole-spin-based electronic devices in conventional III-V heterostructures has been limited by fabrication challenges. Here, we show that gate-tunable hole quantum dots can be formed in InSb nanowires and used to demonstrate Pauli spin blockade and electrical control of single hole spins. The devices are fully tunable between hole and electron quantum dots, which allows the hyperfine interaction strengths, g-factors and spin blockade anisotropies to be compared directly in the two regimes.

Spectroscopy of spin-orbit quantum bits in indium antimonide nanowires.

A double quantum dot in the few-electron regime is achieved using local gating in an InSb nanowire. The spectrum of two-electron eigenstates is investigated using electric dipole spin resonance. Singlet-triplet level repulsion caused by spin-orbit interaction is observed. The size and the anisotropy of singlet-triplet repulsion are used to determine the magnitude and the orientation of the spin-orbit effective field in an InSb nanowire double dot. The obtained results are confirmed using spin blockade leakage current anisotropy and transport spectroscopy of individual quantum dots.

Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices.

Majorana fermions are particles identical to their own antiparticles. They have been theoretically predicted to exist in topological superconductors. Here, we report electrical measurements on indium antimonide nanowires contacted with one normal (gold) and one superconducting (niobium titanium nitride) electrode. Gate voltages vary electron density and define a tunnel barrier between normal and superconducting contacts. In the presence of magnetic fields on the order of 100 millitesla, we observe bound, midgap states at zero bias voltage. These bound states remain fixed to zero bias, even when magnetic fields and gate voltages are changed over considerable ranges. Our observations support the hypothesis of Majorana fermions in nanowires coupled to superconductors.

Suppression of Zeeman gradients by nuclear polarization in double quantum dots.

We use electric dipole spin resonance to measure dynamic nuclear polarization in InAs nanowire quantum dots. The resonance shifts in frequency when the system transitions between metastable high and low current states, indicating the presence of nuclear polarization. We propose that the low and the high current states correspond to different total Zeeman energy gradients between the two quantum dots. In the low current state, dynamic nuclear polarization efficiently compensates the Zeeman gradient due to the g-factor mismatch, resulting in a suppressed total Zeeman gradient. We present a theoretical model of electron-nuclear feedback that demonstrates a fixed point in nuclear polarization for nearly equal Zeeman splittings in the two dots and predicts a narrowed hyperfine gradient distribution.

Spin-orbit qubit in a semiconductor nanowire.

Motion of electrons can influence their spins through a fundamental effect called spin-orbit interaction. This interaction provides a way to control spins electrically and thus lies at the foundation of spintronics. Even at the level of single electrons, the spin-orbit interaction has proven promising for coherent spin rotations. Here we implement a spin-orbit quantum bit (qubit) in an indium arsenide nanowire, where the spin-orbit interaction is so strong that spin and motion can no longer be separated. In this regime, we realize fast qubit rotations and universal single-qubit control using only electric fields; the qubits are hosted in single-electron quantum dots that are individually addressable. We enhance coherence by dynamically decoupling the qubits from the environment. Nanowires offer various advantages for quantum computing: they can serve as one-dimensional templates for scalable qubit registers, and it is possible to vary the material even during wire growth. Such flexibility can be used to design wires with suppressed decoherence and to push semiconductor qubit fidelities towards error correction levels. Furthermore, electrical dots can be integrated with optical dots in p-n junction nanowires. The coherence times achieved here are sufficient for the conversion of an electronic qubit into a photon, which can serve as a flying qubit for long-distance quantum communication.

Strong coupling between single-electron tunneling and nanomechanical motion.

Nanoscale resonators that oscillate at high frequencies are useful in many measurement applications. We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 10(5) allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Additional evidence for the strong coupling of mechanical motion and electron tunneling is provided by an energy transfer to the electrons causing mechanical damping and unusual nonlinear behavior. We also discovered that a direct current through the nanotube spontaneously drives the mechanical resonator, exerting a force that is coherent with the high-frequency resonant mechanical motion.

Tunable few-electron double quantum dots and Klein tunnelling in ultraclean carbon nanotubes.

Quantum dots defined in carbon nanotubes are a platform for both basic scientific studies and research into new device applications. In particular, they have unique properties that make them attractive for studying the coherent properties of single-electron spins. To perform such experiments it is necessary to confine a single electron in a quantum dot with highly tunable barriers, but disorder has prevented tunable nanotube-based quantum-dot devices from reaching the single-electron regime. Here, we use local gate voltages applied to an ultraclean suspended nanotube to confine a single electron in both a single quantum dot and, for the first time, in a tunable double quantum dot. This tunability is limited by a novel type of tunnelling that is analogous to the tunnelling in the Klein paradox of relativistic quantum mechanics.

Electric field control of magnetoresistance in InP nanowires with ferromagnetic contacts.

We demonstrate electric field control of sign and magnitude of the magnetoresistance in InP nanowires with ferromagnetic contacts. The sign change in the magnetoresistance is directly correlated with a sign change in the transconductance. Additionally, the magnetoresistance is shown to persist at such a high bias that Coulomb blockade has been lifted. We also observe the magnetoresistance when one of the ferromagnets is replaced by a nonmagnetic metal. We conclude that it must be induced by a single ferromagnetic contact, and that spin transport can be ruled out as the origin. Our results emphasize the importance of a systematic investigation of spin-valve devices in order to discriminate between ambiguous interpretations.

Universal phase shift and nonexponential decay of driven single-spin oscillations.

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear-spin bath. Because of the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of approximately pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit.

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.

Using a quantum dot as a high-frequency shot noise detector.

We present the experimental realization of a quantum dot (QD) operating as a high-frequency noise detector. Current fluctuations produced in a nearby quantum point contact (QPC) ionize the QD and induce transport through excited states. The resulting transient current through the QD represents our detector signal. We investigate its dependence on the QPC transmission and voltage bias. We observe and explain a quantum threshold feature and a saturation in the detector signal. This experimental and theoretical study is relevant in understanding the backaction of a QPC used as a charge detector.

Kondo effect in the presence of magnetic impurities.

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.

Shot-noise detection in a carbon nanotube quantum dot.

An on-chip detection scheme for high frequency signals is used to detect noise generated by a quantum dot formed in a single wall carbon nanotube. The noise detection is based on photon assisted tunneling in a superconductor-insulator-superconductor junction. Measurements of shot noise over a full Coulomb diamond are reported with excited states and inelastic cotunneling clearly resolved. Super-Poissonian noise is detected in the case of inelastic cotunneling.