Relaxation and dephasing in a two-electron 13C nanotube double quantum dot

Electron Spin Decoherence Dynamics in Magnetic Manganese Hybrid Organic-Inorganic Crystals: The Effect of Lattice Dimensionality

Organic-inorganic metal hybrids with their tailorable lattice dimensionality and intrinsic spin-splitting properties are interesting material platforms for spintronic applications. While the spin decoherence process is extensively studied in lead- and tin-based hybrids, these systems generally show short spin decoherence lifetimes, and their correlation with the lattice framework is still not well-understood. Herein, we synthesized magnetic manganese hybrid single crystals of (4-fluorobenzylamine)2MnCl4, ((R)-3-fluoropyrrolidinium)MnCl3, and (pyrrolidinium)2MnCl4, which represent a change in lattice dimensionality from 2D and 1D to 0D, and studied their spin decoherence processes using continuous-wave electron spin resonance spectroscopy. All manganese hybrids exhibit nanosecond-scale spin decoherence time τ2 dominated by the symmetry-directed spin exchange interaction strengths of Mn2+-Mn2+ pairs, which is much longer than lead- and tin-based metal hybrids. In contrast to the similar temperature variation laws of τ2 in 2D and 0D structures, which first increase and gradually drop afterward, the 1D structure presents a monotonous rise of τ2 with the temperatures, indicating the strong correlation of spin decoherence with the lattice rigidity of the inorganic framework. This is also rationalized on the basis that the spin decoherence is governed by the competitive contributions from motional narrowing (prolonging the τ2) and electron-phonon coupling interaction (shortening the τ2), both of which are thermally activated, with the difference that the former is more pronounced in rigid crystalline lattices.

Novel Nanotube Multiquantum Dot Devices

Addressable quantum states well isolated from the environment are of considerable interest for quantum information science and technology. Carbon nanotubes are an appealing system, since a perfect crystal can be grown without any missing atoms and its cylindrical structure prevents ill-defined atomic arrangement at the surface. Here, we develop a reliable process to fabricate compact multielectrode circuits that can sustain the harsh conditions of the nanotube growth. Nanotubes are suspended over multiple gate electrodes, which are themselves structured over narrow dielectric ridges to reduce the effect of the charge fluctuators of the substrate. We measure high-quality double- and triple-quantum dot charge stability diagrams. Transport measurements through the triple-quantum dot indicate long-range tunneling of single electrons between the left and right quantum dots. This work paves the way to the realization of a new generation of condensed-matter devices in an ultraclean environment, including spin qubits, mechanical qubits, and quantum simulators.

Spin relaxation in a single-electron graphene quantum dot

The relaxation time of a single-electron spin is an important parameter for solid-state spin qubits, as it directly limits the lifetime of the encoded information. Thanks to the low spin-orbit interaction and low hyperfine coupling, graphene and bilayer graphene (BLG) have long been considered promising platforms for spin qubits. Only recently, it has become possible to control single-electrons in BLG quantum dots (QDs) and to understand their spin-valley texture, while the relaxation dynamics have remained mostly unexplored. Here, we report spin relaxation times (T₁) of single-electron states in BLG QDs. Using pulsed-gate spectroscopy, we extract relaxation times exceeding 200 μs at a magnetic field of 1.9 T. The T₁ values show a strong dependence on the spin splitting, promising even longer T₁ at lower magnetic fields, where our measurements are limited by the signal-to-noise ratio. The relaxation times are more than two orders of magnitude larger than those previously reported for carbon-based QDs, suggesting that graphene is a potentially promising host material for scalable spin qubits.

Graphene has long been considered to be a promising host for spin qubits, however a demonstration of long spin relaxation times for a potential qubit has been lacking. Here, the authors report the electrical measurement of the single-electron spin relaxation time exceeding 200 μs in a bilayer graphene quantum dot.

Carbon Nanotube Devices for Quantum Technology

Carbon nanotubes, quintessentially one-dimensional quantum objects, possess a variety of electrical, optical, and mechanical properties that are suited for developing devices that operate on quantum mechanical principles. The states of one-dimensional electrons, excitons, and phonons in carbon nanotubes with exceptionally large quantization energies are promising for high-operating-temperature quantum devices. Here, we discuss recent progress in the development of carbon-nanotube-based devices for quantum technology, i.e., quantum mechanical strategies for revolutionizing computation, sensing, and communication. We cover fundamental properties of carbon nanotubes, their growth and purification methods, and methodologies for assembling them into architectures of ordered nanotubes that manifest macroscopic quantum properties. Most importantly, recent developments and proposals for quantum information processing devices based on individual and assembled nanotubes are reviewed.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Supercurrent and Phase Slips in a Ballistic Carbon Nanotube Bundle Embedded into a van der Waals Heterostructure

We demonstrate long-range superconducting correlations in a several-micrometers-long carbon nanotube bundle encapsulated in a van der Waals stack between hBN and NbSe₂. We show that a substantial supercurrent flows through the nanotube section beneath the NbSe₂ crystal as well as through the 2 μm long section not in contact with it. The large in-plane critical magnetic field of this supercurrent is an indication that even inside the carbon nanotube Cooper pairs enjoy a degree of paramagnetic protection typical of the parent Ising superconductor. As expected for superconductors of nanoscopic cross section, the current-induced breakdown of superconductivity is characterized by resistance steps due to the nucleation of phase slip centers. All elements of our hybrid device are active building blocks of several recently proposed setups for realization of Majorana fermions in carbon nanotubes.

Anisotropic Pauli Spin-Blockade Effect and Spin-Orbit Interaction Field in an InAs Nanowire Double Quantum Dot

We report on experimental detection of the spin-orbit interaction field in an InAs nanowire double quantum dot device. In the spin blockade regime, leakage current through the double quantum dot is measured and is used to extract the effects of spin-orbit interaction and hyperfine interaction on spin state mixing. At finite magnetic fields, the leakage current arising from the hyperfine interaction can be suppressed, and the spin-orbit interaction dominates spin state mixing. We observe dependence of the leakage current on the applied magnetic field direction and determine the direction of the spin-orbit interaction field. We show that the spin-orbit field lies in a direction perpendicular to the nanowire axis but with a pronounced off-substrate-plane angle. The results are expected to have an important implication in employing InAs nanowires to construct spin-orbit qubits and topological quantum devices.

Three-electron spin qubits

The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the exchange-only qubit (Bacon et al 2000 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned physical realization, the implementations of single-qubit operations, as well as the read-out and initialization schemes. Two-qubit gates and decoherence properties are discussed for the RX qubit and the exchange-only qubit, thereby completing the list of requirements for quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). The main focus will be on the exchange-only qubit and its modification, the RX qubit, whose single-qubit operations are realized by driving the qubit at its resonant frequency in the microwave range similar to electron spin resonance. Two different types of two-qubit operations are presented for the exchange-only qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000 Nature 408 339, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Kempe et al 2001 Phys. Rev. A 63 042307, Russ and Burkard 2015 Phys. Rev. B 91 235411). The price to pay for this advantage is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise (Ladd 2012 Phys. Rev. B 86 125408, Mehl and DiVincenzo 2013 Phys. Rev. B 87 195309, Hung et al 2014 Phys. Rev. B 90 045308), in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434), fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise (Setiawan et al 2014 Phys. Rev. B 89 085314, West and Fong 2012 New J. Phys. 14 083002, Rohling and Burkard 2016 Phys. Rev. B 93 205434) while for charge noise it is shown that it is favorable to operate the qubit on the so-called '(double) sweet spots' (Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434, Malinowski et al 2017 arXiv: 1704.01298), which are least susceptible to noise, thus providing a longer lifetime of the qubit.

Fullerene-Containing Electrically Conducting Electron Beam Resist for Ultrahigh Integration of Nanometer Lateral-Scale Organic Electronic Devices

An outstanding issue with organic devices is the difficulty of simultaneously controlling the lateral size and position of structures at submicron or nanometer scales. In this study, nanocomposite electron beam (EB) organic resists are proved to be excellent candidates for electrically conductive and/or memory component materials for submicron or nanometer lateral-scale organic electronic devices. The memory and the resist patterning characteristics are investigated for a positive electron beam resist of ZEP520a containing [6,6]-phenyl-C₆₁ butyric acid methyl ester (PCBM). Regarding the memory characteristics, good programming and excellent retention characteristics are obtained for electrons. The carrier transfer and retention mechanisms are also investigated. Regarding the resist patterning characteristics, it is found that line patterns (square patterns) of ZEP520a containing PCBM can be made with widths (side lengths) of less than 200 nm by using an extremely simple process with only EB exposures and developments. The distribution of PCBM molecules or their aggregations is also clarified in ZEP520a containing PCBM. The results of this study open the door to the simple fabrication of highly integrated flexible memories and electrical wires as well as of single-electron or quantum devices, including quantum information devices and sensitive biosensors for multiplexed and simultaneous diagnoses.

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube

The decay of spin-valley states is studied in a suspended carbon nanotube double quantum dot via the leakage current in Pauli blockade and via dephasing and decoherence of a qubit. From the magnetic field dependence of the leakage current, hyperfine and spin-orbit contributions to relaxation from blocked to unblocked states are identified and explained quantitatively by means of a simple model. The observed qubit dephasing rate is consistent with the hyperfine coupling strength extracted from this model and inconsistent with dephasing from charge noise. However, the qubit coherence time, although longer than previously achieved, is probably still limited by charge noise in the device.

Thermoelectric unipolar spin battery in a suspended carbon nanotube

A quantum dot formed in a suspended carbon nanotube exposed to an external magnetic field is predicted to act as a thermoelectric unipolar spin battery which generates pure spin current. The built-in spin flip mechanism is a consequence of the spin-vibration interaction resulting from the interplay between the intrinsic spin-orbit coupling and the vibrational modes of the suspended carbon nanotube. On the other hand, utilizing thermoelectric effect, the temperature difference between the electron and the thermal bath to which the vibrational modes are coupled provides the driving force. We find that both magnitude and direction of the generated pure spin current are dependent on the strength of spin-vibration interaction, the sublevel configuration in dot, the temperatures of electron and thermal bath, and the tunneling rate between the dot and the pole. Moreover, in the linear response regime, the kinetic coefficient is non-monotonic in the temperature T and it reaches its maximum when [Formula: see text] is about one phonon energy. The existence of a strong intradot Coulomb interaction is irrelevant for our spin battery, provided that high-order cotunneling processes are suppressed.

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

We demonstrate experimentally that noncollinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.

Room temperature manipulation of long lifetime spins in metallic-like carbon nanospheres

The time-window for processing electron spin information (spintronics) in solid-state quantum electronic devices is determined by the spin–lattice and spin–spin relaxation times of electrons. Minimizing the effects of spin–orbit coupling and the local magnetic contributions of neighbouring atoms on spin–lattice and spin–spin relaxation times at room temperature remain substantial challenges to practical spintronics. Here we report conduction electron spin–lattice and spin–spin relaxation times of 175 ns at 300 K in 37±7 nm carbon spheres, which is remarkably long for any conducting solid-state material of comparable size. Following the observation of spin polarization by electron spin resonance, we control the quantum state of the electron spin by applying short bursts of an oscillating magnetic field and observe coherent oscillations of the spin state. These results demonstrate the feasibility of operating electron spins in conducting carbon nanospheres as quantum bits at room temperature.

Electronic decoherence due to spin-orbit and magnetic interactions limits the application of spintronic nanosystems in quantum information processing. Here, the authors report notably long spin-lattice and spin-spin relaxation times of 175 ns at room temperature in carbon nanospheres.

A new regime of Pauli-spin blockade

Pauli-spin blockade (PSB) is a transport phenomenon in double quantum dots that allows for a type of spin to charge conversion often used to probe fundamental physics such as spin relaxation and singlet-triplet coupling. In this paper, we theoretically explore Pauli-spin blockade as a function of magnetic field B applied parallel to the substrate. In the well-studied low magnetic field regime, where PSB occurs in the forward (1, 1) → (0, 2) tunneling direction, we highlight some aspects of PSB that are not discussed in detail in existing literature, including the change in size of both bias triangles measured in the forward and reverse biasing directions as a function of B. At higher fields, we predict a crossover to "reverse PSB" in which current is blockaded in the reverse direction due to the occupation of a spin singlet as opposed to the traditional triplet blockade that occurs at low fields. The onset of reverse PSB coincides with the development of a tail like feature in the measured bias triangles and occurs when the Zeeman energy of the polarized triplet equals the exchange energy in the (0, 2) charge configuration. In Si quantum dots, these fields are experimentally accessible; thus, this work suggests a way to observe a crossover in magnetic field to qualitatively different behavior.

Spin-orbit interaction in bent carbon nanotubes: resonant spin transitions

We develop an effective tight-binding Hamiltonian for spin-orbit (SO) interaction in bent carbon nanotubes (CNT) for the electrons forming the π bonds between the nearest neighbor atoms. We account for the bend of the CNT and the intrinsic spin-orbit interaction which introduce mixing of π and σ bonds between the p(z) orbitals along the CNT. The effect contributes to the main origin of the SO coupling-the folding of the graphene plane into the nanotube. We discuss the bend-related contribution of the SO coupling for resonant single-electron spin and charge transitions in a double quantum dot. We report that although the effect of the bend-related SO coupling is weak for the energy spectra, it produces a pronounced increase of the spin transition rates driven by an external electric field. We find that spin-flipping transitions driven by alternate electric fields have usually larger rates when accompanied by charge shift from one dot to the other. Spin-flipping transition rates are non-monotonic functions of the driving amplitude since they are masked by stronger spin-conserving charge transitions. We demonstrate that the fractional resonances-counterparts of multiphoton transitions for atoms in strong laser fields-occurring in electrically controlled nanodevices already at moderate ac amplitudes-can be used to maintain the spin-flip transitions.

Hole spin coherence in a Ge/Si heterostructure nanowire

Relaxation and dephasing of hole spins are measured in a gate-defined Ge/Si nanowire double quantum dot using a fast pulsed-gate method and dispersive readout. An inhomogeneous dephasing time T2* 0.18 μs exceeds corresponding measurements in III–V semiconductors by more than an order of magnitude, as expected for predominately nuclear-spin-free materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclear-spin-dominated dephasing.

Realization of pristine and locally tunable one-dimensional electron systems in carbon nanotubes

The ability to tune local parameters of quantum Hamiltonians has been demonstrated in experimental systems including ultracold atoms, trapped ions, superconducting circuits and photonic crystals. Such systems possess negligible disorder, enabling local tunability. Conversely, in condensed-matter systems, electrons are subject to disorder, which often destroys delicate correlated phases and precludes local tunability. The realization of a disorder-free and locally-tunable condensed-matter system thus remains an outstanding challenge. Here, we demonstrate a new technique for deterministic creation of locally-tunable, ultralow-disorder electron systems in carbon nanotubes suspended over complex electronic circuits. Using transport experiments we show that electrons can be localized at any position along the nanotube and that the confinement potential can be smoothly moved from location to location. The high mirror symmetry of transport characteristics about the nanotube centre establishes the negligible effects of electronic disorder, thus allowing experiments in precision-engineered one-dimensional potentials. We further demonstrate the ability to position multiple nanotubes at chosen separations, generalizing these devices to coupled one-dimensional systems. These capabilities could enable many novel experiments on electronics, mechanics and spins in one dimension.

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.

Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit

Two level systems that can be reliably controlled and measured hold promise as qubits both for metrology and for quantum information science. Since a fluctuating environment limits the performance of qubits in both capacities, understanding environmental coupling and dynamics is key to improving qubit performance. We show measurements of the level splitting and dephasing due to the voltage noise of a GaAs singlet-triplet qubit during exchange oscillations. Unexpectedly, the voltage fluctuations are non-Markovian even at high frequencies and exhibit a strong temperature dependence. This finding has impacts beyond singlet-triplet qubits since nearly all solid state qubits suffer from some kind of charge noise. The magnitude of the fluctuations allows the qubit to be used as a charge sensor with a sensitivity of 2 × 10(-8)e/sqrt[Hz], 2 orders of magnitude better than a quantum-limited rf single electron transistor. Based on these measurements, we provide recommendations for improving qubit coherence, allowing for higher fidelity operations and improved charge sensitivity.

Valley-spin blockade and spin resonance in carbon nanotubes

The manipulation and readout of spin qubits in quantum dots have been successfully achieved using Pauli blockade, which forbids transitions between spin-triplet and spin-singlet states. Compared with spin qubits realized in III-V materials, group IV materials such as silicon and carbon are attractive for this application because of their low decoherence rates (nuclei with zero spins). However, valley degeneracies in the electronic band structure of these materials combined with Coulomb interactions reduce the energy difference between the blocked and unblocked states, significantly weakening the selection rules for Pauli blockade. Recent demonstrations of spin qubits in silicon devices have required strain and spatial confinement to lift the valley degeneracy. In carbon nanotubes, Pauli blockade can be observed by lifting valley degeneracy through disorder, but this makes the confinement potential difficult to control. To achieve Pauli blockade in low-disorder nanotubes, quantum dots have to be made ultrasmall, which is incompatible with conventional fabrication methods. Here, we exploit the bandgap of low-disorder nanotubes to demonstrate robust Pauli blockade based on both valley and spin selection rules. We use a novel stamping technique to create a bent nanotube, in which single-electron spin resonance is detected using the blockade. Our results indicate the feasibility of valley-spin qubits in carbon nanotubes.

Demonstration of entanglement of electrostatically coupled singlet-triplet qubits

Quantum computers have the potential to solve certain problems faster than classical computers. To exploit their power, it is necessary to perform interqubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor because of their potential for scalability and miniaturization. However, their weak interactions with the environment, which lead to their long coherence times, make interqubit operations challenging. We performed a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography, we measured the full density matrix of the system and determined the concurrence and the fidelity of the generated state, providing proof of entanglement.

Spin-orbit-induced strong coupling of a single spin to a nanomechanical resonator

We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model of quantum electrodynamics in the strong-coupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. The strong intrinsic spin-mechanical coupling allows for detection, as well as manipulation of the spin qubit, and may yield enhanced performance of nanotubes in sensing applications.

Valley-based noise-resistant quantum computation using Si quantum dots

We devise a platform for noise-resistant quantum computing using the valley degree of freedom of Si quantum dots. The qubit is encoded in two polarized (1,1) spin-triplet states with different valley compositions in a double quantum dot, with a Zeeman field enabling unambiguous initialization. A top gate gives a difference in the valley splitting between the dots, allowing controllable interdot tunneling between opposite valley eigenstates, which enables one-qubit rotations. Two-qubit operations rely on a stripline resonator, and readout on charge sensing. Sensitivity to charge and spin fluctuations is determined by intervalley processes and is greatly reduced as compared to conventional spin and charge qubits. We describe a valley echo for further noise suppression.

Measuring the complex admittance of a carbon nanotube double quantum dot

We investigate radio-frequency (rf) reflectometry in a tunable carbon nanotube double quantum dot coupled to a resonant circuit. By measuring the in-phase and quadrature components of the reflected rf signal, we are able to determine the complex admittance of the double quantum dot as a function of the energies of the single-electron states. The measurements are found to be in good agreement with a theoretical model of the device in the incoherent limit. In addition to being of fundamental interest, our results present an important step forward towards noninvasive charge and spin state readout in carbon nanotube quantum dots.

Gate-dependent orbital magnetic moments in carbon nanotubes

We investigate how the orbital magnetic moments of electron and hole states in a carbon nanotube quantum dot depend on the number of carriers on the dot. Low temperature transport measurements are carried out in a setup where the device can be rotated in an applied magnetic field, thus enabling accurate alignment with the nanotube axis. The field dependence of the level structure is measured by excited state spectroscopy and excellent correspondence with a single-particle calculation is found. In agreement with band structure calculations we find a decrease of the orbital magnetic moment with increasing electron or hole occupation of the dot, with a scale given by the band gap of the nanotube.

Transport spectroscopy of an impurity spin in a carbon nanotube double quantum dot

We make use of spin selection rules to investigate the electron spin system of a carbon nanotube double quantum dot. Measurements of the electron transport as a function of the magnetic field and energy detuning between the quantum dots reveal an intricate pattern of the spin state evolution. We demonstrate that the complete set of measurements can be understood by taking into account the interplay between spin-orbit interaction and a single impurity spin coupled to the double dot. The detection and tunability of this coupling are important for quantum manipulation in carbon nanotubes.

Coherent spin-current oscillations in transverse magnetic fields

We address the coherence of the dynamics of spin-currents with components transverse to an external magnetic field for the spin-1/2 Heisenberg chain. We study current autocorrelations at finite temperatures and the real-time dynamics of currents at zero temperature. Besides a coherent Larmor oscillation, we find an additional collective oscillation at higher frequencies, emerging as a coherent many-magnon effect at low temperatures. Using numerical and analytical methods, we analyze the oscillation frequency and decay time of this coherent current-mode versus temperature and magnetic field.

Disorder-mediated electron valley resonance in carbon nanotube quantum dots

We propose a scheme for coherent rotation of the valley isospin of a single electron confined in a carbon nanotube quantum dot. The scheme exploits the ubiquitous atomic disorder of the nanotube crystal lattice, which induces time-dependent valley mixing as the confined electron is pushed back and forth along the nanotube axis by an applied ac electric field. Using experimentally determined values for the disorder strength we estimate that valley Rabi oscillations with a period on the nanosecond time scale are feasible. The valley resonance effect can be detected in the electric current through a double quantum dot in the single-electron transport regime.

Charge and spin state readout of a double quantum dot coupled to a resonator

State readout is a key requirement for a quantum computer. For semiconductor-based qubit devices it is usually accomplished using a separate mesoscopic electrometer. Here we demonstrate a simple detection scheme in which a radio frequency resonant circuit coupled to a semiconductor double quantum dot is used to probe its charge and spin states. These results demonstrate a new noninvasive technique for measuring charge and spin states in quantum dot systems without requiring a separate mesoscopic detector.

Quantum dots and spin qubits in graphene

This is a review on graphene quantum dots and their use as a host for spin qubits. We discuss the advantages but also the challenges to use graphene quantum dots for spin qubits as compared to the more standard materials like GaAs. We start with an overview of this young and fascinating field and then discuss gate-tunable quantum dots in detail. We calculate the bound states for three different quantum dot architectures where a bulk gap allows for confinement via electrostatic fields: (i) graphene nanoribbons with armchair boundaries, (ii) a disc in single-layer graphene, and (iii) a disc in bilayer graphene. In order for graphene quantum dots to be useful in the context of spin qubits, one needs to find reliable ways to break the valley degeneracy. This is achieved here, either by a specific termination of graphene in (i) or in (ii) and (iii) by a magnetic field, without the need of a specific boundary. We further discuss how to manipulate spin in these quantum dots and explain the mechanism of spin decoherence and relaxation caused by spin-orbit interaction in combination with electron-phonon coupling, and by hyperfine interaction with the nuclear-spin system.

Stationary and transient leakage current in the Pauli spin blockade

We study the effects of cotunneling and a nonuniform Zeeman splitting on the stationary and transient leakage current through a double quantum dot in the Pauli spin blockade regime. We find that the stationary current due to cotunneling vanishes at low temperature and large applied magnetic field, allowing for the dynamical (rapid) preparation of a pure spin ground state, even at large voltage bias. Additionally, we analyze current that flows between blocking events, characterized, in general, by a fractional effective charge e*. This charge can be used as a sensitive probe of spin-relaxation mechanisms and can be used to determine the visibility of Rabi oscillations.