Edward Laird

First results from MAST

MAST is one of the new generation of large, purpose-built spherical tokamaks (STs) now becoming operational, designed to investigate the properties of the ST in large, collisionless plasmas. The first six months of MAST operations have been remarkably successful. Operationally, both merging-compression and the more usual solenoid induction schemes have been demonstrated, the former providing over 400 kA of plasma current with no demand on solenoid flux. Good vacuum conditions and operational conditions, particularly after boronization in trimethylated boron, have provided plasma current of over 1 MA with central plasma temperatures (ohmic) of order 1 keV. The Hugill and Greenwald limits can be exceeded and H mode achieved at modest additional NBI power. Moreover, particle and energy confinement show an immediate increase at the L-H transition, unlike the case of START, where this became apparent only at the highest plasma currents. Halo currents are small, with low toroidal peaking factors, in accordance with theoretical predictions, and there is evidence of a resilience to the major disruption.

Coherent spin manipulation in an exchange-only qubit

Initialization, two-spin coherent manipulation, and readout of a three-spin qubit are demonstrated using a few-electron triple quantum dot. The three-spin qubit is designed to allow all operations for full qubit control to be tuned via nearest-neighbor exchange interaction. Fast readout of charge states takes advantage of multiplexed reflectometry. Decoherence measured in a two-spin subspace is found to be consistent with predictions based on gate voltage noise with a uniform power spectrum. The theory of the exchange-only qubit is developed and it is shown that initialization of only two spins suffices for operation. Requirements for full multiqubit control using only exchange and electrostatic interactions are outlined.

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike in conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and valley freedom. The interplay between the two is the focus of this review. The energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are explained, together with their consequences for transport measurements through nanotube quantum dots. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behavior. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, open questions for the field are also clearly stated. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a low level.

A High Quality Factor Carbon Nanotube Mechanical Resonator at 39 GHz

We measure the mechanical resonances of an as-grown suspended carbon nanotube, detected via electrical mixing in the device. A sequence of modes extending to 39 GHz is observed with a quality factor of 35,000 in the highest mode. This unprecedentedly high combination corresponds to a thermal excited state probability below 10(-8) and a relaxation time of 140 ns with microsecond relaxation times for lower modes. The effect of electron tunneling on the mechanical resonance is found to depend on frequency as the tunneling time becomes comparable to the vibration period.

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.

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-State Conditional Operation of a Spin Qubit

We report coherent operation of a singlet-triplet qubit controlled by the spatial arrangement of two confined electrons in an adjacent double quantum dot that is electrostatically coupled to the qubit. This four-dot system is the specific device geometry needed for two-qubit operations of a two-electron spin qubit. We extract the strength of the capacitive coupling between qubit and adjacent double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways toward implementation of a universal set of gates for singlet-triplet spin qubits.

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.

Measurement of temporal correlations of the overhauser field in a double quantum dot.

In quantum dots made from materials with nonzero nuclear spins, hyperfine coupling creates a fluctuating effective Zeeman field (Overhauser field) felt by electrons, which can be a dominant source of spin qubit decoherence. We characterize the spectral properties of the fluctuating Overhauser field in a GaAs double quantum dot by measuring correlation functions and power spectra of the rate of singlet-triplet mixing of two separated electrons. Away from zero field, spectral weight is concentrated below 10 Hz, with approximately 1/f2 dependence on frequency f. This is consistent with a model of nuclear spin diffusion, and indicates that decoherence can be largely suppressed by echo techniques.

Effect of Exchange Interaction on Spin Dephasing in a Double Quantum Dot

We measure singlet-triplet dephasing in a two-electron double quantum dot in the presence of an exchange interaction which can be electrically tuned from much smaller to much larger than the hyperfine energy. Saturation of dephasing and damped oscillations of the spin correlator as a function of time are observed when the two interaction strengths are comparable. Both features of the data are compared with predictions from a quasistatic model of the hyperfine field.