J. R. Petta

Coulomb blockade and the Kondo effect in single-atom transistors

Using molecules as electronic components is a powerful new direction in the science and technology of nanometre-scale systems. Experiments to date have examined a multitude of molecules conducting in parallel, or, in some cases, transport through single molecules. The latter includes molecules probed in a two-terminal geometry using mechanically controlled break junctions or scanning probes as well as three-terminal single-molecule transistors made from carbon nanotubes, C60 molecules, and conjugated molecules diluted in a less-conducting molecular layer. The ultimate limit would be a device where electrons hop on to, and off from, a single atom between two contacts. Here we describe transistors incorporating a transition-metal complex designed so that electron transport occurs through well-defined charge states of a single atom. We examine two related molecules containing a Co ion bonded to polypyridyl ligands, attached to insulating tethers of different lengths. Changing the length of the insulating tether alters the coupling of the ion to the electrodes, enabling the fabrication of devices that exhibit either single-electron phenomena, such as Coulomb blockade, or the Kondo effect.

Spins in few-electron quantum dots

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors

The past decade has seen remarkable progress in isolating and controlling quantum coherence using charges and spins in semiconductors. Quantum control has been established at room temperature, and electron spin coherence times now exceed several seconds, a nine–order-of-magnitude increase in coherence compared with the first semiconductor qubits. These coherence times rival those traditionally found only in atomic systems, ushering in a new era of ultracoherent spintronics. We review recent advances in quantum measurements, coherent control, and the generation of entangled states and describe some of the challenges that remain for processing quantum information with spins in semiconductors.

Triplet-singlet spin relaxation via nuclei in a double quantum dot

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation; spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing.

Spin-Dependent Transport in Molecular Tunnel Junctions

We present measurements of magnetic tunnel junctions made using a self-assembled-monolayer molecular barrier. Ni-octanethiol-Ni samples were fabricated in a nanopore geometry. The devices exhibit significant changes in resistance as the angle between the magnetic moments in the two electrodes is varied, demonstrating that low-energy electrons can traverse the molecular barrier while remaining spin polarized. An analysis of the voltage and temperature dependence of the data suggests that the spin-polarized transport signals can be degraded by localized states in the molecular barriers.

Manipulation of a single charge in a double quantum dot.

We manipulate a single electron in a fully tunable double quantum dot using microwave excitation. Under resonant conditions, microwaves drive transitions between the (1,0) and (0,1) charge states of the double dot. Local quantum point contact charge detectors enable a direct measurement of the photon-induced change in occupancy of the charge states. From charge sensing measurements, we find T1 approximately 16 ns and a lower bound estimate for T*(2) of 400 ps for the charge two-level system.

Circuit quantum electrodynamics with a spin qubit

Electron spins trapped in quantum dots have been proposed as basic building blocks of a future quantum processor. Although fast, 180-picosecond, two-quantum-bit (two-qubit) operations can be realized using nearest-neighbour exchange coupling, a scalable, spin-based quantum computing architecture will almost certainly require long-range qubit interactions. Circuit quantum electrodynamics (cQED) allows spatially separated superconducting qubits to interact via a superconducting microwave cavity that acts as a ‘quantum bus’, making possible two-qubit entanglement and the implementation of simple quantum algorithms. Here we combine the cQED architecture with spin qubits by coupling an indium arsenide nanowire double quantum dot to a superconducting cavity. The architecture allows us to achieve a charge–cavity coupling rate of about 30 megahertz, consistent with coupling rates obtained in gallium arsenide quantum dots. Furthermore, the strong spin–orbit interaction of indium arsenide allows us to drive spin rotations electrically with a local gate electrode, and the charge–cavity interaction provides a measurement of the resulting spin dynamics. Our results demonstrate how the cQED architecture can be used as a sensitive probe of single-spin physics and that a spin–cavity coupling rate of about one megahertz is feasible, presenting the possibility of long-range spin coupling via superconducting microwave cavities.

Relaxation, dephasing, and quantum control of electron spins in double quantum dots

Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here we present a detailed theory for electron-spin dynamics in two-electron double-dot systems that was used to guide those experiments and analyze the results. Specifically, we analyze both spin- and charge-relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron systems. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits.

Correlating the Nanostructure and Electronic Properties of InAs Nanowires

The electronic properties and nanostructure of InAs nanowires are correlated by creating multiple field effect transistors (FETs) on nanowires grown to have low and high defect density segments. 4.2 K carrier mobilities are approximately 4x larger in the nominally defect free segments of the wire. We also find that dark field optical intensity is correlated with the mobility, suggesting a simple route for selecting wires with a low defect density. At low temperatures, FETs fabricated on high defect density segments of InAs nanowires showed transport properties consistent with single electron charging, even on devices with low resistance ohmic contacts. The charging energies obtained suggest quantum dot formation at defects in the wires. These results reinforce the importance of controlling the defect density in order to produce high quality electrical and optical devices using InAs nanowires.

Quantum Coherence in a One-Electron Semiconductor Charge Qubit

We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and noninvasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ∼7 ns at the charge degeneracy point, where the qubit level splitting is first-order insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with numerical simulations and predictions from a 1/f noise model.