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 ͑1͒ the rotation of an electron spin into a superposition of up and down, ͑2͒ the measurement of the quantum state of an individual spin, and ͑3͒ 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 spintronics͒.

Electron transport experiments on two lateral quantum dots coupled in series are reviewed. An introduction to the charge stability diagram is given in terms of the electrochemical potentials of both dots. Resonant tunneling experiments show that the double dot geometry allows for an accurate determination of the intrinsic lifetime of discrete energy states in quantum dots. The evolution of discrete energy levels in magnetic field is studied. The resolution allows one to resolve avoided crossings in the spectrum of a quantum dot. With microwave spectroscopy it is possible to probe the transition from ionic bonding (for weak interdot tunnel coupling) to covalent bonding (for strong interdot tunnel coupling) in a double dot artificial molecule. This review is motivated by the relevance of double quantum dot studies for realizing solid state quantum bits. CONTENTS

We study atomiclike properties of artificial atoms by measuring Coulomb oscillations in vertical quantum dots containing a tunable number of electrons starting from zero. At zero magnetic field the energy needed to add electrons to a dot reveals a shell structure for a two-dimensional harmonic potential. As a function of magnetic field the current peaks shift in pairs, due to the filling of electrons into spin-degenerate single-particle states. When the magnetic field is sufficiently small, however, the pairing is modified, as predicted by Hund's rule, to favor the filling of parallel spins. [S0031-9007(96) PACS numbers: 73.20.Dx, 72.20.My, 73.40.Gk The "addition energy" needed to place an extra electron in a semiconductor quantum dot is analogous to the electron affinity for a real atom [1]. For a fixed number of electrons, small energy excitations can take these electrons to a higher single-particle state. However, due to Coulomb interactions between the electrons, the addition energy is greater than the energy associated with these excitations. Both the addition energy spectrum and the excitation energy spectrum are discrete when the Fermi wavelength and the dot size are comparable. Until now a direct mapping of the observed addition energy, and the single-particle excitation energy, to a calculated spectrum has been hampered, probably due to sample specific inhomogeneities [2].The three-dimensional spherically symmetric potential around atoms gives rise to the shell structure 1s, 2s, 2p, 3s, 3p, . . . . The ionization energy has a large maximum for atomic numbers 2, 10, 18, . . . . Up to atomic number 23 these shells are filled sequentially, and Hund's rule determines whether a spin-down or a spin-up electron is added [3]. Vertical quantum dots have the shape of a disk with a diameter roughly 10 times the thickness [2,4]. The lateral potential has a cylindrical symmetry with a rather soft boundary profile, which can be approximated by a harmonic potential. The symmetry of this twodimensional (2D) harmonic potential leads to a complete filling of shells for 2, 6, 12, . . . electrons. The numbers in this sequence can be regarded as "magic numbers" for a 2D harmonic dot. The shell filling in this manner is previously predicted by self-consistent calculations of a circular dot [5]. In this Letter we report the observation of atomiclike properties in the conductance characteristics of a vertical quantum dot. We find an unusually large addition energy when the electron number coincides with a magic number. We can identify the quantum numbers of the single-particle states by studying the magnetic field dependence. At a sufficiently small magnetic field ͑B , 0.4 T) we see that spin filling obeys Hund's rule. At higher magnetic fields ͑B . 0.4 T) we observe the consecutive filling of states by spin-up and spin-down electrons, which arises from spin degeneracy.The gated vertical quantum dot shown schematically in Fig. 1 is made from a double-barrier heterostructure (DBH). The use of well-defined heterostructure tu...

Classification numbers: 73.23.Hk Electronic transport in mesoscopic systems (Coulomb blockade, single-electron tunneling); 73.63.Kv Electronic transport in nanoscale materials and structures (quantum dots); 73.21.La Electronic states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems (quantum dots) Two tunnel-coupled few-electron quantum dots were fabricated in a GaAs/AlGaAs quantum well. The absolute number of electrons in each dot could be determined from finite bias Coulomb blockade measurements and gate voltage scans of the dots, and allows the number of electrons to be controlled down to zero. The Zeeman energy of several electronic states in one of the dots was measured with an in-plane magnetic field, and the g-factor of the states was found to be no different than that of electrons in bulk GaAs. Tunnel-coupling between dots is demonstrated, and the tunneling strength was estimated from the peak splitting of the Coulomb blockade peaks of the double dot.

We observe spin blockade due to Pauli exclusion in the tunneling characteristics of a coupled quantum dot system when two same-spin electrons occupy the lowest energy state in each dot. Spin blockade only occurs in one bias direction when there is asymmetry in the electron population of the two dots, leading to current rectification. We induce the collapse of the spin blockade by applying a magnetic field to open up a new spin-triplet current-carrying channel.

The isolation of qubits from noise sources, such as surrounding nuclear spins and spin-electric susceptibility , has enabled extensions of quantum coherence times in recent pivotal advances towards the concrete implementation of spin-based quantum computation. In fact, the possibility of achieving enhanced quantum coherence has been substantially doubted for nanostructures due to the characteristic high degree of background charge fluctuations . Still, a sizeable spin-electric coupling will be needed in realistic multiple-qubit systems to address single-spin and spin-spin manipulations . Here, we realize a single-electron spin qubit with an isotopically enriched phase coherence time (20 μs) and fast electrical control speed (up to 30 MHz) mediated by extrinsic spin-electric coupling. Using rapid spin rotations, we reveal that the free-evolution dephasing is caused by charge noise-rather than conventional magnetic noise-as highlighted by a 1/f spectrum extended over seven decades of frequency. The qubit exhibits superior performance with single-qubit gate fidelities exceeding 99.9% on average, offering a promising route to large-scale spin-qubit systems with fault-tolerant controllability.

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The rapid rise of spintronics and quantum information science has led to a strong interest in developing the ability to coherently manipulate electron spins 1 . Electron spin resonance 2 is a powerful technique for manipulating spins that is commonly achieved by applying an oscillating magnetic field. However, the technique has proven very challenging when addressing individual spins 3-5 . In contrast, by mixing the spin and charge degrees of freedom in a controlled way through engineered non-uniform magnetic fields, electron spin can be manipulated electrically without the need of high-frequency magnetic fields 6,7 . Here we report experiments in which electrically driven addressable spin rotations on two individual electrons were realized by integrating a micrometre-size ferromagnet into a double-quantum-dot device. We find that it is the stray magnetic field of the micromagnet that enables the electrical control and spin selectivity. The results suggest that our approach can be tailored to multidot architecture and therefore could open an avenue towards manipulating electron spins electrically in a scalable way.Magnetic resonance was recently used to coherently manipulate the spin of a single electron 5 in a semiconductor structure, called a quantum dot 8,9 , whose tally of electrons can be tuned one by one, down to a single charge 10,11 . However, producing strong and localized oscillating magnetic fields, which is a necessary step for addressing individual spins, is technically demanding. It involves on-chip coils 5,12 , relatively bulky to couple with a single spin, dissipating a significant amount of heat close to the electrons, whose temperature must not exceed a few decikelvins. In comparison, strong and local electric fields can be generated by simply exciting a tiny gate electrode nearby the target spin with low-level voltages. For scalability purposes, it is therefore highly desirable to manipulate electron spins with electric fields instead of magnetic fields.To benefit from the advantages of electrical excitation, a mediating mechanism must be in place to couple the electric field to the electron spin, which usually responds only to magnetic fields. Spin-orbit coupling 13,14 , hyperfine interaction 15 and g-factor modulation 16 work as the mediating mechanism, which attract interest for their physical origins but necessitate refinement in terms of both manipulation speed and scalability. Instead, we controllably mix the spin and charge degrees of freedom in a magnetic-field gradient 6 , very much like the Stern-Gerlach effect 17 . This allows for greater flexibility, because the method is applicable to any semiconductor material. In addition, the magnetic field profile can be engineered to enable the selective manipulation of several spins using a single electrode.Thereby, we demonstrate addressable voltage-driven singlespin electron spin resonance (ESR) in a magnetic-field gradient. Two electrons are confined and spatially separated from each other in a gate-defined double quantum dot 18 (Fig. 1a)...