Phase coherence is a fundamental concept in quantum mechanics. Understanding the loss of coherence is paramount for future quantum information processing. We studied the coherent dynamics of a single central spin (a nitrogen-vacancy center) coupled to a bath of spins (nitrogen impurities) in diamond. Our experiments show that both the internal interactions of the bath and the coupling between the central spin and the bath can be tuned in situ, allowing access to regimes with surprisingly different behavior. The observed dynamics are well explained by analytics and numerical simulations, leading to valuable insight into the loss of coherence in spin systems. These measurements demonstrate that spins in diamond provide an excellent test bed for models and protocols in quantum information.

Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics. Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer.In this tutorial we summarize past and very recent developments which point the way to spin-based quantum computing in the solid-state. After introducing a set of basic requirements for any quantum computer proposal, we offer a brief summary of some of the many theoretical proposals for solid-state quantum computers. We then focus on the Loss-DiVincenzo proposal for quantum computing with the spins of electrons confined to quantum dots. There are many obstacles to building such a quantum device. We address these, and survey recent theoretical, and then experimental progress in the field. To conclude the tutorial, we list some as-yet unrealized experiments, which would be crucial for the development of a quantumdot quantum computer.Recipes for spin-based quantum computing

Kerr rotation measurements on a single electron spin confined in a charge-tunable semiconductor quantum dot demonstrate a means to directly probe the spin off-resonance, thus minimally disturbing the system. Energy-resolved magneto-optical spectra reveal information about the optically oriented spin polarization and the transverse spin lifetime of the electron as a function of the charging of the dot. These results represent progress toward the manipulation and coupling of single spins and photons for quantum information processing.

We report on room-temperature coherent manipulation of the spin of a single nitrogen-vacancy center in diamond and a study of its coherence as a function of magnetic field. We use magnetic resonance to induce Rabi nutations, and apply a Hahn spin echo to remove the effect of low-frequency dephasing. A sharp rise in the decoherence rate is observed at magnetic fields where the nitrogenvacancy center spin couples resonantly to substitutional nitrogen spins via the magnetic dipolar coupling. Finally, we find evidence that away from these energy resonances spin flips of nitrogen electrons are the main source of decoherence.PACS numbers: 76.30. Mi,03.67.Lx,03.65.Yz The study of single quantum systems is interesting both for testing fundamental laws of physics as well as for practical purposes, as computing with quantum systems promises an enormous increase in computing power and quantum communication allows secure information exchange 1 . In the solid state, coherent control of single quantum systems has been achieved in a number of systems, e.g. superconducting Cooper pair boxes 2 and electron spins in quantum dots 3 . Among these, the nitrogenvacancy (N-V) center in diamond 4 is unique, because its spin exhibits a long coherence time that persists up to room-temperature 5 , whereas most other systems only allow coherent control at cryogenic temperatures.Coherent manipulation of N-V centers on large ensembles was first achieved many years ago 6,7 . Recently, however, coherent rotations and spin echoes of a single N-V center spin were reported by Jelezko et al. 8 . This landmark experiment, that has not been reproduced by a different group thus far, demonstrates that the N-V center provides a testbed for quantum manipulation in the solid state at room temperature 9,10 . On the other hand, single-center spectroscopy allows the study of the local environment of the N-V center 11 and has already unveiled anisotropic spin interactions and magnetic dipolar coupling to spins of other defects in diamond 12 . Recent results of these studies include the observation of strong coupling between a single N-V center and the spin of a single substitutional nitrogen atom 13,14 and the measurement of the spin relaxation time of a single nitrogen electron spin 14 . By combining single-center spectroscopy with coherent control, the coherent interaction of the N-V center spin with its environment can be probed, which might ultimately lead to coherent quantum circuits 9 .Here, we report coherent control of the electron spin state of a single N-V center at room temperature. We demonstrate that we can coherently drive single-spin rotations (Rabi nutations) and undo low-frequency dephasing by application of a Hahn spin echo sequence. We use this capability to study the coherence of the N-V center as a function of applied magnetic field. By comparing the magnetic-field dependences of the decoherence rate and the photoluminescence, we find that the coherence of the N-V center spin is strongly affected by the resonant spin exchange with the...

We study biexcitonic states in two tunnel-coupled semiconductor quantum dots and show that such systems provide the possibility to produce polarization-entangled photons or spin-entangled electrons that are spatially separated at production. We distinguish between the various spin configurations and calculate the low-energy biexciton spectrum using the Heitler-London approximation as a function of magnetic and electric fields. The oscillator strengths for the biexciton recombination involving the sequential emission of two photons are calculated. The entanglement of the polarizations resulting from the spin configuration in the biexciton states is quantified as a function of the photon emission angles.

We study a model for a pair of qubits which interact with a single off-resonant cavity mode and, in addition, exhibit a direct inter-qubit coupling. Possible realizations for such a system include coupled superconducting qubits in a line resonator as well as exciton states or electron spin states of quantum dots in a cavity. The emergent dynamical phenomena are strongly dependent on the relative energy scales of the inter-qubit coupling strength, the coupling strength between qubits and cavity mode, and the cavity mode detuning. We show that the cavity mode dispersion enables a measurement of the state of the coupled-qubit system in the perturbative regime. We discuss the effect of the direct inter-qubit interaction on a cavity-mediated two-qubit gate. Further, we show that for asymmetric coupling of the two qubits to the cavity, the direct inter-qubit coupling can be controlled optically via the ac Stark effect.

Self-Assembled Quantum Dots 21 2.3.1 Strain-Driven Self-Alignment 22 2.3.2 Optical Properties and QD Shell Structure 24 2.4 Alternative Epitaxial Quantum Dot Systems 27 2.4.1 Electrically Gated Quantum Dots 27 2.4.2 Advanced MBE Techniques 29 2.4.3 Nanowire Quantum Dots 31 2.5 Chemically-Synthesized Quantum Dots 32 2.5.1 Colloidal Growth 33 2.5.2 Energy Level Structure and Optical Properties 34 3 Theory of Confined States in Quantum Dots 39 3.1 Band Structure of III-V Semiconductors 39 3.1.1 Effective Mass of Crystal Electrons 40 3.1.2 Spin-Orbit Interaction 41 3.1.3 Band Structure Close to the Band Edges 41 3.1.4 Band-Edge Bloch States 42 3.1.5 Coupling of Bands and the Luttinger Hamiltonian 43 Spins in Optically Active Quantum Dots. Concepts and Methods.

I n the field of quantum information science, semiconductor quantum dots (QDs) are of particular interest for their ability to confine a single electron for use as a qubit 1,2. However, to realize the potential offered by quantum information processing, it is necessary to couple two or more qubits. In contrast to coupling individual QDs, we demonstrate the integration of two coupled electronic states within a single QD heterostructure. These chemically synthesized nanocrystals, known as quantumdot quantum wells (QDQWs) 3-7 , comprise concentric layers of different semiconducting materials. We investigate carrier and spin dynamics in these structures using transient absorption and time-resolved Faraday rotation measurements. By tuning the excitation and probe energies, we find that we can selectively initialize and read out spins in different coupled states within the QDQW. These results open a pathway for engineering coupled qubits within a single nanostructure. The samples studied in this work are ensembles consisting of nanocrystals with a 5.5-nm-diameter, low-bandgap (E g = 1.74 eV) CdSe core, surrounded by a three-monolayer (ML), high-bandgap (E g = 3.68 eV) ZnS barrier and a 4 ML outer CdSe shell 7. A cutaway illustration of the sample structure is shown in Fig. 1a. Qualitatively similar results were also obtained on a sample with 6.4 nm core, 2 ML barrier and 4 ML shell. For comparison, a control sample of 6.8-nm-diameter CdSe QDs was also prepared. Figure 1a shows the radial potential of the core-shell structure along with the conduction-(c-) and valence-(v-) band states, 1S e , 2S e , 1S 3/2 and 2S 3/2 (discussed below). The band profile is analogous to a pair of coupled quantum wells, in which the core corresponds to one well and the shell to the other. Indeed, under 2.43 eV excitation the photoluminescence (PL) spectrum of these quantum-dot quantum wells (QDQWs) (Fig. 1b) shows two peaks at 2.18 and 1.92 eV, which have been previously attributed to radiative recombination from an electron-hole pair in the shell and in the core, respectively 7. When the excitation energy is tuned between the core and shell emission to 2.02 eV, only the lowerenergy (core) emission is observed. This behaviour of the PL indicates that two optically active, metastable exciton states exist in the QDQWs, and that by changing the pump energy either the core or both the core and the shell can be selectively excited. We have modelled the electronic states of the coupled core-shell QDQWs within k • p theory, extending our previous model of a single QDQW 8,9. (The theoretical modelling is discussed in more detail in the Supplementary Information.