verse order, as in this case, is the real essence of the Heisenberg uncertainty principle. Besides its fundamental importance, the experimental implementation of such a sequence of basic quantum operations is an essential tool for the full-scale engineering of a quantum light state optimized for a multitude of different tasks (15), including robust quantum communication. As any quantum operation, including non-Gaussian operations, is composed of photon additions and subtractions (i.e, it can be expressed as f ð% a; % a † Þ), our experimental results constitute a step toward the full quantum control of a field and the generation of highly entangled states (16).

We review recent theoretical and experimental advances toward understanding the effects of nuclear spins in confined nanostructures. These systems, which include quantum dots, defect centers, and molecular magnets, are particularly interesting for their importance in quantum information processing devices, which aim to coherently manipulate single electron spins with high precision. On one hand, interactions between confined electron spins and a nuclear-spin environment provide a decoherence source for the electron, and on the other, a strong effective magnetic field that can be used to execute local coherent rotations. A great deal of effort has been directed toward understanding the details of the relevant decoherence processes and to find new methods to manipulate the coupled electron-nuclear system. A sequence of spectacular new results have provided understanding of spin-bath decoherence, nuclear spin diffusion, and preparation of the nuclear state through dynamic polarization and more general manipulation of the nuclear-spin density matrix through ''state narrowing.'' These results demonstrate the richness of this physical system and promise many new mysteries for the future. 1 Introduction The last several years have seen a series of breakthroughs in single-spin measurement and manipulation, motivated in large part by the potential for future quantum information processing devices [1,2]. The spin coherence times for confined electrons in semiconductor quantum dots [3][4][5][6][7][8][9][10], phosphorus donor impurities in silicon [11,12], nitrogen vacancy (NV) centers in diamond [13][14][15], and in molecular magnets [16,17] is typically limited by the interaction between the electron and nuclear spins in the host material. The coherent manipulation of electron spins therefore requires a complete understanding of the nuclear spins in these materials, typically in the presence of localized electrons.A great deal of work has been done many years ago on ensembles of electron spins at donor impurities, including experimental [18][19][20] and theoretical [21,22] studies of

We report the electrical induction and detection of dynamic nuclear polarization in the spin-blockade regime of double GaAs vertical quantum dots. The nuclear Overhauser field measurement relies on bias voltage control of the interdot spin exchange coupling and measurement of dc current at variable external magnetic fields. The largest Overhauser field observed was about 4 T, corresponding to a nuclear polarization approximately 40% for the electronic g factor typical of these devices, |g*| approximately 0.25. A phenomenological model is proposed to explain these observations.