The interaction of electrons and photons lies at the heart of quantum physics. The \nmost notable phenomena which are described by quantum physics but which obviously \ninvalidate a classical description of the electromagnetic field - the photoelectric \neffect, the Compton effect, or the antibunching of photons emitted from a single atom, \nto mention a few - are intimately related to the interaction of electrons and photons. \nElectrons possess an internal degree of freedom, the spin. The spin S of an electron \ncan be described as an internal angular momentum, leading to a magnetic moment \nm due to the electric charge of the electron. Stern and Gerlach have shown that \nthe projection of m onto a quantization axis (defined by an external magnetic field \nin their experiment), e.g., along the z axis, is either mz = g�μB/2 (\\spin up") or \nmz = g�μB=2 (\\spin down"), where �μB � 9:2741 � 10-24 J/T is the Bohr magneton \nand g is the g-factor of the electron (g = 2 for free electrons). \n \n An electron spin \nis therefore usually referred to as a two-level system. Due to this property, the \nspin of electrons which are localized in semiconductor quantum dots has recently \nattracted significant attention regarding the implementation of quantum information \nprocessing: Electron spins can be used as carriers of quantum information. One \ncan define that the spin pointing "up" corresponds to the logical value "0" and \nthe spin pointing "down" corresponds to "1". Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. A system with this property is called a quantum \nbit (qubit). The additional possibilities due to quantum superpositions of qubits are \nexploited, e.g., in the algorithms introduced by Shor and Grover to solve certain tasks \nmuch more efficiently than with a classical computer (i.e., the prime factorization of \nlarge numbers for Shor's algorithm and the search within an unstructured database for \nGrover's algorithm). While quantum computation has presently only been achieved \nin prototypical experiments with few qubits, the implementation of efficient largescale \nquantum computation with many qubits still remains an extremely demanding \ntask. Yet, other quantum mechanical properties of qubits, such as entanglement, \nhave already been exploited experimentally with photons in quantum communication \nschemes, for example, quantum teleportation and quantum data compression. \nIn this thesis, we investigate the interaction of electrons and photons in semiconductor \nquantum dots. Optical transitions in quantum dots enable a direct link between \nelectron spins and photon polarizations due to conservation laws. We show that \n \nentanglement can be transferred from electron spin qubits to qubits defined by the \nphoton polarization, enabling the measurement of entangled spin states via photons. \nThe mechanism under study can also be used for the production of entangled photons, \nfor instance for the implementation of quantum communication protocols. In contrast \nto the presently used sources of entangled photons, the photon source we propose here \nis deterministic, providing entangled photons on demand. It has been demonstrated \nin several recent experiments that the most obvious way to achieve such a transfer of \nentanglement - using the recombination of biexcitons in a single quantum dot - fails \nin the presently available quantum dot structures. We have analyzed the problems \nof this approach. As a solution, we propose schemes based on charged excitons in \nsingle or coupled quantum dots. We discuss the generation of entangled two- and \nfour-photon states. \nIn addition to the transfer of quantum states, photons can also be used to probe \nelectron spin states. We investigate in detail different methods to optically measure \nthe decoherence time of a single electron spin in a quantum dot. The decoherence time \nof a spin establishes the time scale during which coherent manipulation is possible. \nMeasurements of the electron spin decoherence time are therefore highly desirable \nin view of the implementation of spin-based quantum information processing. We \nshow that the schemes we propose can be implemented with current experimental \ntechniques. \nWe then study the magneto-optical effect called Faraday rotation. Using the technique \nof time-resolved Faraday rotation, a recent experiment has demonstrated the \ncoherent transfer of spin between quantum dots coupled by molecules. We calculate \nthe Faraday rotation signal for a coupled dot system and show that a two-site \nHamiltonian with a transfer term captures the essential features observed in this experiment. \nWe also present results for a system of two coupled dots doped with a \nsingle electron. \nWe finally show that the coupled states of two qubits can be detected via the optical \ninteraction with a cavity in the dispersive regime. We present a Schrieffer-Wolff \ntransformation which removes the coupling of the two qubits to the cavity in leading \norder. The different two-qubit states lead to a different spectral shift of the cavity \nline. For a sufficiently low cavity linewidth, this enables the direct readout of a \ntwo-qubit system.
The interaction of electrons and photons lies at the heart of quantum physics. The \nmost notable phenomena which are described by quantum physics but which obviously \ninvalidate a classical description of the electromagnetic field - the photoelectric \neffect, the Compton effect, or the antibunching of photons emitted from a single atom, \nto mention a few - are intimately related to the interaction of electrons and photons. \nElectrons possess an internal degree of freedom, the spin. The spin S of an electron \ncan be described as an internal angular momentum, leading to a magnetic moment \nm due to the electric charge of the electron. Stern and Gerlach have shown that \nthe projection of m onto a quantization axis (defined by an external magnetic field \nin their experiment), e.g., along the z axis, is either mz = g�μB/2 (\spin up") or \nmz = g�μB=2 (\spin down"), where �μB � 9:2741 � 10-24 J/T is the Bohr magneton \nand g is the g-factor of the electron (g = 2 for free electrons). \n \n An electron spin \nis therefore usually referred to as a two-level system. Due to this property, the \nspin of electrons which are localized in semiconductor quantum dots has recently \nattracted significant attention regarding the implementation of quantum information \nprocessing: Electron spins can be used as carriers of quantum information. One \ncan define that the spin pointing "up" corresponds to the logical value "0" and \nthe spin pointing "down" corresponds to "1". Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. A system with this property is called a quantum \nbit (qubit). The additional possibilities due to quantum superpositions of qubits are \nexploited, e.g., in the algorithms introduced by Shor and Grover to solve certain tasks \nmuch more efficiently than with a classical computer (i.e., the prime factorization of \nlarge numbers for Shor's algorithm and the search within an unstructured database for \nGrover's algorithm). While quantum computation has presently only been achieved \nin prototypical experiments with few qubits, the implementation of efficient largescale \nquantum computation with many qubits still remains an extremely demanding \ntask. Yet, other quantum mechanical properties of qubits, such as entanglement, \nhave already been exploited experimentally with photons in quantum communication \nschemes, for example, quantum teleportation and quantum data compression. \nIn this thesis, we investigate the interaction of electrons and photons in semiconductor \nquantum dots. Optical transitions in quantum dots enable a direct link between \nelectron spins and photon polarizations due to conservation laws. We show that \n \nentanglement can be transferred from electron spin qubits to qubits defined by the \nphoton polarization, enabling the measurement of entangled spin states via photons. \nThe mechanism under study can also be used for the production of entangled photons, \nfor instance for the implementation of quantum communication protocols. In contrast \nto the presently used sources of entangled photons, the photon source we propose here \nis deterministic, providing entangled photons on demand. It has been demonstrated \nin several recent experiments that the most obvious way to achieve such a transfer of \nentanglement - using the recombination of biexcitons in a single quantum dot - fails \nin the presently available quantum dot structures. We have analyzed the problems \nof this approach. As a solution, we propose schemes based on charged excitons in \nsingle or coupled quantum dots. We discuss the generation of entangled two- and \nfour-photon states. \nIn addition to the transfer of quantum states, photons can also be used to probe \nelectron spin states. We investigate in detail different methods to optically measure \nthe decoherence time of a single electron spin in a quantum dot. The decoherence time \nof a spin establishes the time scale during which coherent manipulation is possible. \nMeasurements of the electron spin decoherence time are therefore highly desirable \nin view of the implementation of spin-based quantum information processing. We \nshow that the schemes we propose can be implemented with current experimental \ntechniques. \nWe then study the magneto-optical effect called Faraday rotation. Using the technique \nof time-resolved Faraday rotation, a recent experiment has demonstrated the \ncoherent transfer of spin between quantum dots coupled by molecules. We calculate \nthe Faraday rotation signal for a coupled dot system and show that a two-site \nHamiltonian with a transfer term captures the essential features observed in this experiment. \nWe also present results for a system of two coupled dots doped with a \nsingle electron. \nWe finally show that the coupled states of two qubits can be detected via the optical \ninteraction with a cavity in the dispersive regime. We present a Schrieffer-Wolff \ntransformation which removes the coupling of the two qubits to the cavity in leading \norder. The different two-qubit states lead to a different spectral shift of the cavity \nline. For a sufficiently low cavity linewidth, this enables the direct readout of a \ntwo-qubit system.
In the last few years there has been a growing interest in the possible applications of quantum properties of different physical systems in well established technologies. This was motivated by the miniaturization of electronic devices. For very small systems, the laws of quantum mechanics start to govern their behavior and it is then to expect that for instance electronic components reach their "quantum limit". A good example of the introduction of quantum properties into conventional technologies is the case of the electron spin, which offers an alternative to electron-charge for the storage and transport of information in electronics. The idea of using electron spins in electronics gave rise to the new and exciting field of spintronics and was encouraged by experiments that showed coherent spin transport over long distances (over hundred micrometers) in semiconductors and long electron spin dephasing times. In addition to its applications in conventional technologies, the use of the electron spin as information-carrier has been suggested for the new field of quantum information processing. An important advantage of the electron spin with respect to other quantum information-carriers proposed is that it can profit from the well developed semiconductor industry and its related technologies. For the long-range transport of information, however, the highly interacting environment in solid-state devices represents a difficulty to the use of electron spins. In contrast, photons are very weekly coupled to their environment, and therefore more suitable for the transfer of information over long distances (on the order of kilometers), required, for instance, in quantum communication. Furthermore, the technology needed for the transport of photons over such long distances is well developed. Thus, an efficient transfer of quantum information between electron spins and photons is highly desirable. \n \nIn this dissertation, we show that the transfer of entanglement, a quantum correlation, from electron spins to the polarization of photons is not only theoretically possible, but also feasible under realistic experimental conditions. We study the transport of an entangled pair of electron spins through Fermi leads which split them spatially until they reach spin-LEDs, semiconductor structures containing quantum dots. In these structures, the electrons optically recombine with holes, producing then photons. We analyze the polarization state of the out-coming photons and give the conditions for which the entanglement of the electron spins is fully recovered in the photon-polarizations. We further show that it is possible to produce four-photon entanglement. \n \nWe also include in this work the study of coherent spin-transfer between quantum dots layers bridged by molecules. This study was motivated by an experiment showing that the molecules act not only as binders to construct the multilayer structures, but also as "wires" for the information through electron spins in the quantum dots. We show that a two-site Hamiltonian captures some of the essential features of the experiment. We calculate the dependence of the experimentally observed Faraday rotation (FR) signal as a function of probe energy on microscopic parameters such as spin transfer probabilities. The Faraday angle is related to the difference in the dielectric response for different polarizations of the light. We calculate the dielectric response functions of coupled quantum dots and derive an analytical expression for the FR angle in terms of electron transfer probabilities and Heisenberg exchange splittings.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n
The recent discovery of efficient quantum algorithms for factoring and database search has shown that quantum computing would allow to solve important problems which are intractable with conventional computers. In contrast to the very demanding task of building a large-scale quantum computer, there are quantum communication protocols, e.g. quantum key distribution for cryptography, which—though still difficult—require much less effort and can be implemented with current technology. Apart from the technological motivation, the study of quantum information offers (at least) two additional benefits. First, new insight into fundamental questions on quantum mechanics, e.g. concerning non-locality and entanglement, are gained from an information-theoretical approach. And second, investigating a particular physical implementation of quantum information can give rise to independent physical results. Spintronics, the use of spin as opposed to charge in (classical) electronics is a new field for which some results presented here could be relevant. In this dissertation we investigate several theoretical aspects of the physical implementation of quantum computation and communication in which the fundamental unit of quantum information, the qubit, is represented by the spin of electrons in semiconductor quantum dots. The required coupling between the spins can be obtained by allowing for tunneling of electrons between adjacent dots, leading to a Heisenberg exchange coupling J S1 · S2 between the spins, a scenario which we study for laterally coupled quantum dots in a two-dimensional electron system, and for a three-dimensional setup with vertically coupled quantum dots. Furthermore, an alternative scheme to couple the spins via the interaction with an optical cavity mode is presented. Quantum error correction represents one of the important ingredients for the physical implementation of a quantum computer by protecting \nit from the e�ects of a noisy environment. As a �rst test for errorcorrection \nin a solid-state device using spins, we propose an optimized \nimplementation of the most primitive error correction scheme (the threebit \ncode). In this context, we introduce parallel switching, allowing \nto operate a quantum computer more e�ciently than the usual serial \nswitching. \nCoupling spins with the exchange interaction J S1 �S2 is not su�cient \nfor quantum computation; the spins also have to be addressed individually \nusing controllable local magnetic �elds or g-factors giBi �Si in order \nto allow for single-qubit operations. On the one hand, we discuss several \nschemes for overcoming the di�culty of applying local magnetic �elds \n(requiring large gradients), e.g. g-factor engineering, which allows for \nall-electric operation of the device. On the other hand, we show that \nat the expense of additional devices (spins) and switching operations, \nsingle-spin rotations can be dispensed with completely. \nAddressing the feasibility of quantum communication with entangled \nelectrons in mesoscopic wires, i.e. interacting many-body environments, \nwe propose an interference experiment using a scattering set-up with an \nentangler and a beam splitter. The current noise for electronic singlet \nstates turns out to be enhanced (bunching), while it is reduced for triplets \n(antibunching). Due to interactions, the �delity of the entangled singlet \nand triplet states is reduced by z4F \nin a conductor described by Fermi \nliquid theory, zF being the quasiparticle weight factor. \nFinally, we study the related but more general problem of the noise of \nthe cotunneling current through one or several tunnel-coupled quantum \ndots in the Coulomb blockade regime. The various regimes of weak and \nstrong, elastic and inelastic cotunneling are analyzed for quantum-dot \nsystems (QDS) with few-level, nearly-degenerate, and continuous electronic \nspectra. In contrast to sequential tunneling, the noise in inelastic \ncotunneling can be super-Poissonian. In order to investigate strong cotunneling \nwe develop a microscopic theory of cotunneling based on the \ndensity-operator formalism and using the projection operator technique. \nWe have derived the master equation for the QDS and the current and \nnoise in cotunneling in terms of the stationary state of the QDS. These \nresults are then applied to QDS with a nearly degenerate and continuous \nspectrum.
The aim of this thesis is to theoretically investigate two possible applications of semiconductor quantum dots for the growing field of quantum information and communication. The first one is the generation of entangled photons, which can be created by the radiative recombination of a quantum dot biexciton. This non-classical state of light is for instance used for teleportation of quantum information over distance. Although other methods of creating entangled photons exist, they suffer from problems such as inefficiency and unreliability, and an alternative which can produce an entangled photon pair on-demand within a given time interval would be most welcome. The second application is the implementation of a quantum bit using the intrinsic angular momentum of a single electron confined to a quantum dot. The quantum bit is the basic element of any quantum computer and is used to store quantum information. The work is divided into four main parts. We begin with an introduction which contains a short description about entanglement and quantum information followed by a brief review about the electron structure of semiconductors. This review aims to provide knowledge about some key methods and results from the semiconductor physics, which we will need in the following chapters. In the second part we will turn our attention to the generation of entangled light by the recombination of semiconductor biexcitons, which are composed of two excitons. We will discover that the excitons show an energy structure which requires extending the semiconductor theory from the introduction to be able to properly describe the observed effects. Once the exciton energy structure is known, we will examine a method to improve the quality of the emitted light with respect to entanglement. The third part considers effects from interactions between nuclear and electron spins. Focusing on storing one quantum bit using a single electron spin, we investigate the possible loss of information caused by interaction with the nuclear spins. We find that the temporal fluctuations of the nuclear spins give rise to an upper limit on the electron coherence time, during which quantum information can be accurately stored. We also investigate possible techniques to reduce the fluctuations and prolong the coherence time. In the fourth part we combine knowledge about the nuclear spins with the biexciton recombination process to investigate what effect exciton-nuclear spin interaction has on the entangled light. We find that the interaction with nuclear spins degrades the entanglement of the emitted light. To restore the quality of the entanglement, we investigate the effect of polarizing the nuclear spins and find that this can improve the entanglement.
The computer industry has seen an immense development in the last decades. \nPersonal computers have become available for everybody living in industrialized \ncountries with rapidly increasing performance in terms of speed and storage capacities. \nHowever, the performance of nowadays' computers is fundamentally limited by the \nlaws of classical physics: a classical bit can only take on either of the two distinct \nvalues `0' or `1'. \nIn contrast, a quantum computer could, in principle, make direct use \nof quantum phenomena, such as state superpositions \n-- a quantum bit can be in both states `0' and `1' simultaneously --, \nto perform complex computational tasks much faster than any classical computer. \n \nThe idea of building computers that work according to the laws of quantum physics \nhas opened various fields of research, one of which is the search for the best \nphysical system to use as a quantum bit (qubit). One important criterion for determining \nthe optimal qubit system is the lifetime of state superpositions. \nTypically, once initialized, such superpositions are destroyed on remarkably short \ntimescales due to interactions with the environment -- a process which is referred to \nas decoherence --, posing the question which physical qubit candidate system might show a high-enough robustness against the \ninfluence of the `outside world' to allow for viable quantum computation. \n \nIn this thesis, we will consider three particular realizations of one specific and \nvery promising type of qubit candidate system: \nan electron (or hole) confined to a quantum dot -- a nanoscale structure \nwithin a (typically semiconducting) material --, where the spin states `down' \nand `up' of our electron (or hole) encode the logical states `0' and `1'. \nOur task will be to study the decay of spin-state superpositions in such quantum-dot \nsystems. The main objective of this thesis is to understand the most important physical \nprocesses that lead to spin decoherence and to show ways to suppress this undesirable effect. \nIt turns out that at low temperatures, the main source of decoherence \nis the coupling of the electron (hole) to the surrounding nuclear spins. \n \nThis thesis is divided into three logical parts, corresponding to the three qubit candidate \nsystems under consideration. First we will study electron-spin qubits in III-V semiconductor \nquantum dots, where the electron spin interacts with the nuclear spins of the semiconducting \nhost material \nvia the isotropic Fermi contact hyperfine interaction. Second we consider quantum-dot-confined \nheavy holes and the decoherence of their (pseudo-)spin states due to anisotropic interactions with the \nnuclear spins. Third and last, we study electron-spin qubits made from carbon-nanotube and \ngraphene quantum dots. Quantum dots made of carbon have the advantage of a low abundance \nof spin-carrying nuclear isotopes, therefore reducing decoherence effects significantly. \n \nFor each of the systems under consideration, we will carry out analytical calculations on \nthe nuclear-spin interactions and the spin dynamics of the qubit. Although one main goal of \nthis thesis is to show ways to extend spin decoherence times, we will also focus on physically more \nfundamental questions. Not only the timescale of the decay is relevant for \nthe system's applicability as a qubit, but also the form of the decay which can vary \nsignificantly from system to system. For example, the decay of spin-state superpositions \ncan follow an exponential, super-exponential or power-law decay, and can even pass through \nvarious stages. This is not only of academic interest, but also important for practical \npurposes, such as the implementation of quantum error-correction schemes in a potential \nquantum computer. \n
Preface Spin and Charge Qubits 1. Coded Qubit Based on Electron Spin M. Korkusinski and P. Hawrylak 2. Quantum Optical Studies of Single Coupled Quantum Dot Pairs G. J. Beirne, M. Jetter, and P. Michler 3. Nuclear Spin Bi-stability in Semiconductor Quantum Dots A. I. Tartakovskii, M. S. Skolnick, A. Russell, and V. I. Fal'ko 4. Nonequilibrium Optical Spin Cooling in Charged Quantum Dots I. A. Akimov, D. H. Feng, and F. Henneberger Qubit Control, Readout, and Transfer 5. Electron Spin Quantum Bits in Quantum Dots: Initialization, Decoherence, and Control A. Greilich, D. R. Yakovlev, M. Bayer, A. Shabaev, and A. L. Efros 6. Optical Control of Quantum-Dot Spin States M. Atat ure, J. Dreiser, A. Badolato, and A. Imamo_glu 7. Optical Read-out of Single Carrier Spin in Semiconductor Quantum Dots F. Troiani, I. Wilson-Rae, and C. Tejedor 8. Quantum State Transfer from a Photon to an Electron Spin in Quantum Dots and Quantum Dynamics of Electron-Nuclei Coupled System T. Takagahara and O. ^ Cakir Qubit Decoherence 9. Spin Quantum-bits and Decoherence in InAs/GaAs Quantum Dots B. Urbaszek, T. Amand, O. Krebs, P. Renucci, and X. Marie 10. Electron and Hole Spin Dynamics and Decoherence in Quantum Dots D. Klauser, D. V. Bulaev, W. A. Coish, and D. Loss 11. Microscopic Theory of Energy Dissipation and Decoherence in Semiconductor Nanodevices F. Rossi 12. Transient Four-wave Mixing of Excitons in Quantum Dots from Ensembles and Individuals P. Borri and W. Langbein Flying Qubits 13. Light-matter Interaction in Single Quantum Dot - Micropillar Cavity Systems S. Reitzenstein, J.-P. Reithmaier, and A. Forchel 14. Entangled Photons via Biexciton-Resonant Hyperparemetric Scattering K. Edamatsu 15. Entangled Photon Pair Emission and Interference from Single Quantum Dots R. M. Stevenson, R. J. Young, and A. J. Shields Qubit Applications 16. Telecom-wavelength Single-photon Sources Based on Single Quantum Dots M. B. Ward, A. J. Shields, B. Alloing, C. Zinoni, C. Monat, and A. Fiore 17. Quantum Information Processing with Quantum Dots in Photonic Crystals J. Vu_ckovi_c, D. Englund, A. Faraon, I. Fushman, and E. Waks 18. High-Speed Quantum Computers with Semiconductor Spins T. D. Ladd, K. Sanaka, K. M. C. Fu, S. Koseki, D. Press, S. M. Clark, K. De Greve, and Y. Yamamoto 19. Quantum Dots: Single-Photon Sources for Quantum Information M. Scholz, T. Aichele, and O. Benson Author Index Subject Index