We briefly review the physics of gate operations between quantum dot spin-qubits and analyze the dynamics of quantum entanglement in such processes. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations that go beyond simple antisymmetrization effects. We also summarize further recent results concerning this type of quantum correlations of indistinguishable particles. Finally we discuss decoherence properties of spin-qubits when coupled to surrounding nuclear spins in a semiconductor nanostructure
We briefly review the physics of gate operations between quantum dot spin-qubits and analyze the dynamics of quantum entanglement in such processes. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations that go beyond simple antisymmetrization effects. We also summarize further recent results concerning this type of quantum correlations of indistinguishable particles. Finally we discuss decoherence properties of spin-qubits when coupled to surrounding nuclear spins in a semiconductor nanostructure
Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.
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.
Electron spins confined in quantum dots (QDs) are among the leading contenders for implementing quantum information processing. In this Thesis we address two of the most significant technological challenges towards developing a scalable quantum information processor based on spins in quantum dots: (i) decoherence of the electronic spin qubit due to the surrounding nuclear spin bath, and (ii) long-range spin-spin coupling between remote qubits. To this end, we develop novel strategies that turn the unavoidable coupling to the solid-state environment (in particular, nuclear spins and phonons) into a valuable asset rather than a liability. In the first part of this Thesis, we investigate electron transport through single and double QDs, with the aim of harnessing the (dissipative) coupling to the electronic degrees of freedom for the creation of coherence in both the transient and steady-state behaviour of the ambient nuclear spins. First, we theoretically show that intriguing features of coherent many-body physics can be observed in electron transport through a single QD. To this end, we first develop a master-equation-based formalism for electron transport in the Coulomb-blockade regime assisted by hyperfine (HF) interaction with the nuclear spin ensemble in the QD. This general tool is then used to study the leakage current through a single QD in a transport setting. When starting from an initially uncorrelated, highly polarized state, the nuclear system experiences a strong correlation buildup, due to the collective nature of the coupling to the central electron spin. We demonstrate that this results in a sudden intensity burst in the electronic tunneling current emitted from the QD system, which exceeds the maximal current of a corresponding classical system by several orders of magnitude. This gives rise to the new paradigm of electronic superradiance. Second, building upon the insight that the nuclear spin dynamics are governed by collective interactions giving rise to coherent effects such as superradiance, we propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics is shown to lead to intriguing effects such as multistability and criticality in the steady-state solutions. In the second part of this Thesis, our focus turns towards the realization of long-range spin-spin coupling between remote qubits. We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezo-active materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range, can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitations can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits. In summary, this thesis provides contributions towards developing a scalable quantum information processor based on spins in quantum dots in two different aspects. The first part is dedicated to a deeper understanding of the nuclear spin dynamics in quantum dots. In the second part we put forward a novel sound-based strategy to realize long-range spin-spin coupling between remote qubits. This completes a broad picture of spin-based quantum information processing which integrates different perspectives, ranging from the single-qubit level to a broader quantum network level.
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
The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.