In this Thesis, we study open quantum spin systems from di↵erent perspectives.The first part is motivated by technological challenges of quantum computation.An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication.We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity.Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields.A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins.High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence.Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot.The second part of this Thesis is devoted to fundamental studies of dissipative spin systems.We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled.This system enables the study of non-equilibrium and steady state physics of open and driven spin systems.We find, that the steady state expectation values of di↵erent spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation.This e↵ect can be used to dissipatively probe the spectrum of the Hamiltonian.We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state.Finally,
In this Thesis, we study open quantum spin systems from di↵erent perspectives.The first part is motivated by technological challenges of quantum computation.An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication.We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity.Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields.A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins.High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence.Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot.The second part of this Thesis is devoted to fundamental studies of dissipative spin systems.We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled.This system enables the study of non-equilibrium and steady state physics of open and driven spin systems.We find, that the steady state expectation values of di↵erent spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation.This e↵ect can be used to dissipatively probe the spectrum of the Hamiltonian.We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state.Finally,
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.
Single electron spin in a semiconductor quantum dot (QD) and single photon wavepacket propagating in an optical waveguide are investigated as carriers of quantum bit (qubit) for information processing. Cavity quantum electrodynamics of the coupled system composed of charged QD, microcavity and waveguide provides a quantum interface for the interplay of stationary spin qubits and flying photon qubits via cavity assisted optical control. This interface forms the basis for a wide range of essential functions of a quantum network, including transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single photon wavepacket with arbitrarily specified shape. The cavity assisted optical process also made possible ultrafast initialization and QND readout of the spin qubit in QD. In addition, the strong optical nonlinearity of dot-cavity-waveguide coupled system enables phase gate and entanglement operation for flying single photon qubits in waveguides. The coherence of the electron spin is the wellspring of these quantum applications being investigated. At low temperature and strong magnetic field, the dominant cause of electron spin decoherence is the coupling with the interacting lattice nuclear spins. We present a quantum solution to the coupled dynamics of the electron with the nuclear spin bath. The decoherence is treated in terms of quantum entanglement of the electron with the nuclear pair-flip excitations driven by the various nuclear interactions. A novel nuclear interaction, mediated by virtue spin-flips of the single electron, plays an important role in single spin free-induction decay (FID). The spin echo not only refocuses the dephasing by inhomogeneous broadening in ensemble dynamics but also eliminates the decoherence by electron-mediated nuclear interaction. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The quantum theory of decoherence also leads to a method of coherence recovery of the electron by disentanglement, realized through maneuvering the nuclear bath evolution by control of the electron spin-flip. The studies form the basis to outline the construction of a solid-state quantum network for scalable and distributed processing of quantum information
Indium gallium arsenide self-assembled quantum dots have attracted a lot of attention due to their ability to trap single electrons and holes whose spin can be manipulated optically. This makes them attractive as qubits and light sources in various quantum computing and communication schemes. However, the spin of electrons and holes rapidly decoheres due to hyper-fine interaction with the atomic nuclei of the dot. The theme of this thesis is to find ways of overcoming this decoherence, in particular to allow generation of photonic cluster states from quantum dots. This was first approached by designing theoretical schemes to measure and compensate for the source of the decoherence, which were experimentally tested. Two new systems were then theoretically designed where the effects of decoherence could be mitigated. It is shown theoretically that exciting a quantum dot with a laser of well-defined polarisation and monitoring the polarisation of emitted photons, it is possible to determine the vector polarisation of the nuclear spin ensemble. It is shown through simulation that this measurement can be performed on and possibly faster than the time-scale of nuclear fluctuations. The fundamental concept behind the measurement procedure is proved in an experiment using coupled quantum dots. Through the course of the experiment anomalous behaviour of the dots was discovered. A second theoretical proposal is made for a system allowing the fast application of an effective field to compensate for the decoherence mechanism. It is then shown by simulation that a coupled dot system with a prepared in-plane nuclear spin polarisation, can allow optical spin rotation and entanglement generation. A different system is then theoretically proposed where the electron spin in quantum dot can be replaced with another qubit, such as embedded manganese atoms. It is shown through simulation that this system also allows the generation of photonic cluster states.
Semiconductor quantum dots can be used as sources of entangled single photons, which constitute a crucial resource for optical quantum computing. We present theoretical research on entanglement verification and nuclear spin physics, leading to results that are relevant to both experimental work and the theory of quantum optics and mesoscopic quantum systems. Optical quantum computing requires large entangled photonic states, yet characterizing even few-photon states is a challenge in current experiments due to low photon detection efficiencies. We present a lower bound on a measure of computational usefulness of a potentially large quantum state that requires only measured values of three-photon correlations. Hence this bound provides a simple and applicable benchmarking method for quantum dot experiments. We then turn to the critical issue of the interaction between electron and nuclear spins in quantum dots. This interaction gives rise to decoherence that stands in the way of generating entangled photons as well as nuclear phenomena that might help to overcome this challenge. We formulate a quantum mechanical model of the nuclear spin system in a quantum dot driven by continuous-wave laser light. Based on the analytical steady state solution of this model we predict a novel nuclear spin effect, giving rise to nuclear spin polarization that counteracts the effect of an external magnetic field. Beyond the decoherence problem nuclear spins give rise to randomly time-varying transition energies. A quantum mechanical model of this noise as well as the effect of photon scattering is developed, leading to the insight that optical driving can continuously probe the electron transition energy and thereby prevent it from changing.
The motivating background for this thesis lies in the recent development in the coherent optical control of electron spin states in semiconductor quan- tum dots. One possible and attractive application for these achievements is a physical implementation of a quantum computer based on spin qubits (quan- tum bit) in quantum dots. However, one of the obstacles in building such quantum computer is decoherence caused by the interaction of the electron spins with nuclear spins of the host material. In this thesis we theoretically investigate the effects caused by the hyperfine interaction in optically active semiconductor quantum dots. In Chapter 2 we assume optically induced rotations of single electron spins in semiconductor quantum dots. The optical control of the electron spin states is considered to be conducted by means of Raman type optical transitions between electron spin states. We investigate the influence of nuclear spins on the performance of the single-qubit gates by incorporating the additional effect of the Overhauser field into the electron spin dynamics. To calculate the errors caused by the hyperfine interaction, we determine average fidelities of rotations around characteristic axes in the Bloch sphere in the presence of nuclear spins analytically with perturbation theory up to second order in the Overhauser field. By applying numerical averaging over the nuclear field distribution we find the average fidelity to the arbitrary orders of the hyper- fine interaction. In Chapter 3 we investigate the dynamics of spin qubits interacting by means of an optical cavity. The qubits are represented by a single electron spin each confined to a quantum dot. Knowing that electron spins in III-V semiconduc- tor quantum dots are affected by the decoherence due to the hyperfine inter- action with nuclear spins, we find that the interaction between two qubits is consequently influenced by the Overhauser field. Assuming an unpolarizied nuclear ensemble, we investigate the fidelities for two-qubit gates depending on the Overhauser field. We include the hyperfine interaction perturbatively to second order in our analytical results, and to arbitrary precision numeri cally. Quantum dots can be used not only as physical systems for qubits, but also as sources for entangled photons. In chapter 4 we consider an emission of entangled photons by spontaneous decay of the biexciton state to the ground state. Due to electron-hole exchange interaction, the intermediate excitonic states have a finite fine structure splitting. The electron spins of the excitons also interact via hyperfine interaction with the nuclear spins. We study the temporal and fine structure splitting dependance of the coherence measures considering the effect of the nuclear magnetic field. We find that the hy perfine interaction contributes considerably to the reduction of the photon coherence. One of the possibilities to minimize the decoherence effects of the hyperfine interaction is to polarize the nuclear spins to 100%. However, up to date it was not possible to reach such degree of the nuclear polarization in experi- ments. In a recent experiment by Chekhovich et al. it was shown that high nuclear spin polarization can be achieved in self-assembled quantum dots by exploiting an optically forbidden transition between a heavy hole and a trion state. A fully polarized state in this case was predicted by a classical rate equation, but could not be obtained experimentally. Therefore we theoret- ically investigate this problem with the help of a quantum master equation in Chapter 5, and we show that a fully polarized state cannot be achieved due to formation of a nuclear dark state. Moreover, we demonstrate that the maximal degree of polarization depends on the form of the electron wave function inside of the quantum dot.
Quantum networks lie at the heart of distributed quantum computing and secure quantum communication - research areas that have seen a strong increase of interest over the last decade. Their basic architecture consist of stationary nodes composed of quantum processors which are linked via photonic channels. The key requirement, and at the same time the most demanding challenge, is the efficient distribution of entanglement between distant nodes. The two ground states of single spins confined in self-assembled InGaAs quantum dots provide an effective two-level system for the implementation of quantum bits. Moreover, they offer strong transition dipole moments with outstanding photonic properties allowing for the realisation of close to ideal, high-bandwidth spin-photon interfaces. These properties are combined with the benefits of working in the solid state, such as scalability and integrability of devices, to form a promising candidate for the implementation of fast entanglement distribution. In this dissertation we provide the first implementation of a unit cell of a quantum network based on single electron spins in InGaAs. We use a probabilistic scheme based on spin-photon entanglement and the erasure of which path information to project the two distant spins into a maximally entangled Bell state. The successful generation of entanglement is verified through a reconstruction of the final two-spin state and we achieve an average fidelity of 61.6±2.3% at a record-high generation rate of 5.8kHz. One of the main constraints to the achieved fidelity is the limited coherence of the electron spin. We show that it can be extended by three orders of magnitude through decoupling techniques and develop a new measurement technique, allowing us to investigate the origins of the decoherence which has previously been obscured by nuclear feedback processes. Our results evidence that further extension of coherence is ultimately limited by intrinsic mechanisms closely related to local strain due to the growth method of self-assembled quantum dots. After establishing the intrinsic limits to the electron coherence we investigate the coherence properties of the single hole spin as an alternative two-level system with the potential for higher coherence times. We show that the hole spin coherence is indeed superior to the one of the electron and realise the first successful dynamic decoupling scheme implemented in these systems. We find that the decoherence at low external magnetic fields is still governed by coupling to the nuclear spins whereas it is dominated by electrical noise for fields exceeding a few Tesla. This noise source is extrinsic to the quantum dots and a better understanding offers the potential for further improvement of the coherence time. The findings of this work present a complete study of the coherence of the charge carriers in self-assembled quantum dots and provide the knowledge needed to improve the implementation of a quantum-dot based quantum network. In particular, the combination of spin-spin entanglement and the hole coherence times enable further research towards multidimensional photonic cluster states.