Spin degrees of freedom have been extensively explored in the context of quantum information processing. Many proposals of quantum computation architectures use spins as carriers of quantum of information. A central problem is to efficiently generate quantum entanglement between spin qubits which proves to be a crucial resource for quantum information tasks. On the other hand, uncontrollable spin degrees of freedom in the environment of spin qubits are the major causes of errors at low temperature, for example, the lattice nuclear spins hyperfine coupled to single electron spin qubit localized in semiconductor nano-structures. An outstanding problem for scalable quantum computation is to suppress the collective fluctuations from such spin baths so that the coherence time of the spin qubit can be improved. With these two motivations, the problems of suppressing collective spin fluctuations and generating entanglement in various spin ensembles are addressed in this thesis.\n\n\n\nIn the first half of the thesis, two approaches are introduced for suppressing the collective fluctuations in the nuclear spin bath so that the quantum coherence time of electron spin qubit in semiconductor quantum dots can be improved. The first approach works for a coupled double dot system. A theory for the interaction with the nuclear spins is developed when the two-electron singlet state is in resonance with one of the triplet state in moderate external magnetic field. At this resonance condition, the nuclear-electron flip-flop process caused by the hyperfine interaction can lead to a feedback mechanism, which can be used to suppress the nuclear hyperfine field. The second approach works for a single dot system. It is shown that strong pumping of the nuclear spins in dynamic nuclear polarization processes can saturate the nuclear spin bath towards the collective “dark states”. In such dark states, the transverse nuclear field fluctuation can be substantially suppressed compared to the value at thermal equilibrium. Two physical schemes are proposed to realize the nuclear dark states for suppression of the nuclear field fluctuations.\n\n\n\nIn the second half of the thesis, schemes are presented for generating large scale quantum entanglement in two types of spin qubit systems. For atomic spin qubits in optical lattices, schemes are proposed on how to prepare pure spin coherent state (SCS) with low collective spin by incoherent pumping with collective spin raising and lowering operations. Such SCS realize networks of mutually entangled spins which can be idea resources for the quantum telecloning algorithm. For donor nuclear spin qubits in silicon architecture, proposals are shown on how to deterministic prepare Dicke states which constitute an important class of multipartite entangled states. Our scheme is capable of preparing both symmetric and asymmetric Dicke states which form a complete basis set of the spin Hilbert space. The required controls are in situ to the prototype Kane’s quantum computer. The preparation is robust because each desired Dicke state is the steady state under designed pumping process. The schemes presented here also make possible the construction of decoherence free subspaces where quantum information is protected from collective noises.
Spin degrees of freedom have been extensively explored in the context of quantum information processing. Many proposals of quantum computation architectures use spins as carriers of quantum of information. A central problem is to efficiently generate quantum entanglement between spin qubits which proves to be a crucial resource for quantum information tasks. On the other hand, uncontrollable spin degrees of freedom in the environment of spin qubits are the major causes of errors at low temperature, for example, the lattice nuclear spins hyperfine coupled to single electron spin qubit localized in semiconductor nano-structures. An outstanding problem for scalable quantum computation is to suppress the collective fluctuations from such spin baths so that the coherence time of the spin qubit can be improved. With these two motivations, the problems of suppressing collective spin fluctuations and generating entanglement in various spin ensembles are addressed in this thesis.\n\n\n\nIn the first half of the thesis, two approaches are introduced for suppressing the collective fluctuations in the nuclear spin bath so that the quantum coherence time of electron spin qubit in semiconductor quantum dots can be improved. The first approach works for a coupled double dot system. A theory for the interaction with the nuclear spins is developed when the two-electron singlet state is in resonance with one of the triplet state in moderate external magnetic field. At this resonance condition, the nuclear-electron flip-flop process caused by the hyperfine interaction can lead to a feedback mechanism, which can be used to suppress the nuclear hyperfine field. The second approach works for a single dot system. It is shown that strong pumping of the nuclear spins in dynamic nuclear polarization processes can saturate the nuclear spin bath towards the collective “dark states”. In such dark states, the transverse nuclear field fluctuation can be substantially suppressed compared to the value at thermal equilibrium. Two physical schemes are proposed to realize the nuclear dark states for suppression of the nuclear field fluctuations.\n\n\n\nIn the second half of the thesis, schemes are presented for generating large scale quantum entanglement in two types of spin qubit systems. For atomic spin qubits in optical lattices, schemes are proposed on how to prepare pure spin coherent state (SCS) with low collective spin by incoherent pumping with collective spin raising and lowering operations. Such SCS realize networks of mutually entangled spins which can be idea resources for the quantum telecloning algorithm. For donor nuclear spin qubits in silicon architecture, proposals are shown on how to deterministic prepare Dicke states which constitute an important class of multipartite entangled states. Our scheme is capable of preparing both symmetric and asymmetric Dicke states which form a complete basis set of the spin Hilbert space. The required controls are in situ to the prototype Kane’s quantum computer. The preparation is robust because each desired Dicke state is the steady state under designed pumping process. The schemes presented here also make possible the construction of decoherence free subspaces where quantum information is protected from collective noises.
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.
Spins localized in semiconductor nanostructures have been intensively investigated for quantum spintronics. These include the spin of single electron localized by quantum dots or impurities, and spins of the lattice nuclei. These localized spins can be exploited as carriers of quantum information, while in some circumstances they also play the role of deleterious noise sources for other quantum objects through their couplings. Quantum control of the spins in semiconductor nanostructures is therefore of central interest for quantum applications. In this thesis, we address several problems related to the quantum control of electron or hole spin and nuclear spins in semiconductor quantum dots and impurity centers. The first problem studied is the control of nuclear spin bath for a hole spin qubit in III-V semiconductor quantum dot. In quantum dots formed on III-V compounds, the direct band gap of the host material allows ultrafast optical addressability of a single electron or hole spin qubit. However, nonzero nuclear spins of group III and group V elements result in a large statistical fluctuation in the Zeeman splitting of the spin qubit which then dephases in nanosecond time scale. We present a novel feedback scheme to suppress the statistical fluctuation of the nuclear spin field for enhancing the coherence time of the hole spin qubit. We also find positive feedback control which can amplify the magnitude of the nuclear field, so that a bimodal distribution can develop, realizing a quantum environment that can not be described by a single temperature. The second problem addressed here is the control of donor spin qubits in silicon architecture which have ultra-long quantum coherence time. We developed the quantum control scheme to realize the quantum metrology of magnetic field gradient, based on the celebrated Kane’s architecture for quantum computation. The scheme can also be generalized to calibrate the locations of the donors. In the third part of the thesis, we investigate a novel type of quantum dot formed in a new class of two-dimensional semiconductors, monolayer transition metal dichalcogenides (TMDs), which exhibit interesting spin and pseudospin physics. This novel quantum dot system may offer new opportunity for quantum spintronics in the ultimate 2D limit, and we investigate here the valley pseudospin as a possible quantum bit carrier. A main finding is that, contrary to the intuition, the lateral confinement by the quantum dot potential does not lead to noticeable valley hybridization, and therefore the valley pseudospin in monolayer TMDs QD can well inherit the valley physics such as the valley optical selection rules from the 2D bulk which implies a variety of quantum control possibilities.
Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations.\n\n\n\nThe focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*.\n\n\n\nWe probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled.\n\n\n\nThis work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.
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
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,
This dissertation is a study of the decoherence of a solid-state spin qubit, either that of a localized electron spin or a donor nucleus, caused by a nuclear spin bath relevant to semiconductor quantum computer architectures. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the qubit spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The qubit spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is motivated, developed, and tested for the spectral diffusion problem. The method is applicable to any ideal pulse sequence applied to the qubit. Dynamical decoupling sequences, which aim to prolong qubit coherence, are analyzed. In particular, concatenated dynamical decoupling sequences are shown to prolong not only the coherence time over the entire sequence but also the length of time between pulses necessary to maintain coherence. This is shown to result from successive low-order cancellations in applicable perturbative expansions with each level of concatenation. Each cancellation, however, will require the inclusion, in the cluster expansion, of increasingly large clusters to obtain the lowest-order results. These larger clusters in the lowest order often dominate decoherence and therefore invalidate, as being overly optimistic, the pair approximation as a means to study the effect of concatenated dynamical decoupling. We present numerical results from our cluster expansion technique for echoes of single (Hahn), concatenated, and periodic pulse sequences using realistic models of a localized electron in phosphorus doped Si and in a GaAs quantum dot and of a P donor nucleus in Si or GaAs. In the Si:P electron spin decoherence problem, we consider, along with spectral diffusion, the effects of anisotropic hyperfine (AHF) interactions and suggest a technique to suppress electron spin echo envelope modulations (ESEEM), an additional source of decoherence resulting from the AHF interactions. Our calculations for the Si:P Hahn echoes, including the effects of both anisotropic hyperfine interactions and spectral diffusion, are in excellent agreement with experimental results. Our calculations of concatenated pulse sequence echoes offer important predictions for the effectiveness of a promising strategy to preserve qubit coherence in semiconductor quantum computer architectures.