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Quantum dots for quantum information processing

Martin J. A. Schuetz

Published Jan 1, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.5282/edoc.18730

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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.
Recent studies in self-assembled InAs quantum dots (QDs) for applications in quantum information processing have demonstrated initialization, readout and long decoherence time of an electron spin confined in a single QD. These arguably fulfill three out of the five DiVincenzo criteria for the physical implementation of quantum computation. Based on recent developments self-assembled InAs quantum dot molecules (QDMs), several advancements in the optical manipulation of two-electron spin states have been made. As a continuation of these studies towards a full two-qubit system, this thesis addresses one of the remaining criteria concerning a universal set of quantum gates. The physical platform for two-qubit gates is provided by two electrons confined in the QDM where the Coulomb exchange interaction gives rise to the singlet and triplet manifolds. In a transverse magnetic field, an eight-level system consisting of four singlet-triplet spin states, four optical excited states and twelve dipole allowed transitions arises. Spin initialization via multi-laser optical pumping is demonstrated with near unity fidelity for three of the spin states, while the remaining one can, in principle, be achieved by coherent optical pumping using four CW lasers. The effects of dynamic nuclear spin polarization, arising from the coupling between the electrons and the surrounding nuclei, is evident in the frequency pulling and pushing lineshapes in absorption profiles. This thesis shows that the optical nuclear spin locking that was demonstrated in a single QD earlier is effective in QDMs, yielding a long spin decoherence time of about 1 microsecond. Spectroscopic evidence suggests that this is accompanied by the first evidence of a narrowing in the Overhauser field distribution. The results reveal that stabilization of nuclear spin polarization in both QDs is achieved by optical manipulations in the top QD, demonstrating the effect of non-local nuclear spin locking. Finally, it is shown theoretically that pulsed excitation results in single spin rotations and in conjunction with the Coulomb exchange interaction, provides the ingredients for a universal two-qubit gate. A feasible experimental demonstration of the two-qubit gate is proposed, along with the methodology for the population readout of individual spin states.
Electron spins confined to self-assembled quantum dots are considered as nodes for a coherent optical network capable of supporting distributed quantum states. Through a series of experiments, the work contributing to this dissertation examines some of the key criteria for constructing such a network. First, the ability to optically extract a coherent spin state from the quantum dot without perturbing the nuclear environment is explored: nuclear feedback is an issue that has frustrated previous studies into electron spin coherence in these systems. With the novel techniques we develop, we identify and characterise the previously undetermined intrinsic mechanisms that govern the coherence of the central spin. We show how the coherence of the electron spin is intimately related to the growth of these strained nanostructures. Second, a model network is constructed in which two spins confined to separate quantum dots are projected into a highly entangled state. This is the first time electron spins in distant quantum dots have been entangled, and in doing so we demonstrate controllable entanglement generation at the highest rates recorded for optically accessible qubit definitions. We investigate the realisation of a hybrid quantum network by demonstrating the first interconnect between wholly different single quantum systems: a semiconductor quantum dot and a trapped ytterbium ion. In forming an optical link between these two complementary qubit definitions, we show that we can circumvent their intrinsic optical differences through coherent photon generation at the quantum dot. A network built from these diverse constituents could combine the ultrafast operations self-assembled quantum dots enable with the long coherence times states in trapped ions experience. Finally, in a step towards truly scalable entanglement generation between quantum dot spins, we design minimally invasive structures that will funnel large proportions of the optical dipole field from the optically dense material that surrounds the quantum dot. The techniques developed in this work and the knowledge gained from their operation should enable the demonstration the creation of high-order nonlocal states between quantum dot spins, single photons and trapped ions, as well as the development of new optically active systems that will benefit from enhanced spin coherence.
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,
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.
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 leads to multistability and criticality in the steady-state solutions.
Quantum physics governs the world at the microscopic scale and determines the properties of matter. While classical computers exploit quantum phenomena passively by relying on transistor technology, the concept of a quantum computer with active control over quantum states promises unprecedented possibilities for information encoding and processing. Already developed quantum algorithms are known to perform certain tasks faster than any existing classical algorithms, and quantum computers also promise the possibility for precise simulations of complex quantum systems, a task infeasible for classical computers. These points emphasize the need for the development of quantum computers. Considering quantum computers, the fundamental unit of information is a qubit, a two-level quantum system. Qubits, in contrast to classical bits which are either in state 0 or 1, can exist in quantum superposition of the states 0 and 1, allowing for more complex and parallel computations. While there are many options to encode a logical qubit in a physical system, spin 1/2 particles are considered a natural choice because their spin degree of freedom defines a qubit intrinsically. Semiconductors are a promising platform for hosting spin qubits, as they enable the confinement of electrons with spin 1/2 either through gate-defined quantum dots (QDs) or donor atoms. Among the possible choices of donor atoms, phosphorous 31P is particularly noteworthy because its nucleus has nuclear spin 1/2. Nuclear spins are prime candidates for qubit implementation because they demonstrated exceptionally long coherence times, but the underlying good isolation from their environment is a challenge when it comes to readout and control. In this thesis, we face this challenge by proposing a hybrid quantum dot-donor (QDD) system consisting of a gate defined silicon (Si) QD and a thereto laterally displaced 31P phosphorous donor atom implanted in the Si host material. A single electron is presumed to be confined in the system, which can be moved between the QD and the donor on demand. If its wave function overlaps with the donor atom, electron spin and the donor nuclear spin interact via the hyperfine interaction and the electron can act as a mediator between the nuclear spin qubit and the environment for readout and control, whereas the nuclear spin qubit can be set in an idling mode by shifting the electron to the QD. Importantly, the proposed system can be embedded in circuit quantum electrodynamics (cQED) architectures enabling strong coupling between the system’s electron spin and microwave resonator photons. This coupling is fundamental for the research presented in this thesis. Analyzing the envisioned system, we first propose a novel method for nuclear-spin readout by probing the resonator transmission. This method is based on the observation that the signature of strong electron spin-photon coupling in the resonator transmission is altered due to the hyperfine interaction, in such a manner that well separated signatures for the electron spin-photon coupling conditioned on the state of the nuclear spin arise. As the next step, we turn our attention to the control of nuclear spin qubits and especially to the challenge of realizing a two-qubit gate between distant nuclear spins. In this course, we derive an effective nuclear spin-photon coupling. While expected to be weak, this interaction can be harnessed to couple the nuclear spins of two distant QDD systems dispersively to a microwave resonator resulting in an entangling nuclear spin two-qubit √iSWAP gate with a gate fidelity approaching 90%. These two key findings represent a significant and valuable contribution to the field of quantum information processing using nuclear spins.