In this thesis, I study quantum transport of electron (e.g., current and noise) in quantum dots exploring microscopic processes responsible for spin-relaxation in double quantum dots in Pauli spin blockade regime. This is a regime where current is blocked due to the spin configuration of electrons in the dot. The Pauli \nspin blockade provides a means for preparation, manipulation and readout in spin qubits. Hence, understanding the underlying mechanism which lifts this blockade is extremely important. \n \nFirst, I have developed a theory of spin-flip cotunneling (higher order tunneling) processes in double quantum dots in the Pauli spin blockade regime. Utilizing this \ntheory, I have calculated the full analytical dependence of the stationary current on applied magnetic fields, gate voltages, and an inter-dot tunnel coupling in Pauli \nspin blockade. This work is important for understanding the nature of leakage, especially in systems where other spin-flip mechanisms (due, e.g., hyperfine coupling \nto nuclear spins or spin-orbit coupling) are weak, including silicon and carbon nanotube or graphene quantum dots. This theory explains recent experiments on \ncarbon nanotubes and silicon double quantum dot. \n \nIn addition, I propose a new scheme based on the current noise to probe spin relaxation mechanisms in double quantum dot in the Pauli spin blockade regime, where spin-selection rule applies. As a result, I provide a simple closed-form expression which can be used to fit experimental data to extract multiple spin-relaxation \nrates, even at very low energy splitting. This method allows for the characterization of different aspects of decay process in these systems.
In this thesis, I study quantum transport of electron (e.g., current and noise) in quantum dots exploring microscopic processes responsible for spin-relaxation in double quantum dots in Pauli spin blockade regime. This is a regime where current is blocked due to the spin configuration of electrons in the dot. The Pauli \nspin blockade provides a means for preparation, manipulation and readout in spin qubits. Hence, understanding the underlying mechanism which lifts this blockade is extremely important. \n \nFirst, I have developed a theory of spin-flip cotunneling (higher order tunneling) processes in double quantum dots in the Pauli spin blockade regime. Utilizing this \ntheory, I have calculated the full analytical dependence of the stationary current on applied magnetic fields, gate voltages, and an inter-dot tunnel coupling in Pauli \nspin blockade. This work is important for understanding the nature of leakage, especially in systems where other spin-flip mechanisms (due, e.g., hyperfine coupling \nto nuclear spins or spin-orbit coupling) are weak, including silicon and carbon nanotube or graphene quantum dots. This theory explains recent experiments on \ncarbon nanotubes and silicon double quantum dot. \n \nIn addition, I propose a new scheme based on the current noise to probe spin relaxation mechanisms in double quantum dot in the Pauli spin blockade regime, where spin-selection rule applies. As a result, I provide a simple closed-form expression which can be used to fit experimental data to extract multiple spin-relaxation \nrates, even at very low energy splitting. This method allows for the characterization of different aspects of decay process in these systems.
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.
Spin qubits in semiconductor quantum circuits have been identified as a compelling platform for large scale quantum computing. Today an ongoing effort of the community is aiming at the scaling of such systems by filling larger and larger arrays. In this context the development of tuning and readout protocols allowing to reduce the inherent complexity of such systems seems to be a necessity.In the first part of my thesis, I demonstrate array partitioning of a linear triple quantum dot defined in a AlGaAs/GaAs heterostructure via a highly tunable interdot tunnel coupling. This allows us to operate independently smaller sections of the array which reduces the number of available charge states for the system and therefore reduces its complexity during the tuning.The second part of my thesis is focused on reducing the hardware overhead necessary to extract information during the readout of the spin qubits. In semiconductor spin qubits, high fidelity read-out is obtained through Pauli spin blockade in a double quantum dot with two electrons probed by a local electrometer. One electron is the qubit, the second is the ancilla and only one bit of information is extracted. To obtain the full two-bit information of the two-electron spin states, more quantum hardware is necessary (either dots, electrometers, or reservoirs).Based on an original protocol, I develop in this thesis a complete single-shot read-out procedure for two-electron spin states in a double quantum dot discriminating between S, T0, T+ and T-. It uses successively three distinct spin-to-charge conversion protocols interleaved with charge configuration measurements. The strategy is based on four novel experimental achievements:First, the control from the GHz to sub-Hz regime of the interdot tunnel coupling at the nanosecond timescale.Second, the separation of the spin-to-charge conversion and the charge read-out in the voltage gate space.Third, the suppression of spin relaxation process during the read-out procedure.Finally, the repetition of three distinct spin-to-charge conversion protocols.The read-out procedure is tested on various initialized populations and implemented in more complex spin manipulation sequences to assess its validity.
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.
In this thesis I find an analytic expression for the conductance of a single electron transistor in the regime when temperature, level spacing, and charging energy of an island are all of the same order. I also study the correction to the spacing between Coulomb blockade peaks due to finite dot-lead tunnel couplings. I find analytic expressions for both correction to the spacing averaged over mesoscopic fluctuations and the rms of the correction fluctuations. In the second part of the thesis I discuss the feasibility of quantum dot based spin- and charge-qubits. Firstly, I study the effect of mesoscopic fluctuations on the magnitude of errors that can occur in exchange operations on quantum dot spin-qubits. Mid-size double quantum dots, with an odd number of electrons in the range of a few tens in each dot, are investigated through the constant interaction model using realistic parameters. It is found that the number of independent parameters per dot that one should tune depends on the configuration and ranges from one to four. Then, I study decoherence of a quantum dot charge qubit due to coupling to piezoelectric acoustic phonons in the Born-Markov approximation. After including appropriate form factors, I find that phonon decoherence rates are one to two orders of magnitude weaker than was previously predicted. My results suggest that mechanisms other than phonon decoherence play a more significant role in current experimental setups.
We describe time-dependent single-electron transport through quantum dots in the Coulomb blockade regime. Coherent dynamics of a single charge qubit in a double quantum dot is discussed with full one-qubit manipulation. Strength of decoherence is controlled with the applied voltage, but uncontrolled decoherence arises from electron–phonon coupling and background fluctuations. Then energy-relaxation dynamics is discussed for orbital and spin degree of freedom in a quantum dot. The electron–phonon interaction and spin–orbit coupling can be investigated as the dissipation problem. Finally, charge detection measurement is presented for statistical analysis of single-electron tunnelling transitions and for a sensitive qubit read-out device.