Spins and orbits in semiconductor quantum dots

Spins in semiconductor quantum dots are among the most promising candidates for the realization of a scalable quantum bit (qubit), the basic building block of a quantum computer. With this motivation, spin and orbital properties of quantum dots in three different semiconductor systems are investigated in this thesis: depletion mode quantum dots in GaAs/AlGaAs heterostructures as well as in silicon-germanium core-shell nanowires (GeSi NW), and accumulation mode quantum dots formed in a fin field-effect transistor (FinFET). The chronological order of this thesis reflects two major shifts of focus of the semiconductor spin qubit research in recent years: a transition from lateral GaAs quantum dots towards scalable, silicon-based systems and a change from electrons towards holes as the host of the spin qubit because of better prospects for spin manipulation and spin coherence. In a lateral GaAs single electron quantum dot, a new in-plane magnetic-field-assisted spectroscopy is demonstrated, which allows one to deduce the three dimensional confinement potential landscape of the quantum dot orbitals, which gives insight into the alignment of the ellipsoidal quantum dot with respect to the crystal axes. With this full model of the confinement at hand, the dependence of the spin relaxation on the direction and strength of an in-plane magnetic field is investigated. To mitigate the spin relaxation anisotropy due to anisotropic in-plane confinement of the quantum dot, said confinement is symmetrized by tuning the gate voltages to obtain a circular quantum dot. Then, the experimentally observed spin relaxation anisotropy can be attributed to the interplay of Rashba and Dresselhaus spin-orbit interaction (SOI) present in GaAs. By using a theoretical model, the strength and the relative sign of the Rashba and Dresselhaus SOI was obtained for the first time in such a quantum dot. From the dependence of the spin relaxation on the magnetic field strength, hyperfine induced phonon mediated spin relaxation was demonstrated -- a process predicted more than 15 years ago. Here, the hyperfine interaction leads to a mixing of spin and orbital degrees of freedom and facilitates spin relaxation. Limited by this relaxation process, a spin relaxation time of 57 +/- 15 s was measured -- setting the current record for spin lifetime in a nanostructure. Inspired by the unprecedented knowledge of the confinement and the SOI in the quantum dots used, a new theory to quantify the various corrections to the g-factor was developed. Later, these theoretical predictions have been experimentally validated by measurements of the g-factor anisotropy using pulsed-gate spectroscopy. Due to short spin qubit coherence time in GaAs, which is limited by the nuclear spins, a better approach is to build a spin qubit in a semiconductor vacuum with little or no nuclear spins. Because holes have minimal overlap with the nuclei of the semiconductor due to the p-type symmetry of their wave function, this type of decoherence is strongly suppressed when changing the host of the spin qubit from electrons to holes. The longer coherence times in combination with the predicted emergence of a direct type of Rashba SOI (DRSOI) -- a particularly strong and electrically controllable SOI -- motivated the investigation of hole quantum dots in GeSi NW. In this system, anisotropic behavior of the leakage current through a double quantum dot in Pauli spin blockade was observed. This anisotropy is qualitatively explained by a phenomenological model, which involves an anisotropic g-factor and an effective spin-orbit field. While the dominant type of SOI could not be resolved conclusively, the obtained data is not inconsistent with the expectation of DRSOI. Because each wire has to be placed manually, this NW based system lacks scalability. Hole and electron quantum dots in an industry-compatible silicon FinFET structure, conversely, are promising candidates for scalable spin qubits and, therefore, hold the potential to be used in a spin-based quantum computer. Recently, DRSOI was predicted to also emerge in narrow silicon channels such as FinFETs. In this thesis, the formation of accumulation mode hole quantum dots in such a FinFET structure is reported -- an important first step towards the realization of a scalable, all-electrically controllable, DRSOI hole spin qubit

Orbital effects of a strong in-plane magnetic field on a gate-defined quantum dot

We theoretically investigate the orbital effects of an in-plane magnetic field on the spectrum of a quantum dot embedded in a two-dimensional electron gas (2DEG). We derive an effective two-dimensional Hamiltonian where these effects enter in proportion to the flux penetrating the 2DEG. We quantify the latter in detail for harmonic, triangular, and square potential of the heterostructure. We show how the orbital effects allow one to extract a wealth of information, for example, on the heterostructure interface, the quantum dot size and orientation, and the spin-orbit fields. We illustrate the formalism by extracting this information from recent measured data [L.~C.~Camenzind, et al., arXiv:1804.00162; Nat. Commun. 9, 3454 (2018)].Comment: 14 pages, 9 figures; minor changes resulting from refereeing and proof

G-factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

We analyze orbital effects of an in-plane magnetic field on the spin structure of states of a gated quantum dot based in a two-dimensional electron gas. Starting with a $k \cdot p$ Hamiltonian, we perturbatively calculate these effects for the conduction band of GaAs, up to the third power of the magnetic field. We quantify several corrections to the g-tensor and reveal their relative importance. We find that for typical parameters, the Rashba spin-orbit term and the isotropic term, $H_{43} \propto {\bf P}^2 {\bf B} \cdot \boldsymbol{\sigma}$, give the largest contributions in magnitude. The in-plane anisotropy of the g-factor is, on the other hand, dominated by the Dresselhaus spin-orbit term. At zero magnetic field, the total correction to the g-factor is typically 5-10% of its bulk value. In strong in-plane magnetic fields, the corrections are modified appreciably.Comment: 24 pages, 8 figures; v2 is in content identical to the version published in PRB. Compared to v1, the minor changes adopted in v2 are reflecting the PRB referees' suggestion

A spin qubit in a fin field-effect transistor

Quantum computing's greatest challenge is scaling up. Several decades ago, classical computers faced the same problem and a single solution emerged: very-large-scale integration using silicon. Today's silicon chips consist of billions of field-effect transistors (FinFETs) in which current flow along the fin-shaped channel is controlled by wrap-around gates. The semiconductor industry currently employs fins of sub-10$\,$nm width, small enough for quantum applications: at low temperature, an electron or hole can be trapped under the gate and serve as a spin qubit. An attractive benefit of silicon's advantageous scaling properties is that quantum hardware and its classical control circuitry can be integrated in the same package. This, however, requires qubit operation at temperatures greater than 1$\,$K where the cooling is sufficient to overcome the heat dissipation. Here, we demonstrate that a silicon FinFET is an excellent host for spin qubits that operate even above 4$\,$K. We achieve fast electrical control of hole spins with driving frequencies up to 150$\,$MHz and single-qubit gate fidelities at the fault-tolerance threshold. The number of spin rotations before coherence is lost at these "hot" temperatures already matches or exceeds values on hole spin qubits at mK temperatures. While our devices feature both industry compatibility and quality, they are fabricated in a flexible and agile way to accelerate their development. This work paves the way towards large-scale integration of all-electrical and ultrafast spin qubits

Spectroscopy of Quantum-Dot Orbitals with In-Plane Magnetic Fields

We show that in-plane-magnetic-field assisted spectroscopy allows extraction of the in-plane orientation and full 3D shape of the quantum mechanical orbitals of a single electron GaAs lateral quantum dot with sub-nm precision. The method is based on measuring orbital energies in a magnetic field with various strengths and orientations in the plane of the 2D electron gas. As a result, we deduce the microscopic quantum dot confinement potential landscape, and quantify the degree by which it differs from a harmonic oscillator potential. The spectroscopy is used to validate shape manipulation with gate voltages, agreeing with expectations from the gate layout. Our measurements demonstrate a versatile tool for quantum dots with one dominant axis of strong confinement.Comment: 4 pages, 3 color figures, including supplementary on arXi

Rapid single-shot parity spin readout in a silicon double quantum dot with fidelity exceeding 99 %

Silicon-based spin qubits offer a potential pathway toward realizing a scalable quantum computer owing to their compatibility with semiconductor manufacturing technologies. Recent experiments in this system have demonstrated crucial technologies, including high-fidelity quantum gates and multiqubit operation. However, the realization of a fault-tolerant quantum computer requires a high-fidelity spin measurement faster than decoherence. To address this challenge, we characterize and optimize the initialization and measurement procedures using the parity-mode Pauli spin blockade technique. Here, we demonstrate a rapid (with a duration of a few us) and accurate (with >99% fidelity) parity spin measurement in a silicon double quantum dot. These results represent a significant step forward toward implementing measurement-based quantum error correction in silicon

Hyperfine-phonon spin relaxation in a single-electron GaAs quantum dot

Understanding and control of the spin relaxation time T-1 is among the key challenges for spinbased qubits. A larger T-1 is generally favored, setting the fundamental upper limit to the qubit coherence and spin readout fidelity. In GaAs quantum dots at low temperatures and high inplane magnetic fields B, the spin relaxation relies on phonon emission and spin-orbit coupling. The characteristic dependence T-1 alpha B-5 and pronounced B-field anisotropy were already confirmed experimentally. However, it has also been predicted 15 years ago that at low enough fields, the spin-orbit interaction is replaced by the coupling to the nuclear spins, where the relaxation becomes isotropic, and the scaling changes to T-1 alpha B-3. Here, we establish these predictions experimentally, by measuring T-1 over an unprecedented range of magnetic fields-made possible by lower temperature-and report a maximum T-1 = 57 +/- 15 s at the lowest fields, setting a record electron spin lifetime in a nanostructure

Silicon quantum dot devices with a self-aligned second gate layer

We implement silicon quantum dot devices with two layers of gate electrodes using a self-alignment technique, which allows for ultra-small gate lengths and intrinsically perfect layer-to-layer alignment. In a double quantum dot system, we investigate hole transport and observe current rectification due to Pauli spin blockade. Magnetic field measurements indicate that hole spin relaxation is dominated by spin-orbit interaction, and enable us to determine the effective hole $g$-factor $\simeq1.6$. From an avoided singlet-triplet crossing, occurring at high magnetic field, the spin-orbit coupling strength $\simeq0.27$meV is obtained, promising fast and all-electrical spin control

Hamiltonian Phase Error in Resonantly Driven CNOT Gate Above the Fault-Tolerant Threshold

Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating the gate errors are useful to improve the gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled-phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gate-set tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity controlled-phase gate.Comment: Main article: 22 pages, 4 figures; Supplementary material: 6 pages, 5 figures, 1 tabl