Charge State Manipulation Of Silicon Based Donor Spin Qubits

In the race for quantum computing, these last years silicon has become a material of choice for the implementation of spin qubits. Such devices are fabricated in CEA using CMOS technologies, in order to facilitate their large-scale integration. This thesis covers the modeling of these qubits andin particular the manipulation of the spin state with an electric field. To that end, we use a set numerical tools to compute the potential and electronic structure in the qubits (in particular tightbinding and k.p methods), in order to be as close as possible to the experimental devices. These simulations allowed us to study two important experimental results: on one hand the observation of the electrical manipulation of an electron spin, and on the other hand the characterization of the anisotropy of the Rabi frequency of a hole spin qubit. The first one was rather unexpected, since the spin-orbit coupling is very low in the silicon conduction band. We develop a model, confirmed by thesimulations and some experimental results, that highlights the essential role of the intervalley spinorbit coupling, enhanced by the low symmetry of the system. We use these results to propose and test numerically a scheme for electrical manipulation which consists in switching reversibly betweena spin qubit and a valley qubit. Concerning the hole qubits, the relatively large spin-orbit coupling allows for electrical spin manipulation. However the experimental measurements of Rabi frequency anisotropy show a complex physics, insufficiently described by the usual models. Therefore we developa formalism which allows to characterize simply the Rabi frequency as a function of the magnetic field, and that can be applied to other types of spin-orbit qubits. The simulations reproduce the experimental features, underline the important role of strain.

Here is a discussion of the state of the art of spin resonance in low dimensional structures, such as two-dimensional electron systems, quantum wires, and quantum dots. Leading scientists report on recent advances and discuss open issues and perspectives.

The project goals are to fabricate qubits in quantum dots in Si/SiGe modulation-doped heterostructures, to characterize and understand those structures, and to develop the technology necessary for a Si/SiGe quantum dot quantum computer. The physical qubit in our approach is the spin of an electron confined in a top-gated silicon quantum dot in a Si/SiGe modulation-doped heterostructure. Operations on such a qubit may be performed by controlling the voltages on gates in-between neighboring quantum dots. A quantum computer and qubits in silicon offer potential advantages, both fundamental and practical. Electron spins in silicon quantum dots are expected to have long coherence times. Silicon has an isotope, Si, which has zero nuclear spin and thus no nuclear magnetic moment. As a result, electron spins in silicon have longer coherence times than they would in the presence of a fluctuating nuclear spin background. From a practical perspective, modern classical computers are made in silicon, and one hopes that this will lead to synergy in the future with a silicon quantum computer. This QCCM includes both theory and experiment focusing on (i) the development of qubits in the form of electron spins in silicon quantum dots, (ii) the measurement and manipulation of those qubits, and (iii) the science essential for understanding the properties of such qubits.

This book features the proceedings of the NATO Advanced Study Institute "Manipulating Quantum Coherence in Solid State Systems", held in Cluj-Napoca, Romania, August 2005, which presented a fundamental introduction to solid-state approaches to achieving quantum computation. This proceedings volume describes the properties of quantum coherence in semiconductor spin-based systems and the behavior of quantum coherence in superconducting systems.

Single-Atom Nanoelectronics covers the fabrication of single-atom devices and related technology, as well as the relevant electronic equipment and the intriguing new phenomena related to single-atom and single-electron effects in quantum devices. It also covers the alternative approaches related to both silicon- and carbon-based technologies, also

The finding of algorithms for factoring and data base search that promise substantially increased computational power, as well as the expectation for efficient simulation of quantum systems have spawned an intense interest in the realization of quantum information processors [1]. Solid state implementations of quantum computers scaled to>1000 quantum bits ('qubits') promise to revolutionize information technology, but requirements with regard to sources of decoherence in solid state environments are sobering. Here, we briefly review basic approaches to impurity spin based qubits and present progress in our effort to form prototype qubit test structures. Since Kane's bold silicon based spin qubit proposal was first published in 1998 [2], several groups have taken up the challenge of fabricating elementary building blocks [3-5], and several exciting variations of single donor qubit schemes have emerged [6]. Single donor atoms, e. g. {sup 31}P, are 'natural quantum dots' in a silicon matrix, and the spins of electrons and nuclei of individual donor atoms are attractive two level systems for encoding of quantum information. The coupling to the solid state environment is weak, so that decoherence times are long (hours for nuclear spins, and {approx}60 ms for electron spins of isolated P atoms in silicon [7]), while control over individual spins for one qubit operations becomes possible when individual qubits are aligned to electrodes that allow shifting of electron spin resonances in global magnetic fields by application of control voltages. Two qubit operations require an interaction that couples, and entangles qubits. The exchange interaction, J, is a prime candidate for mediation of two qubit operations, since it can be turned on and off by variation of the wave function overlap between neighboring qubits, and coherent manipulation of quantum information with the exchange interaction alone has been shown to be universal [8]. However, detailed band structure calculations and theoretical analysis of J coupling between electrons bound to phosphorus atoms at low temperatures in silicon revealed strong oscillations of the coupling strength as a function of donor spacing on a sub-nm length scale [9]. These oscillations translate into scattering of interaction strength for ensembles of qubit spacings which in turn poses a serious obstacle to scalability [10]. Two alternatives to J coupling are dipolar coupling [11] and spin coherent shuttling of electrons between donor sites [12]. Readout of single electron spins poses another critical challenge [13, 14], and inferring spin orientations from charge measurements in spin dependent charge transfer reactions seems to be viable route to single shot single spin readout. This readout can be accomplished with single electron transistors, which are used as sensitive electrometers [15]. Impurity spin based qubit schemes in silicon have to overcome a significant nanofabrication challenge so that a test bed regime can be entered where fundamental properties and rudimentary operations can be investigated. In order to form such test devices, three key components have to be integrated: (1) an array of single dopant atoms has to be formed; (2) single dopant atoms are aligned to control gates; and (3) single dopant atoms are also aligned to a readout device.

A Si:P electron-spin qubit architecture was developed in 2008, based upon research outcomes over the four-year QCCM grant. Single-shot spin readout will proceed via spin-dependent tunneling to a Si MOS rf-SET, which we have demonstrated to posses charge sensitivities equal to or better than Al rf-SETs. Spin manipulation will occur using local electron-spin resonance (ESR), which we have used to observe hyperfine-split electron spin resonances in P-doped Si MOSFETs. This spin qubit concept has been incorporated into the bi-linear array quantum computer design developed in parallel over 2004-2008 by the theory programs, which was one of the first quantum computer architectures quantitatively analyzed for the fault-tolerant threshold. Preliminary measurements on ion-implanted spin qubit devices have demonstrated transfer of P-donor electrons to a Si-SET detector with a large signal of ~0.2e, while tunneling structures have enabled transport spectroscopy of singly occupied (D0) and doubly occupied (D- ) P-donor electron states. These measurements are strongly supported by the NEMO-TCAD program allowing donor species and position to be determined through transport spectroscopy. Single-ion implantation using on-chip PIN detectors now routinely produces Si:P devices with accurately positioned single donors, such as a 2-P-atom charge qubit device, in which electron transfer events and charge-state relaxation times have been measured. Using STM atom-scale lithography the narrowest conducting doped wires in silicon have been demonstrated and used to fabricate the first in-plane-gated dot architecture. Measurements of these dots highlight the stability of in-plane gates compared with top gates and provide a pathway to atomically precise single donor architectures. Ab-initio and self-consistent tight-binding approaches have made progress in describing the essential physics of these highlydoped nanostructures.

The Advanced School on Quantum Foundations and Open Quantum Systems was an exceptional combination of lectures. These comprise lectures in standard physics and investigations on the foundations of quantum physics.On the one hand it included lectures on quantum information, quantum open systems, quantum transport and quantum solid state. On the other hand it included lectures on quantum measurement, models for elementary particles, sub-quantum structures and aspects on the philosophy and principles of quantum physics.The special program of this school offered a broad outlook on the current and near future fundamental research in theoretical physics.The lectures are at the level of PhD students.