There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

/pdf/spins-in-few-electron-quantum-dots-27qv5vqmqp.pdf

Spins in few-electron quantum dots

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future

Quantum Computing

An object is to provide a semiconductor device of which a manufacturing process is not complicated and by which cost can be suppressed, by forming a thin film transistor using an oxide semiconductor film typified by zinc oxide, and a manufacturing method thereof. For the semiconductor device, a gate electrode is formed over a substrate; a gate insulating film is formed covering the gate electrode; an oxide semiconductor film is formed over the gate insulating film; and a first conductive film and a second conductive film are formed over the oxide semiconductor film. The oxide semiconductor film has at least a crystallized region in a channel region.

Semiconductor device, and manufacturing method thereof

International Technology Roadmap for Semiconductors 2003の要求清浄度について － シリコンウエハ表面と雰囲気環境に要求される清浄度, 分析方法の現状について －

We demonstrate the controlled incorporation of P dopant atoms in Si(001), presenting a new path toward the creation of atomic-scale electronic devices. We present a detailed study of the interaction of ${\mathrm{P}\mathrm{H}}_{3}$ with Si(001) and show that it is possible to thermally incorporate P atoms into Si(001) below the H-desorption temperature. Control over the precise spatial location at which P atoms are incorporated was achieved using STM H lithography. We demonstrate the positioning of single P atoms in Si with $\ensuremath{\sim}1\text{ }\text{ }\mathrm{n}\mathrm{m}$ accuracy and the creation of nanometer wide lines of incorporated P atoms.

https://arxiv.org/pdf/cond-mat/0307599.pdf

Atomically precise placement of single dopants in si.

Solid-state quantum computer architectures with qubits encoded using single atoms are now feasible given recent advances in the atomic doping of semiconductors. Here we present a charge qubit consisting of two dopant atoms in a semiconductor crystal, one of which is singly ionized. Surface electrodes control the qubit and a radio-frequency single-electron transistor provides fast readout. The calculated single gate times, of order 50 ps or less, are much shorter than the expected decoherence time. We propose universal one- and two-qubit gate operations for this system and discuss prospects for fabrication and scale up.

/pdf/charge-based-quantum-computing-using-single-donors-in-t4vtho47w6.pdf

Charge-based quantum computing using single donors in semiconductors

We report the fabrication and measurement of silicon quantum dots with tunable tunnel barriers in a narrow-channel field-effect transistor. Low-temperature transport spectroscopy is performed in both the many-electron (∼100 electrons) regime and the few-electron (∼10 electrons) regime. Excited states in the bias spectroscopy provide evidence of quantum confinement. These results demonstrate that depletion gates are an effective technique for defining quantum dots in silicon.

Gate-defined quantum dots in intrinsic silicon.

We demonstrate a method for the controlled implantation of single ions into a silicon substrate with energy of sub-20‐keV The method is based on the collection of electron-hole pairs generated in the substrate by the impact of a single ion We have used the method to implant single 14‐keV P31 ions through nanoscale masks into silicon as a route to the fabrication of devices based on single donors in silicon

Controlled shallow single ion implantation in silicon using an active substrate for sub-20 keV ions

The quest to build a quantum computer has been inspired by the recognition of the formidable computational power such a device could offer. In particular silicon-based proposals, using the nuclear or electron spin of dopants as qubits, are attractive due to the long spin relaxation times involved, their scalability, and the ease of integration with existing silicon technology. Fabrication of such devices, however, requires atomic scale manipulation --- an immense technological challenge. We demonstrate that it is possible to fabricate an atomically precise linear array of single phosphorus bearing molecules on a silicon surface with the required dimensions for the fabrication of a silicon-based quantum computer. We also discuss strategies for the encapsulation of these phosphorus atoms by subsequent silicon crystal growth.

https://arxiv.org/pdf/cond-mat/0104569.pdf

R. G. Clark

Papers

Atomically precise placement of single dopants in si.

Charge-based quantum computing using single donors in semiconductors

Gate-defined quantum dots in intrinsic silicon.

Controlled shallow single ion implantation in silicon using an active substrate for sub-20 keV ions

Towards the fabrication of phosphorus qubits for a silicon quantum computer