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Quantum systems with engineered Hamiltonians can be used as simulators of many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for quantum simulation of generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium 4$\times$2 quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively-coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays., Comment: 15 pages and 13 figures

Charge noise in the host semiconductor degrades the performance of spin-qubits and poses an obstacle to control large quantum processors. However, it is challenging to engineer the heterogeneous material stack of gate-defined quantum dots to improve charge noise systematically. Here, we address the semiconductor-dielectric interface and the buried quantum well of a $^{28}$Si/SiGe heterostructure and show the connection between charge noise, measured locally in quantum dots, and global disorder in the host semiconductor, measured with macroscopic Hall bars. In 5 nm thick $^{28}$Si quantum wells, we find that improvements in the scattering properties and uniformity of the two-dimensional electron gas over a 100 mm wafer correspond to a significant reduction in charge noise, with a minimum value of 0.29$\pm$0.02 $\mu$eV/sqrt(Hz) at 1 Hz averaged over several quantum dots. We extrapolate the measured charge noise to simulated dephasing times to cz-gate fidelities that improve nearly one order of magnitude. These results point to a clean and quiet crystalline environment for integrating long-lived and high-fidelity spin qubits into a larger system.

Coherent links between qubits separated by tens of micrometers are expected to facilitate scalable quantum computing architectures for spin qubits in electrically-defined quantum dots. These links create space for classical on-chip control electronics between qubit arrays, which can help to alleviate the so-called wiring bottleneck. A promising method of achieving coherent links between distant spin qubits consists of shuttling the spin through an array of quantum dots. Here, we use a linear array of four tunnel-coupled quantum dots in a 28Si/SiGe heterostructure to create a short quantum link. We move an electron spin through the quantum dot array by adjusting the electrochemical potential for each quantum dot sequentially. By pulsing the gates repeatedly, we shuttle an electron forward and backward through the array up to 250 times, which corresponds to a total distance of approximately 80 {\mu}m. We make an estimate of the spin-flip probability per hop in these experiments and conclude that this is well below 0.01% per hop., Comment: 11 pages, 3 main figures, 6 appendix figures

The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-$\text{S}^{-1}$ gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can preserve the state of the data qubit by applying a refocusing pulse to the ancilla qubit. In addition, we implement a phase flip code on three qubits, making use of a Toffoli-like gate for the final correction step. Both the quality and quantity of the qubits will require significant improvement to achieve fault-tolerance. However, the capability to implement quantum error correction codes enables co-design development of quantum hardware and software, where codes tailored to the properties of spin qubits and advances in fabrication and operation can now come together to scale semiconductor quantum technology toward universal quantum computers., Comment: 8 pages, 4 figures

We demonstrate a 36$\times$36 gate electrode crossbar that supports 648 narrow-channel field effect transistors (FET) for gate-defined quantum dots, with a quadratic increase in quantum dot count upon a linear increase in control lines. The crossbar is fabricated on an industrial $^{28}$Si-MOS stack and shows 100% FET yield at cryogenic temperature. We observe a decreasing threshold voltage for wider channel devices and obtain a normal distribution of pinch-off voltages for nominally identical tunnel barriers probed over 1296 gate crossings. Macroscopically across the crossbar, we measure an average pinch-off of 1.17~V with a standard deviation of 46.8 mV, while local differences within each unit cell indicate a standard deviation of 23.1~mV. These disorder potential landscape variations translate to 1.2 and 0.6 times the measured quantum dot charging energy, respectively. Such metrics provide means for material and device optimization and serve as guidelines in the design of large-scale architectures for fault-tolerant semiconductor-based quantum computing.

We design, fabricate, and study a hole bilayer in a strained germanium double quantum well. Magnetotransport characterisation of double quantum well field-effect transistors as a function of gate voltage reveals the population of two hole channels with a high combined mobility of 3.34$\times$10$^5$ cm$^2$/Vs and a low percolation density of 2.38$\times$10$^{10}$ cm$^{-2}$. We resolve the individual population of the channels from the interference patterns of the Landau fan diagram. At a density of 2.0$\times$10$^{11}$ cm$^{-2}$ the system is in resonance and we observe an anti-crossing of the first two bilayer subbands characterized by a symmetric-antisymmetric gap of $\sim$0.69 meV, in agreement with Schr\"odinger-Poisson simulations.

We demonstrate that a lightly-strained germanium channel ($\varepsilon_{//}$ = -0.41%) in an undoped Ge/Si$_{0.1}$Ge$_{0.9}$ heterostructure field effect transistor supports a 2D hole gas with mobility in excess of 1$\times$10$^{6}$ cm$^{2}$/Vs and percolation density less than 5$\times$10$^{10}$ cm$^{-2}$. This low disorder 2D hole system shows tunable fractional quantum Hall effect at low density and low magnetic field. The low-disorder and small effective mass (0.068$m_e$) defines lightly-strained germanium as a basis to tune the strength of the spin-orbit coupling for fast and coherent quantum hardware.

We determine the energy splitting of the conduction-band valleys in two-dimensional (2D) electrons confined in silicon metal oxide semiconductor (Si-MOS) Hall-bar transistors. These Si-MOS Hall bars are made by advanced semiconductor manufacturing on 300 mm Si wafers and support a 2D electron gas of high quality with a maximum mobility of 17.6$\times$10$^3$cm$^2$/Vs and minimum percolation density of 3.45$\times$10$^{10}$cm$^{-2}$. Because of the low disorder, we observe beatings in the Shubnikov-de Haas oscillations that arise from the energy-split two low-lying conduction band valleys. From the analysis of the oscillations beating patterns up to T = 1.7 K, we estimate a maximum valley splitting of 8.2 meV at a density of 6.8$\times$10$^{12}$cm$^{-2}$. Furthermore, the valley splitting increases with density at a rate consistent with theoretical predictions for a near-ideal semiconductor/oxide interface.

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbour pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology., Comment: Main text 9 pages, 3 figures. Supp Info 21 pages, 7 figures, 8 tables

Single-charge pumps are the main candidates for quantum-based standards of the unit ampere because they can generate accurate and quantized electric currents. In order to approach the metrological requirements in terms of both accuracy and speed of operation, in the past decade there has been a focus on semiconductor-based devices. The use of a variety of semiconductor materials enables the universality of charge pump devices to be tested, a highly desirable demonstration for metrology, with GaAs and Si pumps at the forefront of these tests. Here, we show that pumping can be achieved in a yet unexplored semiconductor, i.e. germanium. We realise a single-hole pump with a tunable-barrier quantum dot electrostatically defined at a Ge/SiGe heterostructure interface. We observe quantized current plateaux by driving the system with a single sinusoidal drive up to a frequency of 100 MHz. The operation of the prototype was affected by accidental formation of multiple dots, probably due to disorder potential, and random charge fluctuations. We suggest straightforward refinements of the fabrication process to improve pump characteristics in future experiments., Comment: 7 pages, 4 figures

Full-scale quantum computers require the integration of millions of quantum bits. The promise of leveraging industrial semiconductor manufacturing to meet this requirement has fueled the pursuit of quantum computing in silicon quantum dots. However, to date, their fabrication has relied on electron-beam lithography and, with few exceptions, on academic style lift-off processes. Although these fabrication techniques offer process flexibility, they suffer from low yield and poor uniformity. An important question is whether the processing conditions developed in the manufacturing fab environment to enable high yield, throughput, and uniformity of transistors are suitable for quantum dot arrays and do not compromise the delicate qubit properties. Here, we demonstrate quantum dots hosted at a 28Si/28SiO2 interface, fabricated in a 300 mm semiconductor manufacturing facility using all-optical lithography and fully industrial processing. As a result, we achieve nanoscale gate patterns with remarkable homogeneity. The quantum dots are well-behaved in the multi-electron regime, with excellent tunnel barrier control, a crucial feature for fault-tolerant two-qubit gates. Single-spin qubit operation using magnetic resonance reveals relaxation times of over 1 s at 1 Tesla and coherence times of over 3 ms, matching the quality of silicon spin qubits reported to date. The feasibility of high-quality qubits made with fully-industrial techniques strongly enhances the prospects of a large-scale quantum computer, Comment: 23 pages, 4 figures, 12 supplementary figures

The prospect of building quantum circuits using advanced semiconductor manufacturing positions quantum dots as an attractive platform for quantum information processing. Extensive studies on various materials have led to demonstrations of two-qubit logic in gallium arsenide, silicon, and germanium. However, interconnecting larger numbers of qubits in semiconductor devices has remained an outstanding challenge. Here, we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable coupling along both directions. Qubit logic is implemented all-electrically and the exchange interaction can be pulsed to freely program one-qubit, two-qubit, three-qubit, and four-qubit operations, resulting in a compact and high-connectivity circuit. We execute a quantum logic circuit that generates a four-qubit Greenberger-Horne-Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are an important step towards quantum error correction and quantum simulation with quantum dots., Comment: 7 pages, 5 figures, supplementary materials with 11 figures and 2 tables in separate file

Quantum dots fabricated using techniques and materials that are compatible with semiconductor manufacturing are promising for quantum information processing. While great progress has been made toward high-fidelity control of quantum dots positioned in a linear arrangement, scalability along two dimensions is a key step toward practical quantum information processing. Here we demonstrate a two-dimensional quantum dot array where each quantum dot is tuned to single-charge occupancy, verified by simultaneous measuring with two integrated radio frequency charge sensors. We achieve this by using planar germanium quantum dots with low disorder and small effective mass, allowing the incorporation of dedicated barrier gates to control the coupling of the quantum dots. We demonstrate hole charge filling consistent with a Fock-Darwin spectrum and show that we can tune single-hole quantum dots from isolated quantum dots to strongly exchange coupled quantum dots. These results motivate the use of planar germanium quantum dots as building blocks for quantum simulation and computation., Comment: 7 pages, 4 figures

We engineer planar Ge/SiGe heterostructures for low disorder and quiet hole quantum dot operation by positioning the strained Ge channel 55~nm below the semiconductor/dielectric interface. In heterostructure field effect transistors, we measure a percolation density for two-dimensional hole transport of $2.1\times10^{10}~\text{cm}^{-2}$, indicative of a very low disorder potential landscape experienced by holes in the buried Ge channel. These Ge heterostructures support quiet operation of hole quantum dots and we measure charge noise levels that are below the detection limit $\sqrt{S_\text{E}}=0.2~\mu \text{eV}/\sqrt{\text{Hz}}$ at 1 Hz. These results establish planar Ge as a promising platform for scaled two-dimensional spin qubit arrays.

We investigate hole spin relaxation in the single- and multi-hole regime in a 2x2 germanium quantum dot array. We use radiofrequency (rf) charge sensing and observe Pauli Spin-Blockade (PSB) for every second interdot transition up to the (1,5)-(0,6) anticrossing, consistent with a standard Fock-Darwin spectrum. We find spin relaxation times $T_1$ as high as 32 ms for a quantum dot with single-hole occupation and 1.2 ms for a quantum dot occupied by five-holes, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate the qubit addressability and sensitivity to electric fields by measuring the resonance frequency dependence of each qubit on gate voltages. We are able to tune the resonance frequency over a large range for both the single and multi-hole qubit. Simultaneously, we find that the resonance frequencies are only weakly dependent on neighbouring gates, and in particular the five-hole qubit resonance frequency is more than twenty times as sensitive to its corresponding plunger gate. The excellent individual qubit tunability and long spin relaxation times make holes in germanium promising for addressable and high-fidelity spin qubits in dense two-dimensional quantum dot arrays for large-scale quantum information., Comment: 7 Pages (6 Main + 1 Supplementary Information) 5 Figures (4 Main, 1 Supplementary Information)

Solid-state qubits integrated on semiconductor substrates currently require at least one wire from every qubit to the control electronics, leading to a so-called wiring bottleneck for scaling. Demultiplexing via on-chip circuitry offers an effective strategy to overcome this bottleneck. In the case of gate-defined quantum dot arrays, specific static voltages need to be applied to many gates simultaneously to realize electron confinement. When a charge-locking structure is placed between the quantum device and the demultiplexer, the voltage can be maintained locally. In this study, we implement a switched-capacitor circuit for charge-locking and use it to float the plunger gate of a single quantum dot. Parallel plate capacitors, transistors and quantum dot devices are monolithically fabricated on a Si/SiGe-based substrate to avoid complex off-chip routing. We experimentally study the effects of the capacitor and transistor size on the voltage accuracy of the floating node. Furthermore, we demonstrate that the electrochemical potential of the quantum dot can follow a 100 Hz pulse signal while the dot is partially floating, which is essential for applying this strategy in qubit experiments.

Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their inherent compatibility with standard semiconductor manufacturing. While early on it was recognized that holes may offer a multitude of favourable properties for fast and scalable quantum control, research thus far has remained almost exclusively restricted to the simpler electron system. However, recent developments with holes have led to separate demonstrations of single-shot readout and fast quantum logic, albeit only in the multi-hole regime. Here, we establish a single-hole spin qubit in germanium and demonstrate the integration of single-shot readout and quantum control. Moreover, we make use of Pauli spin blockade, allowing to arbitrarily set the qubit resonance frequency, while providing large readout windows. We deplete a planar germanium double quantum dot to the last hole, confirmed by radio-frequency reflectrometry charge sensing, and achieve single-shot spin readout. To demonstrate the integration of the readout and qubit operation, we show Rabi driving on both qubits and find remarkable electric control over their resonance frequencies. Finally, we analyse the spin relaxation time, which we find to exceed one millisecond, setting the benchmark for hole-based spin qubits. The ability to coherently manipulate a single hole spin underpins the quality of strained germanium and defines an excellent starting point for the construction of novel quantum hardware., Comment: 6 pages, 4 figures

Electrons and holes confined in quantum dots define an excellent building block for quantum emergence, simulation, and computation. In order for quantum electronics to become practical, large numbers of quantum dots will be required, necessitating the fabrication of scaled structures such as linear and 2D arrays. Group IV semiconductors contain stable isotopes with zero nuclear spin and can thereby serve as excellent host for spins with long quantum coherence. Here we demonstrate group IV quantum dot arrays in silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe) and strained germanium (Ge/SiGe). We fabricate using a multi-layer technique to achieve tightly confined quantum dots and compare integration processes. While SiMOS can benefit from a larger temperature budget and Ge/SiGe can make ohmic contact to metals, the overlapping gate structure to define the quantum dots can be based on a nearly identical integration. We realize charge sensing in each platform, for the first time in Ge/SiGe, and demonstrate fully functional linear and two-dimensional arrays where all quantum dots can be depleted to the last charge state. In Si/SiGe, we tune a quintuple quantum dot using the N+1 method to simultaneously reach the few electron regime for each quantum dot. We compare capacitive cross talk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. These results constitute an excellent base for quantum computation with quantum dots and provide opportunities for each platform to be integrated with standard semiconductor manufacturing., Comment: Main text: 8 pages, 6 figures. Supporting Info: 5 pages, 3 figures

Continuing advancements in quantum information processing have caused a paradigm shift from research mainly focused on testing the reality of quantum mechanics to engineering qubit devices with numbers required for practical quantum computation. One of the major challenges in scaling toward large-scale solid-state systems is the limited input/output (I/O) connectors present in cryostats operating at sub-kelvin temperatures required to execute quantum logic with high-fidelity. This interconnect bottleneck is equally present in the device fabrication-measurement cycle, which requires high-throughput and cryogenic characterization to develop quantum processors. Here we multiplex quantum transport of two-dimensional electron gases at sub-kelvin temperatures. We use commercial off-the-shelf CMOS multiplexers to achieve an order of magnitude increase in the number of wires. Exploiting this technology we advance 300 mm epitaxial wafers manufactured in an industrial CMOS fab to a record electron mobility of (3.9$\pm$0.6)$\times$10$^5$ cm$^2$\slash Vs and percolation density of (6.9$\pm$0.4)$\times$10$^{10}$ cm$^{-2}$, representing a key step toward large silicon qubit arrays. We envision that the demonstration will inspire the development of cryogenic electronics for quantum information and because of the simplicity of assembly, low-cost, yet versatility, we foresee widespread use of similar cryo-CMOS circuits for high-throughput quantum measurements and control of quantum engineered systems.

We report density-dependent effective hole mass measurements in undoped germanium quantum wells. We are able to span a large range of densities ($2.0-11\times10^{11}$ cm$^{-2}$) in top-gated field effect transistors by positioning the strained buried Ge channel at different depths of 12 and 44 nm from the surface. From the thermal damping of the amplitude of Shubnikov-de Haas oscillations, we measure a light mass of $0.061m_e$ at a density of $2.2\times10^{11}$ cm$^{-2}$. We confirm the theoretically predicted dependence of increasing mass with density and by extrapolation we find an effective mass of $\sim0.05m_e$ at zero density, the lightest effective mass for a planar platform that demonstrated spin qubits in quantum dots.

The promise of quantum computation with quantum dots has stimulated widespread research. Still, a platform that can combine excellent control with fast and high-fidelity operation is absent. Here, we show single and two-qubit operations based on holes in germanium. A high degree of control over the tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder and by working in a virtual gate space. Spin-orbit coupling obviates the need for microscopic elements and enables rapid qubit control with Rabi frequencies exceeding 100 MHz and a single-qubit fidelity of 99.3 %. We demonstrate fast two-qubit CX gates executed within 75 ns and minimize decoherence by operating at the charge symmetry point. Planar germanium thus matured within one year from a material that can host quantum dots to a platform enabling two-qubit logic, positioning itself as a unique material to scale up spin qubits for quantum information., Comment: 6 pages, 5 figures

Silicon spin qubits form one of the leading platforms for quantum computation. As with any qubit implementation, a crucial requirement is the ability to measure individual quantum states rapidly and with high fidelity. As the signal from a single electron spin is minute, different spin states are converted to different charge states. Charge detection so far mostly relied on external electrometers, which hinders scaling to two-dimensional spin qubit arrays. As an alternative, gate-based dispersive read-out based on off-chip lumped element resonators were introduced, but here integration times of 0.2 to 2 ms were required to achieve single-shot read-out. Here we connect an on-chip superconducting resonant circuit to two of the gates that confine electrons in a double quantum dot. Measurement of the power transmitted through a feedline coupled to the resonator probes the charge susceptibility, distinguishing whether or not an electron can oscillate between the dots in response to the probe power. With this approach, we achieve a signal-to-noise ratio (SNR) of about six within an integration time of only 1 $\mu$s. Using Pauli's exclusion principle for spin-to-charge conversion, we demonstrate single-shot read-out of a two-electron spin state with an average fidelity of $>$98% in 6 $\mu$s. This result may form the basis of frequency multiplexed read-out in dense spin qubit systems without external electrometers, therefore simplifying the system architecture., Comment: 5 pages, 3 figures

We investigate the structural and quantum transport properties of isotopically enriched $^{28}$Si/$^{28}$SiO$_2$ stacks deposited on 300 mm Si wafers in an industrial CMOS fab. Highly uniform films are obtained with an isotopic purity greater than 99.92\%. Hall-bar transistors with an equivalent oxide thickness of 17 nm are fabricated in an academic cleanroom. A critical density for conduction of $1.75\times10^{11}$ cm$^{-2}$ and a peak mobility of 9800 cm$^2$/Vs are measured at a temperature of 1.7 K. The $^{28}$Si/$^{28}$SiO$_2$ interface is characterized by a roughness of $\Delta=0.4$ nm and a correlation length of $\Lambda=3.4$ nm. An upper bound for valley splitting energy of 480 $\mu$eV is estimated at an effective electric field of 9.5 MV/m. These results support the use of wafer-scale $^{28}$Si/$^{28}$SiO$_2$ as a promising material platform to manufacture industrial spin qubits., Comment: 5 pages, 3 figures

Buried-channel semiconductor heterostructures are an archetype material platform to fabricate gated semiconductor quantum devices. Sharp confinement potential is obtained by positioning the channel near the surface, however nearby surface states degrade the electrical properties of the starting material. In this paper we demonstrate a two-dimensional hole gas of high mobility ($5\times 10^{5}$ cm$^2$/Vs) in a very shallow strained germanium channel, which is located only 22 nm below the surface. This high mobility leads to mean free paths $\approx6 \mu m$, setting new benchmarks for holes in shallow FET devices. Carriers are confined in an undoped Ge/SiGe heterostructure with reduced background contamination, sharp interfaces, and high uniformity. The top-gate of a dopant-less field effect transistor controls the carrier density in the channel. The high mobility, along with a percolation density of $1.2\times 10^{11}\text{ cm}^{-2}$, light effective mass (0.09 m$_e$), and high g-factor (up to $7$) highlight the potential of undoped Ge/SiGe as a low-disorder material platform for hybrid quantum technologies.

We fabricate Josephson field-effect-transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a transparent interface, confirmed by analyzing the excess current. These demonstrations of ballistic superconducting transport are promising for hybrid quantum technology in germanium.

Superconductors and semiconductors are crucial platforms in the field of quantum computing. They can be combined to hybrids, bringing together physical properties that enable the discovery of new emergent phenomena and provide novel strategies for quantum control. The involved semiconductor materials, however, suffer from disorder, hyperfine interactions or lack of planar technology. Here we realise an approach that overcomes these issues altogether and integrate gate-defined quantum dots and superconductivity into a material system with strong spin-orbit coupling. In our germanium heterostructures, heavy holes with mobilities exceeding 500,000 cm$^2$/Vs are confined in shallow quantum wells that are directly contacted by annealed aluminium leads. We demonstrate gate-tunable superconductivity and find a characteristic voltage $I_cR_n$ that exceeds 10 $\mu$V. Germanium therefore has great promise for fast and coherent quantum hardware and, being compatible with standard manufacturing, could become a leading material in the quantum revolution., Comment: 7 pages, 5 figures

We report the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot and the microwave photon is stored in an on-chip high-impedance superconducting resonator. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet. This result opens the way to the realization of large networks of quantum dot based spin qubit registers, removing a major roadblock to scalable quantum computing with spin qubits.

Extending chip performance beyond current limits of miniaturisation requires new materials and functionalities that integrate well with the silicon platform. Germanium fits these requirements and has been proposed as a high-mobility channel material,[1] a light emitting medium in silicon-integrated lasers,[2,3] and a plasmonic conductor for bio-sensing.[4,5] Common to these diverse applications is the need for homogeneous, high electron densities in three-dimensions (3D). Here we use a bottom-up approach to demonstrate the 3D assembly of atomically sharp doping profiles in germanium by a repeated stacking of two-dimensional (2D) high-density phosphorus layers. This produces high-density (10^19 to 10^20 cm-3) low-resistivity (10^-4 Ohmcm) metallic germanium of precisely defined thickness, beyond the capabilities of diffusion-based doping technologies.[6] We demonstrate that free electrons from distinct 2D dopant layers coalesce into a homogeneous 3D conductor using anisotropic quantum interference measurements, atom probe tomography, and density functional theory.

We report experimental evidence of a remarkable spontaneous time reversal symmetry breaking in two dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P $\delta-$layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two dimensional electrons are confined to narrow half-filled impurity bands.

In this paper we demonstrate atomic-scale lithography on hydrogen terminated Ge(001. The lithographic patterns were obtained by selectively desorbing hydrogen atoms from a H resist layer adsorbed on a clean, atomically flat Ge(001) surface with a scanning tunneling microscope tip operating in ultra-high vacuum. The influence of the tip-to-sample bias on the lithographic process have been investigated. Lithographic patterns with feature-sizes from 200 nm to 1.8 nm have been achieved by varying the tip-to-sample bias. These results open up the possibility of a scanning-probe lithography approach to the fabrication of future atomic-scale devices in germanium.

We present a systematic study of the influence of the encapsulation temperature on dopant confinement and electrical properties of Ge:P delta-doped layers. For increasing growth temperature we observe an enhancement of the electrical properties accompanied by an increased segregation of the phosphorous donors, resulting in a slight broadening of the delta-layer. We demonstrate that a step-flow growth achieved at 530 C provides the best compromise between high crystal quality and minimal dopant redistribution, with an electron mobility ~ 128 cm^2/Vs at a carrier density 1.3x10^14 cm-2, and a 4.2 K phase coherence length of ~ 180 nm., Comment: Phys. Rev. B, in press (2009)

Phosphorus (P) in germanium (Ge) delta-doped layers are fabricated in ultra-high vacuum by adsorption of phosphine molecules onto an atomically flat clean Ge(001) surface followed by thermal incorporation of P into the lattice and epitaxial Ge overgrowth by molecular beam epitaxy. Structural and electrical characterizations show that P atoms are confined, with minimal diffusion, into an ultra-narrow 2-nm-wide layer with an electrically-active sheet carrier concentration of 4x10^13 cm-2 at 4.2 K. These results open up the possibility of ultra-narrow source/drain regions with unprecedented carrier densities for Ge n-channel field effect transistors.

We report on the fabrication and electronic transport characterisation of Schottky-gated strongly confined Si/SiGe quantum point contacts (QPC). At zero magnetic field and T=450mK the QPC conductance as a function of gate voltage shows a quantization in units of e^2/h, indicative of transport through 1D modes which appear to lack both spin and valley degeneracy., Comment: 2 pages, 2 figure, to be published in Proc. ICPS-28

We fabricated strongly confined Schottky-gated quantum point contacts by etching Si/SiGe heterostructures and observed intriguing conductance quantization in units of approximately 1e2/h. Non-linear conductance measurements were performed depleting the quantum point contacts at fixed mode-energy separation. We report evidences of the formation of a half 1e2/h plateau, supporting the speculation that adiabatic transmission occurs through 1D modes with complete removal of valley and spin degeneracies., Comment: to appear in Physical Review B

Low field magnetotransport revealing signatures of ballistic transport effects in strained Si/SiGe cavities is investigated. We fabricated strained Si/SiGe cavities by confining a high mobility Si/SiGe 2DEG in a bended nanowire geometry defined by electron-beam lithography and reactive ion etching. The main features observed in the low temperature magnetoresistance curves are the presence of a zero-field magnetoresistance peak and of an oscillatory structure at low fields. By adopting a simple geometrical model we explain the oscillatory structure in terms of electron magnetic focusing. A detailed examination of the zero-field peak lineshape clearly shows deviations from the predictions of ballistic weak localization theory., Comment: Submitted to Physical Review B, 25 pages, 7 figures