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Carbon implantation at the nanoscale is highly desired for the engineering of defect-based qubits in a variety of materials, including silicon, diamond, SiC and hBN. However, the lack of focused carbon ion beams does not allow for the full disclosure of their potential for application in quantum technologies. Here, we develop and use a carbon source for focused ion beams for the simultaneous creation of two types of quantum emitters in silicon, the W and G centers. Furthermore, we apply a multi-step implantation protocol for the programmable activation of the G centers with sub-100- nm resolution. This approach provides a route for significant enhancement of the creation yield of single G centers in carbon-free silicon wafers. Our experimental demonstration is an important step towards nanoscale engineering of telecom quantum emitters in silicon of high crystalline quality and isotope purity., Comment: 7 pages, 5 figures

The performance of modular, networked quantum technologies will be strongly dependent upon the quality of their quantum light-matter interconnects. Solid-state colour centres, and in particular T centres in silicon, offer competitive technological and commercial advantages as the basis for quantum networking technologies and distributed quantum computing. These newly rediscovered silicon defects offer direct telecommunications-band photonic emission, long-lived electron and nuclear spin qubits, and proven native integration into industry-standard, CMOS-compatible, silicon-on-insulator (SOI) photonic chips at scale. Here we demonstrate further levels of integration by characterizing T centre spin ensembles in single-mode waveguides in SOI. In addition to measuring long spin T_1 times, we report on the integrated centres' optical properties. We find that the narrow homogeneous linewidth of these waveguide-integrated emitters is already sufficiently low to predict the future success of remote spin-entangling protocols with only modest cavity Purcell enhancements. We show that further improvements may still be possible by measuring nearly lifetime-limited homogeneous linewidths in isotopically pure bulk crystals. In each case the measured linewidths are more than an order of magnitude lower than previously reported and further support the view that high-performance, large-scale distributed quantum technologies based upon T centres in silicon may be attainable in the near term.

A highly promising route to scale millions of qubits is to use quantum photonic integrated circuits (PICs), where deterministic photon sources, reconfigurable optical elements, and single-photon detectors are monolithically integrated on the same silicon chip. The isolation of single-photon emitters, such as the G centers and W centers, in the optical telecommunication O-band, has recently been realized in silicon. In all previous cases, however, single-photon emitters were created uncontrollably in random locations, preventing their scalability. Here, we report the controllable fabrication of single G and W centers in silicon wafers using focused ion beams (FIB) with a probability exceeding 50%. We also implement a scalable, broad-beam implantation protocol compatible with the complementary-metal-oxide-semiconductor (CMOS) technology to fabricate single telecom emitters at desired positions on the nanoscale. Our findings unlock a clear and easily exploitable pathway for industrial-scale photonic quantum processors with technology nodes below 100 nm., Comment: 8 pages, 4 figures

Silicon spin qubits promise to leverage the extraordinary progress in silicon nanoelectronic device fabrication over the past half century to deliver large-scale quantum processors. Despite the scalability advantage of using silicon technology, realising a quantum computer with the millions of qubits required to run some of the most demanding quantum algorithms poses several outstanding challenges, including how to control so many qubits simultaneously. Recently, compact 3D microwave dielectric resonators were proposed as a way to deliver the magnetic fields for spin qubit control across an entire quantum chip using only a single microwave source. Although spin resonance of individual electrons in the globally applied microwave field was demonstrated, the spins were controlled incoherently. Here we report coherent Rabi oscillations of single electron spin qubits in a planar SiMOS quantum dot device using a global magnetic field generated off-chip. The observation of coherent qubit control driven by a dielectric resonator establishes a credible pathway to achieving large-scale control in a spin-based quantum computer.

Silicon is host to two separate leading quantum technology platforms: integrated silicon photonics as well as long-lived spin qubits. There is an ongoing search for the ideal photon-spin interface able to hybridize these two approaches into a single silicon platform offering substantially expanded capabilities. A number of silicon defects are known to have spin-selective optical transitions, although very few of these are known to be in the highly desirable telecommunications bands, and those that do often do not couple strongly to light. Here we characterize the T center in silicon, a highly stable silicon defect which supports a short-lived bound exciton that upon recombination emits light in the telecommunications O-band. In this first study of T centers in $^{28}$Si, we present the temperature dependence of the zero phonon line, report ensemble zero phonon linewidths as narrow as 33(2) MHz, and elucidate the excited state spectrum of the bound exciton. Magneto-photoluminescence, in conjunction with magnetic resonance, is used to observe twelve distinct orientational subsets of the T center, which are independently addressable due to the anisotropic g factor of the bound exciton's hole spin. The T center is thus a promising contender for the hybridization of silicon's two leading quantum technology platforms., Comment: 13 pages, 10 figures

Long-distance entanglement distribution is a vital capability for quantum technologies. An outstanding practical milestone towards this aim is the identification of a suitable matter-photon interface which possesses, simultaneously, long coherence lifetimes and efficient telecommunications-band optical access. In this work, alongside its sister publication, we report upon the T center, a silicon defect with spin-selective optical transitions at 1326 nm in the telecommunications O-band. Here we show that the T center in $^{28}$Si offers electron and nuclear spin lifetimes beyond a millisecond and second respectively, as well as optical lifetimes of 0.94(1) $\mu$s and a Debye-Waller factor of 0.23(1). This work represents a significant step towards coherent photonic interconnects between long-lived silicon spins, spin-entangled telecom single-photon emitters, and spin-dependent silicon-integrated photonic nonlinearities for future global quantum technologies., Comment: 5 pages, 3 figures

Spin-orbit coupling fundamentally alters spin qubits, opening pathways to improve the scalability of quantum computers via long distance coupling mediated by electric fields, photons, or phonons. It also allows for new engineered hybrid and topological quantum systems. However, spin qubits with intrinsic spin-orbit coupling are not yet viable for quantum technologies due to their short ($\sim1~\mu$s) coherence times $T_2$, while qubits with long $T_2$ have weak spin-orbit coupling making qubit coupling short-ranged and challenging for scale-up. Here we show that an intrinsic spin-orbit coupled "generalised spin" with total angular momentum $J=\tfrac{3}{2}$, which is defined by holes bound to boron dopant atoms in strained $^{28}\mathrm{Si}$, has $T_2$ rivalling the electron spins of donors and quantum dots in $^{28}\mathrm{Si}$. Using pulsed electron paramagnetic resonance, we obtain $0.9~\mathrm{ms}$ Hahn-echo and $9~\mathrm{ms}$ dynamical decoupling $T_2$ times, where strain plays a key role to reduce spin-lattice relaxation and the longitudinal electric coupling responsible for decoherence induced by electric field noise. Our analysis shows that transverse electric dipole can be exploited for electric manipulation and qubit coupling while maintaining a weak longitudinal coupling, a feature of $J=\tfrac{3}{2}$ atomic systems with a strain engineered quadrupole degree of freedom. These results establish single-atom hole spins in silicon with quantised total angular momentum, not spin, as a highly coherent platform with tuneable intrinsic spin-orbit coupling advantageous to build artificial quantum systems and couple qubits over long distances., Comment: 14 pages, 4 figures + 13 pages, 5 figures of Supplemental material

Luminescence and optical absorption due to radiation damage centers in silicon has been studied exhaustively for decades, but is receiving new interest for applications as emitters for integrated silicon photonic technologies. While a variety of other optical transitions have been found to be much sharper in enriched $^{28}$Si than in natural Si, due to the elimination of inhomogeneous isotopic broadening, this has not yet been investigated for radiation damage centers. We report results for the well-known G, W and C damage centers in highly enriched $^{28}$Si, with optical linewidth improvements in some cases of over two orders of magnitude, revealing previously hidden fine structure in the G center emission and absorption. These results have direct implications for the linewidths to be expected from single center emission, even in natural Si, and for models for the G center structure. The advantages of $^{28}$Si can be readily extended to the study of other radiation damage centers in Si., Comment: 8 pages, 6 figures

We demonstrate that CPMG and XYXY decoupling sequences with non-ideal $\pi$ pulses can reduce dipolar interactions between spins of the same species in solids. Our simulations of pulsed electron spin resonance (ESR) experiments show that $\pi$ rotations with small ($<$~10\%) imperfections refocus instantaneous diffusion. Here, the intractable N-body problem of interacting dipoles is approximated by the average evolution of a single spin in a changing mean field. These calculations agree well with experiments and do not require powerful hardware. Our results add to past attempts to explain similar phenomena in solid state nuclear magnetic resonance (NMR). Although the fundamental physics of NMR are similar to ESR, the larger linewidths in ESR and stronger dipolar interactions between electron spins compared to nuclear spins preclude drawing conclusions from NMR studies alone. For bulk spins, we also find that using XYXY results in less inflation of the deduced echo decay times as compared to decays obtained with CPMG., Comment: 10 pages, 5 figures

We achieve the strong coupling regime between an ensemble of phosphorus donor spins in a highly enriched $^{28}$Si crystal and a 3D dielectric resonator. Spins were polarized beyond Boltzmann equilibrium using spin selective optical excitation of the no-phonon bound exciton transition resulting in $N$ = $3.6\cdot10^{13}$ unpaired spins in the ensemble. We observed a normal mode splitting of the spin ensemble-cavity polariton resonances of 2$g\sqrt{N}$ = 580 kHz (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75,000 ($\gamma \ll \kappa \approx$ 60 kHz where $\gamma$ and $\kappa$ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time (T$_2^*$ = 9 $\mu$s) providing a wide window for viewing the dynamics of the coupled spin ensemble-cavity system. The free induction decay shows up to a dozen collapses and revivals revealing a coherent exchange of excitations between the superradiant state of the spin ensemble and the cavity at the rate $g\sqrt{N}$. The ensemble is found to evolve as a single large pseudospin according to the Tavis-Cummings model due to minimal inhomogeneous broadening and uniform spin-cavity coupling. We demonstrate independent control of the total spin and the initial Z-projection of the psuedospin using optical excitation and microwave manipulation respectively. We vary the microwave excitation power to rotate the pseudospin on the Bloch sphere and observe a long delay in the onset of the superradiant emission as the pseudospin approaches full inversion. This delay is accompanied by an abrupt $\pi$ phase shift in the peusdospin microwave emission. The scaling of this delay with the initial angle and the sudden phase shift are explained by the Tavis-Cummings model., Comment: 9 pages, 7 figures

We present a complete theoretical treatment of Stark effects in doped silicon, whose predictions are supported by experimental measurements. A multi-valley effective mass theory, dealing non-perturbatively with valley-orbit interactions induced by a donor-dependent central cell potential, allows us to obtain a very reliable picture of the donor wave function within a relatively simple framework. Variational optimization of the 1s donor binding energies calculated with a new trial wave function, in a pseudopotential with two fitting parameters, allows an accurate match of the experimentally determined donor energy levels, while the correct limiting behavior for the electronic density, both close to and far from each impurity nucleus, is captured by fitting the measured contact hyperfine coupling between the donor nuclear and electron spin. We go on to include an external uniform electric field in order to model Stark physics: With no extra ad hoc parameters, variational minimization of the complete donor ground energy allows a quantitative description of the field-induced reduction of electronic density at each impurity nucleus. Detailed comparisons with experimental values for the shifts of the contact hyperfine coupling reveal very close agreement for all the donors measured (P, As, Sb and Bi). Finally, we estimate field ionization thresholds for the donor ground states, thus setting upper limits to the gate manipulation times for single qubit operations in Kane-like architectures: the Si:Bi system is shown to allow for A gates as fast as around 10 MHz., Comment: 11 pages, 6 figures

The effects of host isotope mass on the hyperfine interaction of group-V donors in silicon are revealed by pulsed electron nuclear double resonance (ENDOR) spectroscopy of isotopically engineered Si single crystals. Each of the hyperfine-split P-31, As-75, Sb-121, Sb-123, and Bi-209 ENDOR lines splits further into multiple components, whose relative intensities accurately match the statistical likelihood of the nine possible average Si masses in the four nearest-neighbor sites due to random occupation by the three stable isotopes Si-28, Si-29, and Si-30. Further investigation with P-31 donors shows that the resolved ENDOR components shift linearly with the bulk-averaged Si mass., Comment: 5 pages, 4 figures, 1 table

We experimentally demonstrate the inductive readout of optically hyperpolarized phosphorus-31 donor nuclear spins in an isotopically enriched silicon-28 crystal. The concentration of phosphorus donors in the crystal was 1.5 x 10$^{15}$ cm$^{-3}$, three orders of magnitude lower than has previously been detected via direct inductive detection. The signal-to-noise ratio measured in a single free induction decay from a 1 cm$^3$ sample ($\approx 10^{15}$ spins) was 113. By transferring the sample to an X-band ESR spectrometer, we were able to obtain a lower bound for the nuclear spin polarization at 1.7 K of 64 %. The $^{31}$P-T$_{2}$ measured with a Hahn echo sequence was 420 ms at 1.7 K, which was extended to 1.2 s with a Carr Purcell cycle. The T$_1$ of the $^{31}$P nuclear spins at 1.7 K is extremely long and could not be determined, as no decay was observed even on a timescale of 4.5 hours. Optical excitation was performed with a 1047 nm laser, which provided above bandgap excitation of the silicon. The build-up of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the build-up at 1.7 K showed bi-exponential behavior with characteristic time constants of 578 s and 5670 s., Comment: 8 pages, 6 figures

We prove the theorem mentioned in the title, for ${\mathbb{R}}^n$, where $n \ge 3$. The case of the simplex was known previously. Also, the case $n=2$ was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolic $n$-spaces. There we give some necessary conditions for the existence of a convex polytope with given facet areas, and some partial results about sufficient conditions for the existence of (convex) tetrahedra., Comment: 42 pages, small corrections and additions, the final version

The electron and nuclear spins of the shallow donor 31P are promising qubit candidates invoked in many proposed Si-based quantum computing schemes. We have recently shown that the near-elimination of inhomogeneous broadening in highly isotopically enriched 28Si enables an optical readout of both the donor electron and nuclear spins by resolving the donor hyperfine splitting in the near-gap donor bound exciton transitions. We have also shown that pumping these same transitions can very quickly produce large electron and nuclear hyperpolarizations at low magnetic fields, where the equilibrium electron and nuclear polarizations are very small. Here we show preliminary results of the measurement of 31P neutral donor NMR parameters using this optical nuclear hyperpolarization mechanism for preparation of the 31P nuclear spin system, followed by optical readout of the resulting nuclear spin population after manipulation with NMR pulse sequences. This allows for the observation of single-shot NMR signals with very high signal to noise ratio under conditions where conventional NMR is not possible, due to the low concentration of 31P and the small equilibrium polarization., Comment: Invited Presentation at ICPS-30 (2010), Seoul, Korea

Donors in silicon hold considerable promise for emerging quantum technologies, due to the their uniquely long electron spin coherence times. Bi donors in silicon differ from P and other Group V donors in several significant respects: they have the strongest binding energy (70.98 meV), a large nuclear spin (I = 9/2) and strong hyperfine coupling constant (A = 1475.4 MHz). These larger energy scales allow a detailed test of theoretical models describing the spectral diffusion mechanism that is known to govern the electron spin coherence time (T2e) of P-donors in natural silicon. We report the electron nuclear double resonance spectra of the Bi donor, across the range 200 MHz to 1.4 GHz, and confirm that coherence transfer is possible between electron and nuclear spin degrees of freedom at these higher frequencies., Comment: 4 pages, 4 figures, plus supporting information 2 pages, 3 figures

As the deepest group V donor in Si, Bi has by far the largest hyperfine interaction, and also a large I=9/2 nuclear spin. At zero field this splits the donor ground state into states having total spin 5 and 4, which are fully resolved in the photoluminescence spectrum of Bi donor bound excitons. Under a magnetic field, the 60 expected allowed transitions cannot be individually resolved, but the effects of the nuclear spin distribution, -9/2 <= I_z <= 9/2, are clearly observed. A strong hyperpolarization of the nuclear spin, with sign opposite to the expected equilibrium polarization, is observed to result from the nonresonant optical excitation. This is very similar to the recently reported optical hyperpolarization of P donors observed by EPR at higher magnetic fields. We introduce a new model to explain this effect, and predict that it may be very fast., Comment: 4 pages, 3 figures, 1 table

We demonstrate a method which can hyperpolarize both the electron and nuclear spins of 31P donors in Si at low field, where both would be essentially unpolarized in equilibrium. It is based on the selective ionization of donors in a specific hyperfine state by optically pumping donor bound exciton hyperfine transitions, which can be spectrally resolved in 28Si. Electron and nuclear polarizations of 90% and 76%, respectively, are obtained in less than a second, providing an initialization mechanism for qubits based on these spins, and enabling further ESR and NMR studies on dilute 31P in 28Si., Comment: 4 pages, 3 figures

The concept of a gamma-ray telescope based on a Laue lens offers the possibility to increase the sensitivity by more than an order of magnitude with respect to existing instruments. Laue lenses have been developed by our collaboration for several years : the main achievement of this R&D program was the CLAIRE lens prototype. Since then, the endeavour has been oriented towards the development of efficient diffracting elements (crystal slabs), the aim being to step from a technological Laue lens to a scientifically exploitable lens. The latest mission concept featuring a gamma-ray lens is the European Gamma-Ray Imager (GRI) which intends to make use of the Laue lens to cover energies from 200 keV to 1300 keV. Investigations of two promising materials, low mosaicity copper and gradient concentration silicon-germanium are presented in this paper. The measurements have been performed during three runs on beamline ID15A of the European Synchrotron Radiation Facility, and on the GAMS 4 instrument of the Institute Laue-Langevin (both in Grenoble, France) using highly monochromatic beam of energy close to 500 keV. Despite it was not perfectly homogeneous, the presented copper crystal exhibits peak reflectivity of 25% in accordance with theoretical predictions, and a mosaicity around 26 arcsec, the ideal range for the realization of a Laue lens such as GRI. Silicon-germanium featuring a constant gradient have been measured for the very first time at 500 keV. Two samples showed a quite homogeneous reflectivity reaching 26%, which is far from the 48% already observed in experimental crystals but a very encouraging beginning. This results have been used to estimate the performance of the GRI Laue lens design.