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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.

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.

The global quantum internet will require long-lived, telecommunications band photon-matter interfaces manufactured at scale. Preliminary quantum networks based upon photon-matter interfaces which meet a subset of these demands are encouraging efforts to identify new high-performance alternatives. Silicon is an ideal host for commercial-scale solid-state quantum technologies. It is already an advanced platform within the global integrated photonics and microelectronics industries, as well as host to record-setting long-lived spin qubits. Despite the overwhelming potential of the silicon quantum platform, the optical detection of individually addressable photon-spin interfaces in silicon has remained elusive. In this work we produce tens of thousands of individually addressable `$T$ centre' photon-spin qubits in integrated silicon photonic structures, and characterize their spin-dependent telecommunications-band optical transitions. These results unlock immediate opportunities to construct silicon-integrated, telecommunications-band quantum information networks., Comment: 25 pages, 10 figures

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

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

Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic $P$ -donor impurities in isotopically enriched $^{28}Si$ cooled below $10$ K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems., Comment: 7+3 pages, 6 figures, Added new phase diagram and detailed comparison with experiments

We use above-bandgap optical excitation, via a 1047 nm laser, to hyperpolarize the $^{31}$P spins in low-doped (N$_D =6\times10^{15}$ cm$^{-3}$) natural abundance silicon at 4.2 K and 6.7 T, and inductively detect the resulting NMR signal. The $30$ kHz spectral linewidth observed is dramatically larger than the 600 Hz linewidth observed from a $^{28}$Si-enriched silicon crystal. We show that the observed broadening is consistent with previous ENDOR results showing discrete isotope mass effect contributions to the donor hyperfine coupling. A secondary source of broadening is likely due to variations in the local strain, induced by the random distribution of different isotopes in natural silicon. The nuclear spin T$_1$ and the build-up time for the optically-induced $^{31}$P hyperpolarization in the natural abundance silicon sample were observed to be $178\pm47$ s and $69\pm6$ s respectively, significantly shorter than the values previously measured in $^{28}$Si-enriched samples under the same conditions. We also measured the T$_1$ and hyperpolarization build-up time for the $^{31}$P signal in natural abundance silicon at 9.4 T to be $54\pm31$ s and $13\pm2$ s respectively. The shorter build-up and nuclear spin T$_1$ times at high field are likely due to the shorter electron-spin T$_1$, which drives nuclear spin relaxation via non-secular hyperfine interactions. At 6.7 T, the phosphorus nuclear spin T$_{2}$ was measured to be $16.7\pm1.6$ ms at 4.2 K, a factor of 4 shorter than in $^{28}$Si-enriched crystals. This was observed to further shorten to $1.9\pm0.4$ ms in the presence of the infra-red laser., Comment: 5 pages

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

Donor spins in silicon are some of the most promising qubits for upcoming solid-state quantum technologies. The nuclear spins of phosphorus donors in enriched silicon have among the longest coherence times of any solid-state system as well as simultaneous qubit initialization, manipulation and readout fidelities near ~99.9%. Here we characterize the phosphorus in silicon system in the regime of "zero" magnetic field, where a singlet-triplet spin clock transition can be accessed, using laser spectroscopy and magnetic resonance methods. We show the system can be optically hyperpolarized and has ~10 s Hahn echo coherence times, even at Earth's magnetic field and below., Comment: 6 pages, 4 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 report pulsed electron-spin resonance (ESR) measurements on an ensemble of Bismuth donors in Silicon cooled at 10mK in a dilution refrigerator. Using a Josephson parametric microwave amplifier combined with high-quality factor superconducting micro-resonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly 4 orders of magnitude. We demonstrate the detection of 1700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise (SNR) ratio, reduced to just 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance., Comment: Main text : 10 pages, 4 figures. Supplementary text : 16 pages, 8 figures

Electrical detection of spins is an essential tool in understanding the dynamics of spins in semiconductor devices, providing valuable insights for applications ranging from optoelectronics and spintronics to quantum information processing. For electron spins bound to shallow donors in silicon, bulk electrically-detected magnetic resonance has relied on coupling to spin readout partners such as paramagnetic defects or conduction electrons which fundamentally limits spin coherence times. Here we demonstrate electrical detection of phosphorus donor electron spin resonance by transport through a silicon device, using optically-driven donor-bound exciton transitions. We use this method to measure electron spin Rabi oscillations, and, by avoiding use of an ancillary spin for readout, we are able to obtain long intrinsic electron spin coherence times, limited only by the donor concentration. We go on to experimentally address critical issues for adopting this scheme for single spin measurement in silicon nanodevices, including the effects of strain, electric fields, and non-resonant excitation. This lays the foundations for realising a versatile readout method for single spin readout with relaxed magnetic field and temperature requirements compared with spin-dependent tunneling., Comment: 13 pages, 4 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

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

We propose a novel optical and electrical hybrid scheme for the measurement of nuclear spin qubits in silicon. By combining the environmental insensitivity of the integer quantum Hall effect with the optically distinguishable hyperfine states of phosphorus impurities in silicon, our system can simultaneously offer nuclear spin measurement and robustness against environmental defects. 31P donor spins in isotopically purified 28Si are often discussed as very promising quantum memory qubits due to their extremely long decoherence times, and our proposed device offers an effective implementation for such a quantum memory system., Comment: 17 pages, 6 figures

The fourfold degeneracy of the boron acceptor ground state in silicon, which is easily lifted by any symmetry breaking perturbation, allows for a strong inhomogeneous broadening of the boron-related electron paramagnetic resonance (EPR) lines, e.g. by a random distribution of local strains. However, since EPR of boron acceptors in externally unstrained silicon was reported for the first time, neither the line shape nor the magnitude of the residual broadening observed in samples with high crystalline purity were compatible with the low concentrations of carbon and oxygen point defects, being the predominant source of random local strain. Adapting a theoretical model which has been applied to understand the acceptor ground state splitting in the absence of a magnetic field as an effect due to the presence of different silicon isotopes, we show that local fluctuations of the valence band edge due to different isotopic configurations in the vicinity of the boron acceptors can quantitatively account for all inhomogeneous broadening effects in high purity Si with a natural isotope composition. Our calculations show that such an isotopic perturbation also leads to a shift in the g-value of different boron-related resonances, which we could verify in our experiments. Further, our results provide an independent test and verification of the valence band offsets between the different Si isotopes determined in previous works., Comment: 26 pages (preprint), 9 figures

The electron paramagnetic resonance (EPR) linewidths of B acceptors in Si are found to reduce dramatically in isotopically purified 28Si single crystals. Moreover, extremely narrow substructures in the EPR spectra are visible corresponding to either an enhancement or a reduction of the absorbed microwave on resonance. The origin of the substructures is attributed to a combination of simultaneous double excitation and spin relaxation in the four level spin system of the acceptors. A spin population model is developed which qualitatively describes the experimental results., Comment: 4 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