Waveguide-integrated silicon T centres.

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 T1 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.

Linear Hyperfine Tuning of Donor Spins in Silicon Using Hydrostatic Strain.

We experimentally study the coupling of group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts that are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains |ϵ|<10^{-5}. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semiquantitative agreement with the experimental values. Our results provide a framework for making quantitative predictions of donor spins in silicon nanostructures, such as those being used to develop silicon-based quantum processors and memories. The strong spin-strain coupling we measure (up to 150 GHz per strain, for Bi donors in Si) offers a method for donor spin tuning-shifting Bi donor electron spins by over a linewidth with a hydrostatic strain of order 10^{-6}-as well as opportunities for coupling to mechanical resonators.

Reaching the quantum limit of sensitivity in electron spin resonance.

The detection and characterization of paramagnetic species by electron spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology and materials science, from in vivo imaging to distance measurements in spin-labelled proteins. ESR relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession. However, such signals can be very small, prohibiting the application of ESR at the nanoscale (for example, at the single-cell level or on individual nanoparticles). Here, using a Josephson parametric microwave amplifier combined with high-quality-factor superconducting microresonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly four orders of magnitude. We demonstrate the detection of 1,700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise ratio, reduced to 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. The detection volume of our resonator is ∼ 0.02 nl, and our approach can be readily scaled down further to improve sensitivity, providing a new versatile toolbox for ESR at the nanoscale.

Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications.

The push for a semiconductor-based quantum information technology has renewed interest in the spin states and optical transitions of shallow donors in silicon, including the donor bound exciton transitions in the near-infrared and the Rydberg, or hydrogenic, transitions in the mid-infrared. The deepest group V donor in silicon, bismuth, has a large zero-field ground state hyperfine splitting, comparable to that of rubidium, upon which the now-ubiquitous rubidium atomic clock time standard is based. Here we show that the ground state hyperfine populations of bismuth can be read out using the mid-infrared Rydberg transitions, analogous to the optical readout of the rubidium ground state populations upon which rubidium clock technology is based. We further use these transitions to demonstrate strong population pumping by resonant excitation of the bound exciton transitions, suggesting several possible approaches to a solid-state atomic clock using bismuth in silicon, or eventually in enriched (28)Si.

Hybrid optical-electrical detection of donor electron spins with bound excitons in silicon.

Electrical detection of spins is an essential tool for understanding the dynamics of spins, with applications ranging from optoelectronics and spintronics, to quantum information processing. For electron spins bound to 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 donor electron spin resonance in an ensemble by transport through a silicon device, using optically driven donor-bound exciton transitions. We measure electron spin Rabi oscillations, and obtain long electron spin coherence times, limited only by the donor concentration. We also experimentally address critical issues such as non-resonant excitation, strain, and electric fields, laying the foundations for realizing a single-spin readout method with relaxed magnetic field and temperature requirements compared with spin-dependent tunnelling, enabling donor-based technologies such as quantum sensing.

Inductive measurement of optically hyperpolarized phosphorous donor nuclei in an isotopically enriched silicon-28 crystal.

We experimentally demonstrate the first 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 1.5×10(15) cm(-3), 3 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 (≈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-T2 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 T1 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 time scale of 4.5 h. Optical excitation was performed with a 1047 nm laser, which provided above-band-gap excitation of the silicon. The buildup of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the buildup at 1.7 K showed biexponential behavior with characteristic time constants of 578 and 5670 s.

Quantum information storage for over 180 s using donor spins in a 28Si "semiconductor vacuum".

A quantum computer requires systems that are isolated from their environment, but can be integrated into devices, and whose states can be measured with high accuracy. Nuclear spins in solids promise long coherence lifetimes, but they are difficult to initialize into known states and to detect with high sensitivity. We show how the distinctive optical properties of enriched (28)Si enable the use of hyperfine-resolved optical transitions, as previously applied to great effect for isolated atoms and ions in vacuum. Together with efficient Auger photoionization, these resolved hyperfine transitions permit rapid nuclear hyperpolarization and electrical spin-readout. We combine these techniques to detect nuclear magnetic resonance from dilute (31)P in the purest available sample of (28)Si, at concentrations inaccessible to conventional measurements, measuring a solid-state coherence time of over 180 seconds.

Hyperfine structure and nuclear hyperpolarization observed in the bound exciton luminescence of Bi donors in natural Si.

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 < or = I(z) < or = 9/2, are clearly observed. A strong hyperpolarization of the nuclear spin towards I(z) = -9/2 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.

Simultaneous subsecond hyperpolarization of the nuclear and electron spins of phosphorus in silicon by optical pumping of exciton transitions.

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.

Reduction of the linewidths of deep luminescence centers in 28Si reveals fingerprints of the isotope constituents.

Dramatic reductions of the linewidths of well-known deep centers in 28Si reveal "isotopic fingerprints" of the constituents. The approximately 1014 meV Cu center, thought to be either a Cu pair or an isolated Cu, is shown to contain four Cu atoms, and the approximately 780 meV Ag center is shown to contain four Ag. The approximately 944 meV ;{*}Cu center, thought to be a different configuration of a Cu pair, in fact contains three Cu and one Ag, and a new two-Cu two-Ag center is found. The approximately 735 meV center, previously assigned to Fe, actually contains Au and three Cu. This suggests a family of four-atom (Cu, Ag, Au) centers.

Optical detection and ionization of donors in specific electronic and nuclear spin States.

We resolve the remarkably sharp bound exciton transitions of highly enriched 28Si using a single-frequency laser and photoluminescence excitation spectroscopy, as well as photocurrent spectroscopy. Well-resolved doublets in the spectrum of the 31P donor reflect the hyperfine coupling of the electronic and nuclear donor spins. The optical detection of the nuclear spin state, and selective pumping and ionization of donors in specific electronic and nuclear spin states, suggests a number of new possibilities which could be useful for the realization of silicon-based quantum computers.

Temperature dependence of the energy gap of semiconductors in the low-temperature limit.

The temperature dependence of the electronic states and energy gaps of semiconductors is an old but still important experimental and theoretical topic. Remarkably, extant results do not clarify the asymptotic T-->0 behavior. Recent breakthroughs in the spectroscopy of enriched 28Si allow us to measure changes in the band gap over the liquid 4He temperature range with an astounding precision of one part in 10(8), revealing a T4.0+/-0.2 decrease with increasing T. This is in excellent agreement with a theoretical argument predicting an exponent of 4. This power law should apply, in the low temperature limit, to the temperature dependence of the energies of all electronic states in semiconductors and insulators.

Impurity absorption spectroscopy in 28Si: the importance of inhomogeneous isotope broadening.

We report high-resolution infrared absorption spectra of the neutral donors phosphorus and lithium, and the neutral acceptor boron, in isotopically pure 28Si crystals. Surprisingly, many of the transitions are much sharper than previously reported in natural Si. In particular, the 2p(0) line of phosphorus in 28Si has a full width at half maximum of only 4.2 microeV, about 5 times less than the narrowest 2p(0) line previously reported for natural Si, making it the narrowest shallow impurity transition yet observed. The widely held assumptions that the impurity transitions previously reported in high quality samples of natural Si revealed the true, homogeneous linewidths, are thus shown to be incorrect. The sharper transitions in 28Si also reveal new substructures in the boron and lithium spectra.

Origin of the residual acceptor ground-state splitting in silicon.

The residual ground-state splitting of acceptors in high-quality silicon has been studied intensely by different experimental techniques for several decades. Recently, photoluminescence studies of isotopically pure silicon revealed the ground-state splitting to result from the random distribution of isotopes in natural silicon. Here we present a new model that explains these surprising experimental results, and discuss the implications for acceptor ground-state splittings observed in other isotopically mixed semiconductors, as well as for the acceptor ground state in semiconductor alloys.

"Intrinsic" acceptor ground state splitting in silicon: an isotopic effect.

One of the oldest open questions in semiconductor physics is the origin of the small splittings of the neutral acceptor ground state in silicon which lead to a distribution of doublet splittings rather than the fourfold-degenerate state of Gamma(8) symmetry expected in the absence of perturbations. Here we show that these acceptor ground state splittings are absent in the photoluminescence spectra of acceptor bound excitons in isotopically purified 28Si, demonstrating conclusively the surprising result that the splittings previously observed in natural Si result from the randomness of the Si isotopic composition.