Electron spin coherence exceeding seconds in high-purity silicon

Coherent Erbium Spin Defects in Colloidal Nanocrystal Hosts

We demonstrate nearly a microsecond of spin coherence in Er3+ ions doped in cerium dioxide nanocrystal hosts, despite a large gyromagnetic ratio and nanometric proximity of the spin defect to the nanocrystal surface. The long spin coherence is enabled by reducing the dopant density below the instantaneous diffusion limit in a nuclear spin-free host material, reaching the limit of a single erbium spin defect per nanocrystal. We observe a large Orbach energy in a highly symmetric cubic site, further protecting the coherence in a qubit that would otherwise rapidly decohere. Spatially correlated electron spectroscopy measurements reveal the presence of Ce3+ at the nanocrystal surface, which likely acts as extraneous paramagnetic spin noise. Even with these factors, defect-embedded nanocrystal hosts show tremendous promise for quantum sensing and quantum communication applications, with multiple avenues, including core-shell fabrication, redox tuning of oxygen vacancies, and organic surfactant modification, available to further enhance their spin coherence and functionality in the future.

Deconvoluting Monomer- and Dimer-Specific Distance Distributions between Spin Labels in a Monomer/Dimer Mixture Using T1-Edited DEER EPR Spectroscopy

Double electron-electron resonance (DEER) EPR is a powerful tool in structural biology, providing distances between pairs of spin labels. When the sample consists of a mixture of oligomeric species (e.g., monomer and dimer), the question arises as to how to assign the peaks in the DEER-derived probability distance distribution to the individual species. Here, we propose incorporating an EPR longitudinal electron relaxation (T1) inversion recovery experiment within a DEER pulse sequence to resolve this problem. The apparent T1 between dipolar coupled electron spins measured from the inversion recovery time (τinv) dependence of the peak intensities in the T1-edited DEER-derived probability P(r) distance distribution will be affected by the number of nitroxide labels attached to the biomolecule of interest, for example, two for a monomer and four for a dimer. We show that global fitting of all the T1-edited DEER echo curves, recorded over a range of τinv values, permits the deconvolution of distances between spin labels originating from monomeric (longer T1) and dimeric (shorter T1) species. This is especially useful when the trapping of spin labels in different conformational states during freezing gives rise to complex P(r) distance distributions. The utility of this approach is demonstrated for two systems, the β1 adrenergic receptor and a construct of the huntingtin exon-1 protein fused to the immunoglobulin domain of protein G, both of which exist in a monomer-dimer equilibrium.

Electron Spin-Lattice Relaxation of Substitutional Nitrogen in Silicon: The Role of Disorder and Motional Effects

In a previous investigation, the authors proposed nitrogen as a possible candidate for exploiting the donor spin in silicon quantum devices. This system is characterized by a ground state deeper than the other group V impurities in silicon, offering less stringent requirements on the device temperature necessary to access the unionized state. The nitrogen donor is slightly displaced from the substitutional site, and upon heating, the system undergoes a motional transition. In the present article, we show the results from our investigation on the spin-relaxation times in natSi and 28Si substrates and discuss the motional effects on relaxation. The stretched exponential relaxation observed is interpreted as a distribution of spin-lattice relaxation times, whose origin is also discussed. This information greatly contributes to the assessment of a nitrogen-doped silicon system as a potential candidate for quantum devices working at temperatures higher than those required for other group V donors in silicon.

Microwave Fluorescence Detection of Spin Echoes

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.

Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100  G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Dielectrics for Two-Dimensional Transition-Metal Dichalcogenide Applications

Despite over a decade of intense research efforts, the full potential of two-dimensional transition-metal dichalcogenides continues to be limited by major challenges. The lack of compatible and scalable dielectric materials and integration techniques restrict device performances and their commercial applications. Conventional dielectric integration techniques for bulk semiconductors are difficult to adapt for atomically thin two-dimensional materials. This review provides a brief introduction into various common and emerging dielectric synthesis and integration techniques and discusses their applicability for 2D transition metal dichalcogenides. Dielectric integration for various applications is reviewed in subsequent sections including nanoelectronics, optoelectronics, flexible electronics, valleytronics, biosensing, quantum information processing, and quantum sensing. For each application, we introduce basic device working principles, discuss the specific dielectric requirements, review current progress, present key challenges, and offer insights into future prospects and opportunities.

Individually addressable and spectrally programmable artificial atoms in silicon photonics

A central goal for quantum technologies is to develop platforms for precise and scalable control of individually addressable artificial atoms with efficient optical interfaces. Color centers in silicon, such as the recently-isolated carbon-related G-center, exhibit emission directly into the telecommunications O-band and can leverage the maturity of silicon-on-insulator photonics. We demonstrate the generation, individual addressing, and spectral trimming of G-center artificial atoms in a silicon-on-insulator photonic integrated circuit platform. Focusing on the neutral charge state emission at 1278 nm, we observe waveguide-coupled single photon emission with narrow inhomogeneous distribution with standard deviation of 1.1 nm, excited state lifetime of 8.3 ± 0.7 ns, and no degradation after over a month of operation. In addition, we introduce a technique for optical trimming of spectral transitions up to 300 pm (55 GHz) and local deactivation of single artificial atoms. This non-volatile spectral programming enables alignment of quantum emitters into 25 GHz telecommunication grid channels. Our demonstration opens the path to quantum information processing based on implantable artificial atoms in very large scale integrated photonics.

VdW Mediated Strong Magnetic Exchange Interactions in Chains of Hydrogen-Free Sublimable Molecular Qubits

Sulfur-rich molecular complexes of dithiolene-like ligands are appealing candidates as molecular spin qubits because spin coherence properties are enhanced in hydrogen-free environments. Herein, we employ the hydrogen-free mononegative 1,3,2-dithiazole-4-thione-5-thiolate (dttt^-) ligand as an alternative to common dinegative dithiolate ligands. We report the first synthesis and structural characterization of its Cu²⁺, Ni²⁺, and Pt²⁺ neutral complexes. The XPS analysis of thermal deposition of [Cu(dttt)₂] in UHV conditions indicates that films of intact molecules can be deposited on surfaces by sublimation. Thanks to a combined approach employing DC magnetometry and DFT calculations, we highlighted AF exchange interactions of 108 cm^-1 and 36 cm^-1 attributed to the two different polymorph phases. These couplings are exclusively mediated by S···S VdW interactions, which are facilitated by the absence of counterions and made particularly efficient by the diffuse electron density on S atoms. Furthermore, the spin dynamics of solid-state magnetically diluted samples was investigated. The longest observed T _m is 2.3 μs at 30 K, which significantly diverges from the predicted T _m > 100 μs. These results point to the diluting matrix severely affecting the coherence lifetime of Cu²⁺ species via different factors, such as the contributions of neighboring ¹⁴N nuclei and the formation of radical impurities in a non-completely controllable way. However, the ease of processing [Cu(dttt)₂] via thermal sublimation can allow dispersion in matrices better suited for coherent spin manipulation of isolated molecules and the realization of AF-coupled VdW structures on surfaces.

Probing many-body dynamics in a two-dimensional dipolar spin ensemble

The most direct approach for characterizing the quantum dynamics of a strongly interacting system is to measure the time evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate approach is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Here we investigate what the decoherence dynamics of such a probe tells us about the many-body system. In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in nitrogen delta-doped diamond: nitrogen-vacancy colour centres, which we use as probe spins, and a many-body ensemble of substitutional nitrogen impurities. We demonstrate that the many-body system's dimensionality, dynamics and disorder are naturally encoded in the probe spins' decoherence profile. Furthermore, we obtain direct control over the spectral properties of the many-body system, with potential applications in quantum sensing and simulation.

Universal logic with encoded spin qubits in silicon

Quantum computation features known examples of hardware acceleration for certain problems, but is challenging to realize because of its susceptibility to small errors from noise or imperfect control. The principles of fault tolerance may enable computational acceleration with imperfect hardware, but they place strict requirements on the character and correlation of errors1. For many qubit technologies2-21, some challenges to achieving fault tolerance can be traced to correlated errors arising from the need to control qubits by injecting microwave energy matching qubit resonances. Here we demonstrate an alternative approach to quantum computation that uses energy-degenerate encoded qubit states controlled by nearest-neighbour contact interactions that partially swap the spin states of electrons with those of their neighbours. Calibrated sequences of such partial swaps, implemented using only voltage pulses, allow universal quantum control while bypassing microwave-associated correlated error sources1,22-28. We use an array of six 28Si/SiGe quantum dots, built using a platform that is capable of extending in two dimensions following processes used in conventional microelectronics29. We quantify the operational fidelity of universal control of two encoded qubits using interleaved randomized benchmarking30, finding a fidelity of 96.3% ± 0.7% for encoded controlled NOT operations and 99.3% ± 0.5% for encoded SWAP. The quantum coherence offered by enriched silicon5-9,16,18,20,22,27,29,31-37, the all-electrical and low-crosstalk-control of partial swap operations1,22-28 and the configurable insensitivity of our encoding to certain error sources28,33,34,38 all combine to offer a strong pathway towards scalable fault tolerance and computational advantage.

Long-lived electronic spin qubits in single-walled carbon nanotubes

Electron spins in solid-state systems offer the promise of spin-based information processing devices. Single-walled carbon nanotubes (SWCNTs), an all-carbon one-dimensional material whose spin-free environment and weak spin-orbit coupling promise long spin coherence times, offer a diverse degree of freedom for extended range of functionality not available to bulk systems. A key requirement limiting spin qubit implementation in SWCNTs is disciplined confinement of isolated spins. Here, we report the creation of highly confined electron spins in SWCNTs via a bottom-up approach. The record long coherence time of 8.2 µs and spin-lattice relaxation time of 13 ms of these electronic spin qubits allow demonstration of quantum control operation manifested as Rabi oscillation. Investigation of the decoherence mechanism reveals an intrinsic coherence time of tens of milliseconds. These findings evident that combining molecular approaches with inorganic crystalline systems provides a powerful route for reproducible and scalable quantum materials suitable for qubit applications.

An electrically driven single-atom "flip-flop" qubit

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.

Room Temperature Incorporation of Arsenic Atoms into the Germanium (001) Surface

Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focused on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH₃ ) on the germanium (001) surface. We show that, unlike any previously studied dopant precursor on silicon or germanium, arsenic atoms fully incorporate into substitutional surface lattice sites at room temperature. Our results pave the way for the next generation of atomic-scale donor devices combining the superior electronic properties of germanium with the enhanced properties of arsine/germanium chemistry that promises scale-up to large numbers of deterministically placed qubits.

Coherence protection of spin qubits in hexagonal boron nitride

Spin defects in foils of hexagonal boron nitride are an attractive platform for magnetic field imaging, since the probe can be placed in close proximity to the target. However, as a III-V material the electron spin coherence is limited by the nuclear spin environment, with spin echo coherence times of ∽100 ns at room temperature accessible magnetic fields. We use a strong continuous microwave drive with a modulation in order to stabilize a Rabi oscillation, extending the coherence time up to ∽ 4μs, which is close to the 10 μs electron spin lifetime in our sample. We then define a protected qubit basis, and show full control of the protected qubit. The coherence times of a superposition of the protected qubit can be as high as 0.8 μs. This work establishes that boron vacancies in hexagonal boron nitride can have electron spin coherence times that are competitive with typical nitrogen vacancy centres in small nanodiamonds under ambient conditions.

Probing Methyl Group Tunneling in [(CH3)2NH2][Zn(HCOO)3] Hybrid Perovskite Using Co2+ EPR

At low temperature, methyl groups act as hindered quantum rotors exhibiting rotational quantum tunneling, which is highly sensitive to a local methyl group environment. Recently, we observed this effect using pulsed electron paramagnetic resonance (EPR) in two dimethylammonium-containing hybrid perovskites doped with paramagnetic Mn²⁺ ions. Here, we investigate the feasibility of using an alternative fast-relaxing Co²⁺ paramagnetic center to study the methyl group tunneling, and, as a model compound, we use dimethylammonium zinc formate [(CH₃)₂NH₂][Zn(HCOO)₃] hybrid perovskite. Our multifrequency (X-, Q- and W-band) EPR experiments reveal a high-spin state of the incorporated Co²⁺ center, which exhibits fast spin-lattice relaxation and electron spin decoherence. Our pulsed EPR experiments reveal magnetic field independent electron spin echo envelope modulation (ESEEM) signals, which are assigned to the methyl group tunneling. We use density operator simulations to extract the tunnel frequency of 1.84 MHz from the experimental data, which is then used to calculate the rotational barrier of the methyl groups. We compare our results with the previously reported Mn²⁺ case showing that our approach can detect very small changes in the local methyl group environment in hybrid perovskites and related materials.

Near-Surface ^{125}Te^{+} Spins with Millisecond Coherence Lifetime

Impurity spins in crystal matrices are promising components in quantum technologies, particularly if they can maintain their spin properties when close to surfaces and material interfaces. Here, we investigate an attractive candidate for microwave-domain applications, the spins of group-VI ^{125}Te^{+} donors implanted into natural Si at depths as shallow as 20 nm. We show that surface band bending can be used to ionize such near-surface Te to spin-active Te^{+} state, and that optical illumination can be used further to control the Te donor charge state. We examine spin activation yield, spin linewidth, and relaxation (T_{1}) and coherence times (T_{2}) and show how a zero-field 3.5 GHz "clock transition" extends spin coherence times to over 1 ms, which is about an order of magnitude longer than other near-surface spin systems.

Harnessing many-body spin environment for long coherence storage and high-fidelity single-shot qubit readout

There is a growing interest in hybrid solid-state quantum systems where nuclear spins, interfaced to the electron spin qubit, are used as quantum memory or qubit register. These approaches require long nuclear spin coherence, which until now seemed impossible owing to the disruptive effect of the electron spin. Here we study InGaAs semiconductor quantum dots, demonstrating millisecond-long collective nuclear spin coherence even under inhomogeneous coupling to the electron central spin. We show that the underlying decoherence mechanism is spectral diffusion induced by a fluctuating electron spin. These results provide new understanding of the many-body coherence in central spin systems, required for development of electron-nuclear spin qubits. As a demonstration, we implement a conditional gate that encodes electron spin state onto collective nuclear spin coherence, and use it for a single-shot readout of the electron spin qubit with >99% fidelity.

Optical observation of single spins in silicon

The global quantum internet will require long-lived, telecommunications-band photon-matter interfaces manufactured at scale¹. Preliminary quantum networks based on photon-matter interfaces that meet a subset of these demands are encouraging efforts to identify new high-performance alternatives². 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 qubits³. 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 integrate individually addressable 'T centre' photon-spin qubits in 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.

Microwave-Frequency Scanning Gate Microscopy of a Si/SiGe Double Quantum Dot

Conventional transport methods provide quantitative information on spin, orbital, and valley states in quantum dots but lack spatial resolution. Scanning tunneling microscopy, on the other hand, provides exquisite spatial resolution at the expense of speed. Working to combine the spatial resolution and energy sensitivity of scanning probe microscopy with the speed of microwave measurements, we couple a metallic tip to a Si/SiGe double quantum dot (DQD) that is integrated with a charge detector. We first demonstrate that the dc-biased tip can be used to change the occupancy of the DQD. We then apply microwaves through the tip to drive photon-assisted tunneling (PAT). We infer the DQD level diagram from the frequency and detuning dependence of the tunneling resonances. These measurements allow the resolution of ∼65 μeV excited states, an energy consistent with valley splittings in Si/SiGe. This work demonstrates the feasibility of scanning gate experiments with Si/SiGe devices.

Optical Entanglement of Distinguishable Quantum Emitters

Solid-state quantum emitters are promising candidates for the realization of quantum networks, owing to their long-lived spin memories, high-fidelity local operations, and optical connectivity for long-range entanglement. However, due to differences in local environment, solid-state emitters typically feature a range of distinct transition frequencies, which makes it challenging to create optically mediated entanglement between arbitrary emitter pairs. We propose and demonstrate an efficient method for entangling emitters with optical transitions separated by many linewidths. In our approach, electro-optic modulators enable a single photon to herald a parity measurement on a pair of spin qubits. We experimentally demonstrate the protocol using two silicon-vacancy centers in a diamond nanophotonic cavity, with optical transitions separated by 7.4 GHz. Working with distinguishable emitters allows for individual qubit addressing and readout, enabling parallel control and entanglement of both colocated and spatially separated emitters, a key step toward scaling up quantum information processing systems.

Two-qubit silicon quantum processor with operation fidelity exceeding 99

Silicon spin qubits satisfy the necessary criteria for quantum information processing. However, a demonstration of high-fidelity state preparation and readout combined with high-fidelity single- and two-qubit gates, all of which must be present for quantum error correction, has been lacking. We use a two-qubit Si/SiGe quantum processor to demonstrate state preparation and readout with fidelity greater than 97%, combined with both single- and two-qubit control fidelities exceeding 99%. The operation of the quantum processor is quantitatively characterized using gate set tomography and randomized benchmarking. Our results highlight the potential of silicon spin qubits to become a dominant technology in the development of intermediate-scale quantum processors.

Coherent Spin Preparation of Indium Donor Qubits in Single ZnO Nanowires

Shallow donors in ZnO are promising candidates for photon-mediated quantum technologies. Utilizing the indium donor, we show that favorable donor-bound exciton optical and electron spin properties are retained in isolated ZnO nanowires. The inhomogeneous optical line width of single nanowires (60 GHz) is within a factor of 2 of bulk single-crystalline ZnO. Spin initialization via optical pumping is demonstrated and coherent population trapping is observed. The two-photon absorption width approaches the theoretical limit expected due to the hyperfine interaction between the indium nuclear spin and the donor-bound electron.

Giant Isotope Effect of Thermal Conductivity in Silicon Nanowires

Isotopically purified semiconductors potentially dissipate heat better than their natural, isotopically mixed counterparts as they have higher thermal conductivity (κ). But the benefit is low for Si at room temperature, amounting to only ∼10% higher κ for bulk ^{28}Si than for bulk natural Si (^{nat}Si). We show that in stark contrast to this bulk behavior, ^{28}Si (99.92% enriched) nanowires have up to 150% higher κ than ^{nat}Si nanowires with similar diameters and surface morphology. Using a first-principles phonon dispersion model, this giant isotope effect is attributed to a mutual enhancement of isotope scattering and surface scattering of phonons in ^{nat}Si nanowires, correlated via transmission of phonons to the native amorphous SiO_{2} shell. The Letter discovers the strongest isotope effect of κ at room temperature among all materials reported to date and inspires potential applications of isotopically enriched semiconductors in microelectronics.

Five-second coherence of a single spin with single-shot readout in silicon carbide

An outstanding hurdle for defect spin qubits in silicon carbide (SiC) is single-shot readout, a deterministic measurement of the quantum state. Here, we demonstrate single-shot readout of single defects in SiC via spin-to-charge conversion, whereby the defect's spin state is mapped onto a long-lived charge state. With this technique, we achieve over 80% readout fidelity without pre- or postselection, resulting in a high signal-to-noise ratio that enables us to measure long spin coherence times. Combined with pulsed dynamical decoupling sequences in an isotopically purified host material, we report single-spin T₂ > 5 seconds, over two orders of magnitude greater than previously reported in this system. The mapping of these coherent spin states onto single charges unlocks both single-shot readout for scalable quantum nodes and opportunities for electrical readout via integration with semiconductor devices.

Twenty-three-millisecond electron spin coherence of erbium ions in a natural-abundance crystal

Erbium ions embedded in crystals have unique properties for quantum information processing, because of their optical transition at 1.5 μm and of the large magnetic moment of their effective spin-1/2 electronic ground state. Most applications of erbium require, however, long electron spin coherence times, and this has so far been missing. Here, by selecting a host matrix with a low nuclear-spin density (CaWO₄) and by quenching the spectral diffusion due to residual paramagnetic impurities at millikelvin temperatures, we obtain a 23-ms coherence time on the Er³⁺ electron spin transition. This is the longest Hahn echo electron spin coherence time measured in a material with a natural abundance of nuclear spins and on a magnetically sensitive transition. Our results establish Er³⁺:CaWO₄ as a potential platform for quantum networks.

Detecting spins by their fluorescence with a microwave photon counter

Quantum emitters respond to resonant illumination by radiating part of the absorbed energy. A component of this radiation field is phase coherent with the driving tone, whereas another component is incoherent and consists of spontaneously emitted photons, forming the fluorescence signal¹. Atoms, molecules and colour centres are routinely detected by their fluorescence at optical frequencies, with important applications in quantum technology^2,3 and microscopy^4-7. By contrast, electron spins are usually detected by the phase-coherent echoes that they emit in response to microwave driving pulses⁸. The incoherent part of their radiation-a stream of microwave photons spontaneously emitted upon individual spin relaxation events-has not been observed so far because of the low spin radiative decay rate and of the lack of single microwave photon detectors (SMPDs). Here using superconducting quantum devices, we demonstrate the detection of a small ensemble of donor spins in silicon by their fluorescence at microwave frequencies and millikelvin temperatures. We enhance their radiative decay rate by coupling them to a high-quality-factor and small-mode-volume superconducting resonator⁹, and we connect the device output to a newly developed SMPD¹⁰ based on a superconducting qubit. In addition, we show that the SMPD can be used to detect spin echoes and that standard spin characterization measurements (Rabi nutation and spectroscopy) can be achieved with both echo and fluorescence detection. We discuss the potential of SMPD detection as a method for magnetic resonance spectroscopy of small numbers of spins.

Coherent Spin Control of Single Molecules on a Surface

Control of single electron spins constitutes one of the most promising platforms for spintronics, quantum sensing, and quantum information processing. Utilizing single molecular magnets as their hosts establishes an interesting framework since their molecular structure is highly flexible and chemistry-based large-scale synthesis directly provides a way toward scalability. Here, we demonstrate coherent spin manipulation of single molecules on a surface, which we control individually using a scanning tunneling microscope in combination with electron spin resonance. We previously found that iron phthalocyanine (FePc) molecules form a spin-1/2 system when placed on an insulating thin film of magnesium oxide (MgO). Performing Rabi oscillation and Hahn echo measurements, we show that the FePc spin can be coherently manipulated with a phase coherence time T₂^Echo of several hundreds of nanoseconds. Tunneling current-dependent measurements demonstrate that interaction with the tunneling electrons is the dominating source of decoherence. In addition, we perform Hahn echo measurements on small self-assembled arrays of FePc molecules. We show that, despite additional intermolecular magnetic coupling, spin resonance and T₂^Echo are much less perturbed by T₁ spin flip events of neighboring spins than by the tunneling current. This will potentially allow for individual addressable molecular spins in self-assemblies and with application for quantum information processing.

Fully Tunable Hyperfine Interactions of Hole Spin Qubits in Si and Ge Quantum Dots

Hole spin qubits are frontrunner platforms for scalable quantum computers, but state-of-the-art devices suffer from noise originating from the hyperfine interactions with nuclear defects. We show that these interactions have a highly tunable anisotropy that is controlled by device design and external electric fields. This tunability enables sweet spots where the hyperfine noise is suppressed by an order of magnitude and is comparable to isotopically purified materials. We identify surprisingly simple designs where the qubits are highly coherent and are largely unaffected by both charge and hyperfine noise. We find that the large spin-orbit interaction typical of elongated quantum dots not only speeds up qubit operations, but also dramatically renormalizes the hyperfine noise, altering qualitatively the dynamics of driven qubits and enhancing the fidelity of qubit gates. Our findings serve as guidelines to design high performance qubits for scaling up quantum computers.

Room-Temperature Quantum Memories Based on Molecular Electron Spin Ensembles

Whilst quantum computing has recently taken great leaps ahead, the development of quantum memories has decidedly lagged behind. Quantum memories are essential devices in the quantum technology palette and are needed for intermediate storage of quantum bit states and as quantum repeaters in long-distance quantum communication. Current quantum memories operate at cryogenic, mostly sub-Kelvin temperatures and require extensive and costly peripheral hardware. It is demonstrated that ensembles of weakly coupled molecular spins show long coherence times and can be used to store microwave pulses of arbitrary phase. These studies exploit strong coupling of the spin ensemble to special 3D microwave resonators. Most importantly, these systems operate at room temperature.

Low Temperature Relaxation of Donor Bound Electron Spins in ^{28}Si:P

We measure the spin-lattice relaxation of donor bound electrons in ultrapure, isotopically enriched, phosphorus-doped ^{28}Si:P. The optical pump-probe experiments reveal at low temperatures extremely long spin relaxation times which exceed 20 h. The ^{28}Si:P spin relaxation rate increases linearly with temperature in the regime below 1 K and shows a distinct transition to a T^{9} dependence which dominates the spin relaxation between 2 and 4 K at low magnetic fields. The T^{7} dependence reported for natural silicon is absent. At high magnetic fields, the spin relaxation is dominated by the magnetic field dependent single phonon spin relaxation process. This process is well documented for natural silicon at finite temperatures but the ^{28}Si:P measurements validate additionally that the bosonic phonon distribution leads at very low temperatures to a deviation from the linear temperature dependence of Γ as predicted by theory.

Ultrafast hole spin qubit with gate-tunable spin-orbit switch functionality

Quantum computers promise to execute complex tasks exponentially faster than any possible classical computer, and thus spur breakthroughs in quantum chemistry, material science and machine learning. However, quantum computers require fast and selective control of large numbers of individual qubits while maintaining coherence. Qubits based on hole spins in one-dimensional germanium/silicon nanostructures are predicted to experience an exceptionally strong yet electrically tunable spin-orbit interaction, which allows us to optimize qubit performance by switching between distinct modes of ultrafast manipulation, long coherence and individual addressability. Here we used millivolt gate voltage changes to tune the Rabi frequency of a hole spin qubit in a germanium/silicon nanowire from 31 to 219 MHz, its driven coherence time between 7 and 59 ns, and its Landé g-factor from 0.83 to 1.27. We thus demonstrated spin-orbit switch functionality, with on/off ratios of roughly seven, which could be further increased through improved gate design. Finally, we used this control to optimize our qubit further and approach the strong driving regime, with spin-flipping times as short as ~1 ns.

Magneto-Optical Characterization of Trions in Symmetric InP-Based Quantum Dots for Quantum Communication Applications

Magneto-optical parameters of trions in novel large and symmetric InP-based quantum dots, uncommon for molecular beam epitaxy-grown nanostructures, with emission in the third telecom window, are measured in Voigt and Faraday configurations of an external magnetic field. The diamagnetic coefficients are found to be in the range of 1.5–4 μeV/T², and 8–15 μeV/T², respectively out-of-plane and in-plane of the dots. The determined values of diamagnetic shifts are related to the anisotropy of dot sizes. Trion g-factors are measured to be relatively small, in the range of 0.3–0.7 and 0.5–1.3, in both configurations, respectively. Analysis of single carrier g-factors, based on the formalism of spin-correlated orbital currents, leads to similar values for hole and electron of ~0.25 for Voigt and g_e ≈ −5; g_h ≈ +6 for Faraday configuration of the magnetic field. Values of g-factors close to zero measured in Voigt configuration make the investigated dots promising for electrical tuning of the g-factor sign, required for schemes of single spin control in qubit applications.

Exchange Coupling in a Linear Chain of Three Quantum-Dot Spin Qubits in Silicon

Quantum gates between spin qubits can be implemented leveraging the natural Heisenberg exchange interaction between two electrons in contact with each other. This interaction is controllable by electrically tailoring the overlap between electronic wave functions in quantum dot systems, as long as they occupy neighboring dots. An alternative route is the exploration of superexchange-the coupling between remote spins mediated by a third idle electron that bridges the distance between quantum dots. We experimentally demonstrate direct exchange coupling and provide evidence for second neighbor mediated superexchange in a linear array of three single-electron spin qubits in silicon, inferred from the electron spin resonance frequency spectra. We confirm theoretically, through atomistic modeling, that the device geometry only allows for sizable direct exchange coupling for neighboring dots, while next-nearest neighbor coupling cannot stem from the vanishingly small tail of the electronic wave function of the remote dots, and is only possible if mediated.

Engineering long spin coherence times of spin-orbit qubits in silicon

Electron-spin qubits have long coherence times suitable for quantum technologies. Spin-orbit coupling promises to greatly improve spin qubit scalability and functionality, allowing qubit coupling via photons, phonons or mutual capacitances, and enabling the realization of engineered hybrid and topological quantum systems. However, despite much recent interest, results to date have yielded short coherence times (from 0.1 to 1 μs). Here we demonstrate ultra-long coherence times of 10 ms for holes where spin-orbit coupling yields quantized total angular momentum. We focus on holes bound to boron acceptors in bulk silicon 28, whose wavefunction symmetry can be controlled through crystal strain, allowing direct control over the longitudinal electric dipole that causes decoherence. The results rival the best electron-spin qubits and are 10⁴ to 10⁵ longer than previous spin-orbit qubits. These results open a pathway to develop new artificial quantum systems and to improve the functionality and scalability of spin-based quantum technologies.

Influence of nuclear spins on electron spin coherence in isolated, p-doped tin clusters

Magnetic double deflection experiments reveal that nuclear spins diminish electron spin coherence in isolated AlSn12 clusters. A temperature-dependent fraction of the endohedral cage clusters show superatomic response in Stern-Gerlach experiments which allows one to detect spin flips under controlled conditions in a double deflection arrangement. The concentration of nuclear spins in the tin cage is varied by using isotopically enriched tin samples. Hyperfine interaction, nuclear spin statistics and spin dynamics are discussed in detail. It is demonstrated that state-interference in the multistate Landau-Zener system AlSn12 explains why the spin decoherence is significantly increased when one or two nuclear spins are already present in the cluster, while the spin coherence no longer changes significantly with the addition of further nuclear spins.

Developing Single Layer MOS Quantum Dots for Diagnostic Qubits

The design, fabrication and characterization of single metal gate layer, metal-oxide-semiconductor (MOS) quantum dot devices robust against dielectric breakdown are presented as prototypes for future diagnostic qubits. These devices were developed as a preliminary solution to a longer term goal of a qubit platform for intercomparison between materials or for in-line diagnostics, and to provide a testbed for establishing classical measurements predictive of coherence performance. For this stage, we seek a robust MOS design that is compatible with wafer and chip architectures, that has a reduced process overhead and is sufficiently capable of challenging and advancing our measurement capabilities. In this report, we present our initial batch of silicon MOS devices using a single gate layer, which have not exhibited any failures with gate voltage excursions > 10 V, but do exhibit the reduced electrostatic control expected of a single gate layer design. We observe quantum dot formation, capacitive charge sensing between channels, and reasonable effective electron temperatures that enable spin qubit studies. The costs and benefits of the trade-off between device performance and fabrication efficiency will be discussed, as well as opportunities for future improvements.

Optically Detected Magnetic Resonance in Neutral Silicon Vacancy Centers in Diamond via Bound Exciton States

Neutral silicon vacancy (SiV^{0}) centers in diamond are promising candidates for quantum networks because of their excellent optical properties and long spin coherence times. However, spin-dependent fluorescence in such defects has been elusive due to poor understanding of the excited state fine structure and limited off-resonant spin polarization. Here we report the realization of optically detected magnetic resonance and coherent control of SiV^{0} centers at cryogenic temperatures, enabled by efficient optical spin polarization via previously unreported higher-lying excited states. We assign these states as bound exciton states using group theory and density functional theory. These bound exciton states enable new control schemes for SiV^{0} as well as other emerging defect systems.

Valley interference and spin exchange at the atomic scale in silicon

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Coupled donor wavefunctions in silicon are spatially resolved to evidence valley interference processes. An atomic-scale understanding of the interplay between interference, envelope anisotropy and crystal symmetries unveils a placement strategy compatible with existing technology where the exchange is insensitive to interference.

Multimode Storage of Quantum Microwave Fields in Electron Spins over 100 ms

We report long coherence times (up to 300 ms) for near-surface bismuth donor electron spins in silicon coupled to a superconducting microresonator, biased at a clock transition. This enables us to demonstrate the partial absorption of a train of weak microwave fields in the spin ensemble, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. Phase coherence and quantum statistics are preserved in the storage.

Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.

Measurement of Backaction from Electron Spins in a Gate-Defined GaAs Double Quantum dot Coupled to a Mesoscopic Nuclear Spin Bath

Decoherence of a quantum system arising from its interaction with an environment is a key concept for understanding the transition between the quantum and classical world as well as performance limitations in quantum technology applications. The effects of large, weakly coupled environments are often described as a classical, fluctuating field whose dynamics is unaffected by the qubit, whereas a fully quantum description still implies some backaction from the qubit on the environment. Here we show direct experimental evidence for such a backaction for an electron-spin qubit in a GaAs quantum dot coupled to a mesoscopic environment of order 10^{6} nuclear spins. By means of a correlation measurement technique, we detect the backaction of a single qubit-environment interaction whose duration is comparable to the qubit's coherence time, even in such a large system. We repeatedly let the qubit interact with the spin bath and measure its state. Between such cycles, the qubit is reinitialized to different states. The correlations of the measurement outcomes are strongly affected by the intermediate qubit state, which reveals the action of a single electron spin on the nuclear spins.

Controllable freezing of the nuclear spin bath in a single-atom spin qubit

The quantum coherence and gate fidelity of electron spin qubits in semiconductors are often limited by nuclear spin fluctuations. Enrichment of spin-zero isotopes in silicon markedly improves the dephasing time [Formula: see text], which, unexpectedly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom ³¹P qubit in enriched ²⁸Si, we show that the abnormally long [Formula: see text] is due to the freezing of the dynamics of the residual ²⁹Si nuclei, caused by the electron-nuclear hyperfine interaction. Inserting a waiting period when the electron is controllably removed unfreezes the nuclear dynamics and restores the ergodic [Formula: see text] value. Our conclusions are supported by a nearly parameter-free modeling of the ²⁹Si nuclear spin dynamics, which reveals the degree of backaction provided by the electron spin. This study clarifies the limits of ergodic assumptions in nuclear bath dynamics and provides previously unidentified strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.

Operation of a silicon quantum processor unit cell above one kelvin

Quantum computers are expected to outperform conventional computers in several important applications, from molecular simulation to search algorithms, once they can be scaled up to large numbers-typically millions-of quantum bits (qubits)^1-3. For most solid-state qubit technologies-for example, those using superconducting circuits or semiconductor spins-scaling poses a considerable challenge because every additional qubit increases the heat generated, whereas the cooling power of dilution refrigerators is severely limited at their operating temperature (less than 100 millikelvin)^4-6. Here we demonstrate the operation of a scalable silicon quantum processor unit cell comprising two qubits confined to quantum dots at about 1.5 kelvin. We achieve this by isolating the quantum dots from the electron reservoir, and then initializing and reading the qubits solely via tunnelling of electrons between the two quantum dots^7-9. We coherently control the qubits using electrically driven spin resonance^10,11 in isotopically enriched silicon^{12 28}Si, attaining single-qubit gate fidelities of 98.6 per cent and a coherence time of 2 microseconds during 'hot' operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures^13-16. Furthermore, we show that the unit cell can be operated at magnetic fields as low as 0.1 tesla, corresponding to a qubit control frequency of 3.5 gigahertz, where the qubit energy is well below the thermal energy. The unit cell constitutes the core building block of a full-scale silicon quantum computer and satisfies layout constraints required by error-correction architectures^8,17. Our work indicates that a spin-based quantum computer could be operated at increased temperatures in a simple pumped ⁴He system (which provides cooling power orders of magnitude higher than that of dilution refrigerators), thus potentially enabling the integration of classical control electronics with the qubit array^18,19.

Pulsed electron spin resonance spectroscopy in the Purcell regime

In EPR, spin relaxation is typically governed by interactions with the lattice or other spins. However, it has recently been shown that given a sufficiently strong spin-resonator coupling and high resonator quality factor, the spontaneous emission of microwave photons from the spins into the resonator can become the main relaxation mechanism, as predicted by Purcell. With increasing attention on the use of microresonators for EPR to achieve high spin-number sensitivity it is important to understand how this novel regime influences measured EPR signals, for example the amplitude and temporal shape of the spin-echo. We study this regime theoretically and experimentally, using donor spins in silicon, under different conditions of spin-linewidth and coupling homogeneity. When the spin-resonator coupling is distributed inhomogeneously, we find that the effective spin-echo relaxation time measured in a saturation recovery sequence strongly depends on the parameters for the detection echo. When the spin linewidth is larger than the resonator bandwidth, the different Fourier components of the spin echo relax with different characteristic times - due to the role of the resonator in driving relaxation - which results in the temporal shape of the echo becoming dependent on the repetition time of the experiment.

Single-spin qubits in isotopically enriched silicon at low magnetic field

Single-electron spin qubits employ magnetic fields on the order of 1 Tesla or above to enable quantum state readout via spin-dependent-tunnelling. This requires demanding microwave engineering for coherent spin resonance control, which limits the prospects for large scale multi-qubit systems. Alternatively, singlet-triplet readout enables high-fidelity spin-state measurements in much lower magnetic fields, without the need for reservoirs. Here, we demonstrate low-field operation of metal-oxide-silicon quantum dot qubits by combining coherent single-spin control with high-fidelity, single-shot, Pauli-spin-blockade-based ST readout. We discover that the qubits decohere faster at low magnetic fields with [Formula: see text] μs and [Formula: see text] μs at 150 mT. Their coherence is limited by spin flips of residual 29Si nuclei in the isotopically enriched 28Si host material, which occur more frequently at lower fields. Our finding indicates that new trade-offs will be required to ensure the frequency stabilization of spin qubits, and highlights the importance of isotopic enrichment of device substrates for the realization of a scalable silicon-based quantum processor.

Reduction of charge impurities in a silicon metal-oxide-semiconductor quantum dot qubit device patterned with nano-imprint lithography

The silicon metal-oxide-semiconductor quantum dot architecture is a leading approach for the physical implementation of semiconductor quantum computing. One major challenge for scalable quantum dots is the presence of charge impurities. Electron-beam lithography (EBL), almost universally used to fabricate quantum dot devices, is known to create such defects at the Si/SiO₂ interface. To eliminate the need for EBL, we have transferred the metal gate pattern of a quantum dot onto the silicon substrate using nano-imprint lithography. Critical features with 50 nm scale and separation can be dependably reproduced. By characterizing the bias-dependent charge transport through a quantum point contact barrier, the prevalence of impurities is found to be largely diminished in nano-imprinted devices when compared to similar electron-beam-written counterparts. High-quality charge transport and charge sensing of several quantum dots are obtained. Additionally, gate noise is measured with an average of 1.5 μeV Hz^-1/2 equivalent to previous measurements made on devices fabricated with EBL, which suggests that the leading source of impurities produced by EBL are deep, fixed charges. This work offers a path toward reliable quantum dot operation in MOS by improving fabrication techniques to reduce charge impurities.