The nuclear spin state of a phosphorus donor ($^{31}$P) in isotopically enriched silicon-28 is an excellent host to store quantum information in the solid state. The spin's insensitivity to electric fields yields a solid-state qubit with record coherence times, but also renders coupling to other quantum systems very challenging. Here, we describe how to generate a strong electric dipole ($>100$ Debye) at microwave frequencies for the nuclear spin. This is achieved by applying a magnetic drive to the spin of the donor-bound electron, while simultaneously controlling its charge state with electric fields. Under certain conditions, the microwave magnetic drive also renders the nuclear spin resonance frequency and electric dipole strongly insensitive to electrical noise, yielding long ($>1$ ms) dephasing times and robust gate operations. The nuclear spin could then be strongly coupled to microwave resonators, with a vacuum Rabi splitting of order 1 MHz, or to other nuclear spins, nearly half a micrometer apart, via strong electric dipole-dipole interaction. This work brings the $^{31}$P nuclear qubit into the realm of hybrid quantum systems and opens up new avenues in quantum information processing.
Silicon is vital to the computing industry due to the high quality of its native oxide and well-established doping technologies. Isotopic purification has enabled quantum coherence times on the order of seconds, thereby placing silicon at the forefront of efforts to create a solid state quantum processor. We demonstrate strong coupling of a single electron in a silicon double quantum dot to the photonic field of a microwave cavity, as shown by the observation of vacuum Rabi splitting. Strong coupling of a quantum dot electron to a cavity photon would allow for long-range qubit coupling and the…
We demonstrate microwave manipulation of the spin states of electrically injected spin-polarized electrons in silicon. Although the silicon channel is bounded by ferromagnetic metal films, we show that moderate microwave power can be applied to the devices without altering the device operation significantly. Resonant microwave irradiation is used to induce spin rotation of spin-polarized electrons as they travel across a silicon channel, and the resultant spin polarization is subsequently detected by a ferromagnetic Schottky barrier spin detector. These results demonstrate the potential for co…
Over the past decade donor spin qubits in isotopically enriched $^{28}$Si have been intensely studied due to their exceptionally long coherence times. More recently bismuth donor electron spins have become popular because Bi has a large nuclear spin which gives rise to clock transitions (first-order insensitive to magnetic field noise). At every clock transition there are two nearly degenerate transitions between four distinct states which can be used as a pair of qubits. Here it is experimentally demonstrated that these transitions are excited by microwaves of opposite helicity such that they…
Practical quantum networks require low-loss and noise-resilient optical interconnects as well as non-Gaussian resources for entanglement distillation and distributed quantum computation. The latter could be provided by superconducting circuits but - despite growing efforts and rapid progress - existing solutions to interface the microwave and optical domains lack either scalability or efficiency, and in most cases the conversion noise is not known. In this work we utilize the unique opportunities of silicon photonics, cavity optomechanics and superconducting circuits to demonstrate a fully int…
We have fabricated superconducting microwave resonators in a lumped element geometry using single crystal silicon dielectric parallel plate capacitors with C >2 pF. Aluminum devices with resonant frequencies between 4.0 and 6.5 GHz exhibited an average internal quality factor Q_i of 2 x 10^5 in the single photon excitation regime at T = 20 mK. Attributing all the observed loss to the capacitive element, our measurements correspond to a loss tangent of intrinsic silicon of 5 x 10^-6. This level of loss is an order of magnitude lower than is currently observed in structures incorporating amorpho…
Single donors in semiconductor nanostructures represent a key element to develop spin related quantum functionalities in atomic scale devices. Quantum transport through a single Arsenic donor in the channel of a Silicon nano-field effect transistor under microwave irradiation is investigated. The device is characterized at mK temperatures in the regime of Coulomb-blockade. Photon assisted tunneling and microwave induced electron pumping regimes are revealed respectively at low and high microwave power. At sufficiently high power, the microwave irradiation induces tunneling through the first ex…
Fabrication processes involving anhydrous hydrofluoric vapor etching are developed to create high-$Q$ aluminum superconducting microwave resonators on free-standing silicon membranes formed from a silicon-on-insulator wafer. Using this fabrication process, a high-impedance $8.9$GHz coil resonator is coupled capacitively with large participation ratio to a $9.7$MHz micromechanical resonator. Two-tone microwave spectroscopy and radiation pressure back-action are used to characterize the coupled system in a dilution refrigerator down to temperatures of $T_f = 11$~mK, yielding a measured electrome…
Microelectromechanical systems and integrated photonics provide the basis for many reliable and compact circuit elements in modern communication systems. Electro-opto-mechanical devices are currently one of the leading approaches to realize ultra-sensitive, low-loss transducers for an emerging quantum information technology. Here we present an on-chip microwave frequency converter based on a planar aluminum on silicon nitride platform that is compatible with slot-mode coupled photonic crystal cavities. We show efficient frequency conversion between two propagating microwave modes mediated by t…
We present a platform based upon silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Utilizing tensile stress and lithographic patterning of a silicon nitride nanomembrane we are able to reliably realize planar capacitors with vacuum gap sizes down to $s \approx 80$nm. In combination with spiral inductor coils of micron pitch, this yields microwave ($\approx 8$GHz) resonant circuits of high impedance ($Z_{0} \approx 3.4$k$Ω$) suitable for efficient electromechanical coupling to nanosca…
Electron spins in silicon quantum dots are attractive systems for quantum computing due to their long coherence times and the promise of rapid scaling using semiconductor fabrication techniques. While nearest neighbor exchange coupling of two spins has been demonstrated, the interaction of spins via microwave frequency photons could enable long distance spin-spin coupling and "all-to-all" qubit connectivity. Here we demonstrate strong-coupling between a single spin in silicon and a microwave frequency photon with spin-photon coupling rates g_s/(2π) > 10 MHz. The mechanism enabling coherent spi…
Single spin qubits based on phosphorus donors in silicon are a promising candidate for a large-scale quantum computer. Despite long coherence times, achieving uniform magnetic control remains a hurdle for scale-up due to challenges in high-frequency magnetic field control at the nanometre-scale. Here, we present a proposal for a flopping-mode electric dipole spin resonance qubit based on the combined electron and nuclear spin states of a double phosphorus donor quantum dot. The key advantage of utilising a donor-based system is that we can engineer the number of donor nuclei in each quantum do…
Quantum coherence in solid-state systems has been demonstrated in superconducting circuits and in semiconductor quantum dots. This has paved the way to investigate solid-state systems for quantum information processing with the potential benefit of scalability compared to other systems based on atoms, ions and photons. Coherent coupling of superconducting circuits to microwave photons, circuit quantum electrodynamics (QED), has opened up new research directions and enabled long distance coupling of qubits. Here we demonstrate how the electromagnetic field of a superconducting microwave resonat…
We report the instrumentation and experimental results of a cryogenic scanning microwave impedance microscope. The microwave probe and the scanning stage are located inside the variable temperature insert of a helium cryostat. Microwave signals in the distance modulation mode are used for monitoring the tip-sample distance and adjusting the phase of the two output channels. The ability to spatially resolve the metal-insulator transition in a doped silicon sample is demonstrated. The data agree with a semi-quantitative finite-element simulation. Effects of the thermal energy and electric fields…
Nanoscale silicon p(+)-n junctions with very high concentration of boron, 5 10^21 cm-3, are found to demonstrate interesting optical properties. Emission band dominated in near-infrared electroluminescence (EL) spectra possesses high degree of the linear polarization along preferred crystallographic axis which can be controlled by the lateral voltage applied in the plane of the p(+)-n junction. Such behavior together with the temperature dependence of the EL intensity is attributed to the presence of the self-compensating dipole boron centers, B(+)-B(-), with negative correlation energy which …
We demonstrate a hybrid device architecture where the charge states in a double quantum dot (DQD) formed in a Si/SiGe heterostructure are read out using an on-chip superconducting microwave cavity. A quality factor Q = 5,400 is achieved by selectively etching away regions of the quantum well and by reducing photon losses through low-pass filtering of the gate bias lines. Homodyne measurements of the cavity transmission reveal DQD charge stability diagrams and a charge-cavity coupling rate g_c/2pi = 23 MHz. These measurements indicate that electrons trapped in a Si DQD can be effectively couple…
A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of…
Solid-state quantum computers require classical electronics to control and readout individual qubits and to enable fast classical data processing [1-3]. Integrating both subsystems at deep cryogenic temperatures [4], where solid-state quantum processors operate best, may solve some major scaling challenges, such as system size and input/output (I/O) data management [5]. Spin qubits in silicon quantum dots (QDs) could be monolithically integrated with complementary metal-oxide-semiconductor (CMOS) electronics using very-large-scale integration (VLSI) and thus leveraging over wide manufacturing …
The dipole trap model is able to explain the main properties of the apparent metal-to-insulator transition in gated high mobility Si-inversion layers. Our numerical calculations are compared with previous analytical ones and the assumptions of the model are discussed carefully. In general we find a similar behavior but include further details in the calculation. The calculated strong density dependence of the resistivity is not yet in full agreement with the experiment.
The germanium (Ge) hut wire system has strong spin-orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of …
High fidelity entanglement of an on-chip array of spin qubits poses many challenges. Spin-orbit coupling (SOC) can ease some of these challenges by enabling long-ranged entanglement via electric dipole-dipole interactions, microwave photons, or phonons. However, SOC exposes conventional spin qubits to decoherence from electrical noise. Here we propose an acceptor-based spin-orbit qubit in silicon offering long-range entanglement at a sweet spot where the qubit is protected from electrical noise. The qubit relies on quadrupolar SOC with the interface and gate potentials. As required for surface…
We develop a formalism of electric dipole spin resonance (EDSR) based on slanting magnetic field, where we especially investigate the microwave amplitude dependence. With increasing microwave amplitude, the Rabi frequency increases linearly for a spin confined in a harmonic potential. How- ever, when the spin is confined in the double-well potential, the Rabi frequency shows sub-linear dependence with increasing the microwave amplitude.
In this study we investigate magnetic properties, surface morphology and crystal structure in iron nanoclusters electrodeposited on lightly-doped (100) n-type silicon substrates. Our goal is to investigate the spin injection and detection in the Fe/Si lateral structures. The samples obtained under electric percolation were characterized by magnetoresistive and magnetic resonance measurements with cycling the sweeping applied field in order to understand the spin dynamics in the as-produced samples. The observed hysteresis in the magnetic resonance spectra, plus the presence of a broad peak in …
Practical quantum computers require the construction of a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a physical platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and allows hundreds of nanometers inter-qubit distances, therefore facilitating fabrication using current technology. All qubit operations are performed via electrical means on th…
Coherent charge-photon and spin-photon coupling has recently been achieved in silicon double quantum dots (DQD). Here we demonstrate a versatile split-gate cavity-coupler that allows more than one DQD to be coupled to the same microwave cavity. Measurements of the cavity transmission as a function of level detuning yield a charge cavity coupling rate $g_c/2π$ = 58 MHz, charge decoherence rate $γ_c/2π$ = 36 MHz, and cavity decay rate $κ/2π$ = 1.2 MHz. The charge cavity coupling rate is in good agreement with device simulations. Our coupling technique can be extended to enable simultaneous coupl…
Owing to ever increasing gate fidelities and to a potential transferability to industrial CMOS technology, silicon spin qubits have become a compelling option in the strive for quantum computation. In a scalable architecture, each spin qubit will have to be finely tuned and its operating conditions accurately determined. In this prospect, spectroscopic tools compatible with a scalable device layout are of primary importance. Here we report a two-tone spectroscopy technique providing access to the spin-dependent energy-level spectrum of a hole double quantum dot defined in a split-gate silicon …
Defect spins in silicon carbide have become promising platforms with respect to quantum information processing and quantum sensing. Indeed, the optically detected magnetic resonance (ODMR) of defect spins is the cornerstone of the applications. In this work, we systematically investigate the contrast and linewidth of laser-and microwave power-dependent ODMR with respect to ensemble-divacancy spins in silicon carbide at room temperature. The results suggest that magnetic field sensing sensitivity can be improved by a factor of 10 for the optimized laser and microwave power range. The experiment…
Room temperature optically detected magnetic resonance experiments on spin 3/2 Silicon vacancies in 4H-SiC are reported. The $m_s=+1/2\leftrightarrow -1/2$ transition is accessed using a two microwave frequency excitation protocol. The ratio of the Rabi frequencies of the $+3/2 \leftrightarrow +1/2$ and $+1/2\leftrightarrow -1/2$ transitions is measured to be $(0.901\pm 0.013)$. The deviation from $\sqrt{3}/2$ is attributed to small difference in g-factor for different magnetic dipole transitions. Whereas a spin-1/2 system is characterized by a single spin lifetime $T_1$, we experimentally dem…
Quantum computing based on spins in the solid state allows for densely-packed arrays of quantum bits. While high-fidelity operation of single qubits has been demonstrated with individual control pulses, the operation of large-scale quantum processors requires a shift in paradigm towards global control solutions. Here we report the experimental implementation of a new type of qubit protocol - the SMART (Sinusoidally Modulated, Always Rotating and Tailored) protocol. As with a dressed qubit, we resonantly drive a two-level system with a continuous microwave field, but here we add a tailored modu…
We introduce a microwave-assisted spectroscopy technique to determine the relative concentrations of nitrogen vacancy (NV) centers in diamond that are negatively-charged (NV${}^-$) and neutrally-charged (NV${}^0$), and present its application to studying spin-dependent ionization in NV ensembles and enhancing NV-magnetometer sensitivity. Our technique is based on selectively modulating the NV${}^-$ fluorescence with a spin-state-resonant microwave drive to isolate, in-situ, the spectral shape of the NV${}^-$ and NV${}^0$ contributions to an NV-ensemble sample's fluorescence. As well as serving…
Silicon carbide (SiC)-based defects are promising for quantum communications, quantum information processing, and for the next generation of quantum sensors, as they feature long coherence times, frequencies near the telecom, and optical and microwave transitions. For such applications, the efficient initialization of the spin state is necessary. We develop a theoretical description of the spin polarization process by using the intersystem crossing of the silicon vacancy defect, which is enabled by a combination of optical driving, spin-orbit coupling, and interaction with vibrational modes. B…
We discuss the effects of gigahertz photon irradiation on a degenerately phosphorous-doped silicon quantum dot, in particular, the creation of voltage offsets on gate leads and the tunneling of one or two electrons via Coulomb blockade lifting at 4.2K. A semi-analytical model is derived that explains the main features observed experimentally. Ultimately both effects may provide an efficient way to optically control and operate electrically isolated structures by microwave pulses. In quantum computing architectures, these results may lead to the use of microwave multiplexing to manipulate quant…
We report the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot and the microwave photon is stored in an on-chip high-impedance superconducting resonator. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet. This result opens the way to the realization of large networks of quantum dot based spin qubit registers, removing a major road…
Quantum backaction disturbs the measurement of the position of a mechanical oscillator by introducing additional fluctuations. In a quantum backaction measurement technique, the backaction can be evaded, although at the cost of losing part of the information. In this work, we carry out such a quantum backaction measurement using a large 0.5 mm diameter silicon nitride membrane oscillator with 707 kHz frequency, via a microwave cavity readout. The measurement shows that quantum backaction noise can be evaded in the quadrature measurement of the motion of a large object.
Electric control of individual atoms or molecules in a solid-state system offers a promising way to bring quantum mechanical functionalities into electronics. This idea has recently come into the reach of the established domain of silicon technology, leading to the realization of single-atom transistors and to the first measurements of electron spin dynamics in single donors. Here we show that we can electrically couple two donors embedded in a multi-gate silicon transistor, and induce coherent oscillations in their charge states by means of microwave signals. We measure single-electron tunnel…
We examined dipolar field effects on the microwave generation in the domain wall spin-valve by solving simultaneously the Landau-Lifshitz-Gilbert and Zhang-Levy-Fert diffusion equations. By numerically analyzing dipolar field dependence, we showed that the microwave generation needs the dipole-dipole interaction for a 180$^\circ$ domain wall and the amplitude of the microwave voltage signal depends strongly on the exchange length. In order to design a microwave generator using the domain wall spin-valve with high efficiency, we propose that the materials with short exchange length are preferre…
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 en…
We study, both experimentally and by numerical modeling, the magnetic dynamics that can be excited in a magnetic thin-film nanopillar device using the spin torque from a spatially localized current injected via a 10s-of-nm-diameter aperture. The current-driven magnetic dynamics can produce large amplitude microwave emission at zero magnetic field, with a frequency well below that of the uniform ferromagnetic resonance mode. Micromagnetic simulations indicate that the physical origin of this efficient microwave nano-oscillator is the nucleation and subsequent steady-state rotational dynamics of…
In quantum computation, information is processed by gates that must coherently couple separate qubits. In many systems the qubits are naturally coupled, but such an always-on interaction limits the algorithms that may be implemented. Coupling interactions may also be directed in devices and circuits that are provided with additional control wiring. This can be achieved by adjusting the gate voltage in a semiconductor device or an additional flux in a superconducting device. Such control signals must be applied adiabatically (limiting the speed) and the additional wiring provides pathways for n…
Superconducting quantum circuits are one of the leading quantum computing platforms. To advance superconducting quantum computing to a point of practical importance, it is critical to identify and address material imperfections that lead to decoherence. Here, we use terahertz Scanning Near-field Optical Microscopy (SNOM) to probe the local dielectric properties and carrier concentrations of wet-etched aluminum resonators on silicon, one of the most characteristic components of the superconducting quantum processors. Using a recently developed vector calibration technique, we extract the THz pe…
Superconducting boron doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. Here, we study experimentally the electrodynamics of superconducting silicon thin layers patterned in coplanar waveguide resonators, targeting three key properties: kinetic inductance, internal losses, and the variation of these quantities with the read-out power. We report the first observation in a doped semiconductor of…
Spin-based silicon quantum electronic circuits offer a scalable platform for quantum computation, combining the manufacturability of semiconductor devices with the long coherence times afforded by spins in silicon. Advancing from current few-qubit devices to silicon quantum processors with upwards of a million qubits, as required for fault-tolerant operation, presents several unique challenges, one of the most demanding being the ability to deliver microwave signals for large-scale qubit control. Here we demonstrate a potential solution to this problem by using a three-dimensional dielectric r…
First-order perturbation theory and many-body Green function analysis are used to quantify the influence of size, surface reconstruction and surface treatment on exciton transport between small silicon quantum dots. Competing radiative processes are also considered in order to determine how exciton transport efficiency is influenced. The analysis shows that quantum confinement causes small (~1 nm) Si quantum dots to exhibit exciton transport efficiencies far exceeding that of their larger counterparts. We also find that surface reconstruction significantly influences the absorption cross secti…
The ability to apply GHz frequencies to control the quantum state of a single $P$ atom is an essential requirement for the fast gate pulsing needed for qubit control in donor based silicon quantum computation. Here we demonstrate this with nanosecond accuracy in an all epitaxial single atom transistor by applying excitation signals at frequencies up to $\approx$ 13 GHz to heavily phosphorous doped silicon leads. These measurements allow the differentiation between the excited states of the single atom and the density of states in the one dimensional leads. Our pulse spectroscopy experiments co…
Electrically addressing spin systems is predicted to be a key component in developing scalable semiconductor-based quantum processing architectures, to enable fast spin qubit manipulation and long-distance entanglement via microwave photons. However, single spins have no electric dipole, and therefore a spin-orbit mechanism must be integrated in the qubit design. Here, we propose to couple microwave photons to atomically precise donor spin qubit devices in silicon using the hyperfine interaction intrinsic to donor systems and an electrically-induced spin-orbit coupling. We characterise a one-e…
Hybrid spin-mechanical systems are a promising platform for future quantum technologies. Usually they require application of additional microwave fields to project integer spin to a readable state. We develop a theory of optically detected spin-mechanical resonance associated with half-integer spin defects in silicon carbide (SiC) membranes. It occurs when a spin resonance frequency matches a resonance frequency of a mechanical mode, resulting in a shortening of the spin relaxation time through resonantly enhanced spin-phonon coupling. The effect can be detected as an abrupt reduction of the p…
Light-matter interactions at the nanoscale constitute a fundamental ingredient for engineering applications in nanophotonics and quantum optics. To this regard electromagnetic Mie resonances excited in high-refractive index dielectric nanoparticles have recently attracted interest because of their lower losses and better control over the scattering patterns compared to their plasmonic metallic counterparts. The emergence of several resonances in those systems results in an overall high complexity, where the electric and magnetic dipoles have significant overlap in the case of spherical symmetr…
We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two entities manifests itself via dispersive and dissipative effects observed as frequency shifts and linewidth broadenings of the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation calculation is used to model the combined system response and allows for determining both the coherence properties of the double quantum dot and its interdot …
We report record high Si-29 spin polarization obtained using dynamic nuclear polarization in microcrystalline silicon powder. Unpaired electrons in this silicon powder are due to dangling bonds in the amorphous region of this intrinsically heterogeneous sample. Si-29 nuclei in the amorphous region become polarized by forced electron-nuclear spin flips driven by off-resonant microwave radiation while nuclei in the crystalline region are polarized by spin diffusion across crystalline boundaries. Hyperpolarized silicon microparticles have long T1 relaxation times and could be used as tracers for …
