Figure 3 - uploaded by Andrew S. Dzurak
Content may be subject to copyright.
| Nuclear magnetic resonance of a single 31 P nucleus. a-c, Observation of nuclear resonances at B 0 = 1.77 T, while the electron spin is | (a), | (b), or absent, i.e. ionized donor (c). The resonance condition is obtained when |f | drops from the unperturbed value 0.4 to near zero, due to the randomization of the nuclear spin state. In each panel, the top inset shows the plunger gate voltage waveform (grey line) plus NMR/ESR pulse sequence, whilst the bottom-right inset shows the energy levels involved in the NMR transition. d, Dependence of the NMR resonances on the magnetic field B 0. Solid lines are the values predicted using the 31 P nuclear gyromagnetic ratio
Source publication
Detection of nuclear spin precession is critical for a wide range of scientific techniques that have applications in diverse fields including analytical chemistry, materials science, medicine and biology. Fundamentally, it is possible because of the extreme isolation of nuclear spins from their environment. This isolation also makes single nuclear...
Contexts in source publication
Context 1
... exploiting the broadband nature of our on-chip microwave transmission line, we perform a nuclear magnetic resonance (NMR) experiment on the 31 P nuclear spin (Fig. 3). We expect two NMR frequencies depending on the state of the electron: n1 = A/2 + n B 0 when the electron spin is |; and n2 = A/2 − n B 0 when the electron spin is | (Fig. 1b). The nuclear resonance is detected by measuring the absolute difference in electron spin-up counts between the two ESR frequencies, |f | = |f ...
Context 2
... normal value |f | 0.4, as observed in the nuclear spin readout experiments (Fig. 2b), because the nucleus retains its spin state for a very long time. Conversely, an 8 ms long resonant excitation quickly randomizes the nuclear spin state, causing |f | to drop towards zero. n1 is found by applying an NMR burst before the ESR excitation (Fig. 3a), whereas for n2 we swap the order of ESR and NMR, to achieve a higher probability of having the electron spin |, as required to observe the n2 resonance (Fig. ...
Context 3
... an 8 ms long resonant excitation quickly randomizes the nuclear spin state, causing |f | to drop towards zero. n1 is found by applying an NMR burst before the ESR excitation (Fig. 3a), whereas for n2 we swap the order of ESR and NMR, to achieve a higher probability of having the electron spin |, as required to observe the n2 resonance (Fig. ...
Context 4
... we have full control over the charge state of the donor, we can also perform an NMR experiment while the donor is ionized (Fig. 3c), as recently demonstrated in a bulk Si:P sample 45 . In this case there is only one resonance frequency, n0 = n B 0 . The electron is placed back onto the donor after the NMR burst, for the purpose of reading out the nuclear spin state. Fig. 3d shows the magnetic field dependence of the three NMR frequencies, which agree with the ...
Context 5
... the charge state of the donor, we can also perform an NMR experiment while the donor is ionized (Fig. 3c), as recently demonstrated in a bulk Si:P sample 45 . In this case there is only one resonance frequency, n0 = n B 0 . The electron is placed back onto the donor after the NMR burst, for the purpose of reading out the nuclear spin state. Fig. 3d shows the magnetic field dependence of the three NMR frequencies, which agree with the expected values assuming the bulk 31 P gyromagnetic ratio n = 17.23 MHz/T (ref. 40). This observation confirms that the system under study is indeed a single 31 P phosphorus atom. Furthermore, from these measurements we find that g = 1.9987(6) (see ...
Similar publications
We demonstrate the fabrication of single-crystalline diamond nanopillars on a
(111)-oriented chemical vapor deposited diamond substrate. This crystal
orientation offers optimal coupling of nitrogen-vacancy (NV) center emission to
the nanopillar mode and is thus advantageous over previous approaches. We
characterize single native NV centers in these...
We investigate phonon induced electronic dynamics in the ground and excited
states of the negatively charged silicon-vacancy ($\mathrm{SiV}^-$) centre in
diamond. Optical transition line widths, transition wavelength and excited
state lifetimes are measured for the temperature range 4-350 K. The ground
state orbital relaxation rates are measured us...
![FIG. 9. Estimated relative [NV -] concentrations vs. spin resonance...](profile/Joerg-Schmiedmayer/publication/256327387/figure/fig2/AS:341593686069251@1458453689483/Estimated-relative-NV-concentrations-vs-spin-resonance-linewidths-Dashed-lines_Q320.jpg)
We created dense ensembles of negatively charged nitrogen-vacancy (NV-)
centers in diamond by neutron and electron irradiation for applications in
hybrid quantum systems and magnetometry. We characterize fluorescence
intensity, optical and coherence properties of the resulting defects by
confocal microscopy, UV/Vis and FTIR spectroscopy, optically...
The negatively-charged nitrogen vacancy center (NV) in diamond has generated
significant interest as a platform for quantum information processing and
sensing in the solid state. For most applications, high quality optical
cavities are required to enhance the NV zero-phonon line (ZPL) emission. An
outstanding challenge in maximizing the degree of N...
Some of the stable isotopes of silicon and carbon have zero nuclear spin,
whereas many of the other elements that constitute semiconductors consist
entirely of stable isotopes that have nuclear spins. Silicon and diamond
crystals composed of nuclear-spin-free stable isotopes (Si-28, Si-30, or C-12)
are considered to be ideal host matrixes to place...
Citations
... Electronic spins in condensed matter, with their well-defined quantum properties and relatively weak interactions with external excitations, are natural candidates for embodying quantum information; their hyperfine-coupled nuclear spins, which tend to be even more coherent, offer potential as quantum memory elements. Indeed, such systems featured among the earliest theoretical condensed matter quantum information proposals such as that of Kane [29], and various physical examples have been studied experimentally, including paramagnetic defects in semiconductors [30][31][32] and diamond [33,34] and molecular magnets [35,36]. Together, these observations motivate us to explore how a nuclear spin qudit hyperfine-coupled to an electron spin qubit can be used to encode fault-tolerant error correcting protocols [18][19][20]. ...
The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Protocols employing redundancy over multiple physical qubits to encode a single error-protected logical qubit are theoretically effective, but imply a large resource overhead. Alternative, more hardware-efficient, approaches seek to deploy higher-dimensional quantum systems known as qudits. Recently, proposals have emerged for exploiting high-spin magnetic nuclei coupled to condensed matter electron spin qubits to implement fault-tolerant memories. Here, we explore experimentally the simplest of these proposals, a logical qubit encoded on the four states of a I=3/2 nuclear spin hyperfine-coupled to a S=1/2 electron spin qubit; the encoding protects against the dominant decoherence mechanism in such systems, fluctuations of the quantizing magnetic field. We implement the encoding using electron-nuclear double resonance within a subspace of the spin levels in an ensemble of highly coherent manganese defects in zinc oxide. We explore the dynamics of the encoded state both under a controlled application of the fluctuation and under natural decoherence processes. Our results confirm the potential of these proposals for practical, implementable, fault tolerant quantum memories.
... With SU(8) and SU(2) rotations available, we proceed to generate the z-oriented Schrödinger cat state of the high-spin nucleus, |cat 7/2 ⟩ z = |7/2⟩ + e iξ7 |−7/2⟩ / √ 2 (Fig. 1f), using two different methods. The first, based on Givens rotations [34] involves simply preparing the |−7/2⟩ state, applying a π/2 pulse at f 1 to produce |−7/2⟩ − |−5/2⟩ / √ 2, and then a sequence of π pulses between ascending pairs of states (Fig. 3a,b). The quality of the resulting |cat 7/2 ⟩ z state can be assessed by measuring the contrast C p of the parity oscillations around the equator of the Bloch sphere (Fig. 3c). ...
... Our experiments on creation and manipulation of Schrödinger cat states focus on using the ionised 123 Sb nuclear spin, i.e. the donor in the charge-positive D + state. However, reading out the nuclear spin populations requires introducing a hyperfine-coupled electron spin, which acts as a readout ancilla, as first demonstrated in the simpler 31 P system [34]. The electron is reintroduced on the donor by adjusting the voltages on the donor gates. ...
... Starting from the electron |↓⟩, an adiabatic frequency sweep [35] around each of the f ESR m I inverts the electron to the |↑⟩ state if the nucleus is in the state |m I ⟩, i.e. performs a conditional quantum operation on the electron spin ancilla. The measurement is, to a good approximation, of quantum nondemolition (QND) nature [34,36] (see Section SI: 9 B for deviations from QND), and can be repeated multiple times to increase the readout fidelity. Here we use 10 repetitions of the cycle [load |↓⟩ -adiabatic ESR sweep around f ESR m I -measure electron state] for every nuclear orientation m I . ...
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, for instance in continuous-variable states of oscillators such as microwave cavities or the motional modes of trapped ions. Powerful encodings include 'Schr\"odinger cat' states, superpositions of widely displaced coherent states, which also embody the challenge of quantum effects at the large scale. Alternatively, recent proposals suggest encoding logical qubits in high-spin atomic nuclei, which can host hardware-efficient versions of continuous-variable codes on a finite-dimensional system. Here we demonstrate the creation and manipulation of Schr\"odinger cat states using the spin-7/2 nucleus of a single antimony ($^{123}$Sb) atom, embedded and operated within a silicon nanoelectronic device. We use a coherent multi-frequency control scheme to produce spin rotations that preserve the SU(2) symmetry of the qudit, and constitute logical Pauli operations for logical qubits encoded in the Schr\"odinger cat states. The Wigner function of the cat states exhibits parity oscillations with a contrast up to 0.982(5), and state fidelities up to 0.913(2). These results demonstrate high-fidelity preparation of nonclassical resource states and logical control in a single atomic-scale object, opening up applications in quantum information processing and quantum error correction within a scalable, manufacturable semiconductor platform.
... Materials that host atomic defects with well-defined optical and spin transitions garner the most attention. Several systems have been studied in detail [11][12][13][14][15] , but only a few individually addressable defects in diamond and silicon carbide possess quantum coherent spins at room temperature, although with challenging optical properties 2,16,17 . Realizing the ideal spin-photon interface requires engineering existing candidates for better performance, as well as exploring new material systems 3,18 . ...
Solid-state spin–photon interfaces that combine single-photon generation and long-lived spin coherence with scalable device integration—ideally under ambient conditions—hold great promise for the implementation of quantum networks and sensors. Despite rapid progress reported across several candidate systems, those possessing quantum coherent single spins at room temperature remain extremely rare. Here we report quantum coherent control under ambient conditions of a single-photon-emitting defect spin in a layered van der Waals material, namely, hexagonal boron nitride. We identify that the carbon-related defect has a spin-triplet electronic ground-state manifold. We demonstrate that the spin coherence is predominantly governed by coupling to only a few proximal nuclei and is prolonged by decoupling protocols. Our results serve to introduce a new platform to realize a room-temperature spin qubit coupled to a multiqubit quantum register or quantum sensor with nanoscale sample proximity.
... The quick advancement of our expertise drives the progressions in experimentally controlling and directing quantum dynamics across a wide range of systems. These entities span a wide range, including single photons , atoms, and ions, as well as isolated electron and nuclear spins [26][27][28][29][30]. This extends to mesoscopic superconducting systems and nanomechanical devices [31,32]. ...
Quantum correlations, especially time correlations, are crucial in ghost imaging in order to significantly reduce the background noise on the one hand while increasing the imaging resolution. Moreover, the time correlations serve as a critical reference, distinguishing between signal and noise, which in turn enable clear visualization of biological samples. Quantum imaging also addresses the challenge involved in imaging delicate biological structures with minimal photon exposure and sample damage. Here we explore the recent progress in quantum correlation-based imaging, notably its impact on secure imaging and remote sensing protocols as well as on biological imaging. We also exploit the quantum characteristics of heralded single-photon sources (HSPS) combined with decoy-state methods for secure imaging. This method uses Quantum Key Distribution (QKD) principles to reduce measurement uncertainties and protect data integrity. It is highly effective in low-photon-number regimes for producing high-quality, noise-reduced images. The versatility of decoy-state methods with WCSs (WCS) is also discussed, highlighting their suitability for scenarios requiring higher photon numbers. We emphasize the dual advantages of these techniques: improving image quality through noise reduction and enhancing data security with quantum encryption, suggesting significant potential for quantum imaging in various applications, from delicate biological imaging to secure quantum communication.
... Quantum computing has been proven to be more efficient when solving a specific class of problems compared to classical digital computers [2,3]. At present, the technologies for creating and manipulating qubits are implemented in a number of different platforms, including trapped ions [4,5], nuclear spins [6][7][8], superconducting circuits [9,10], and quantum dots [11]. Most recently, qubits based on spin textures [12][13][14][15][16][17] and nano-electromechanical systems [18,19] have been proposed theoretically. ...
... (electron spin resonance, ESR) and electric [18][19][20] (electric dipole spin resonance, EDSR) fields; nuclear qubits are normally driven by nuclear magnetic resonance 23 (NMR), but quadrupolar nuclei can exhibit Electric 24 (NER) or even Acoustic 25 (NAR) resonances. Magnetic drive lends itself to global control methods, where a spatially extended oscillating magnetic field drives multiple qubits 26,27 , whereas electric drive is easier to localise at the nanometre scale. ...
... The antimony donor Like phosphorus 22,23 , arsenic 32 and bismuth 33 , antimony is a group-V donor in silicon. It behaves as a hydrogenic impurity where the Coulomb potential of the nuclear charge loosely binds an electron in a 1slike orbital 14 . ...
... Electron spin resonance (ESR) 22 is achieved by adding the driving termĤ ESR = B 1 γ eŜx cosð2πf ESR m I tÞ toĤ D 0 , where B 1 is the amplitude of an oscillating magnetic field at one of the eight resonance frequencies f ESR m I determined by the nuclear spin projection m I . Similarly, nuclear magnetic resonance (NMR) 23 requires a magnetic drive termĤ NMR = B 1 γ nÎx cosð2πf NMR m I À1$m I tÞ, applicable to both the neutral (NMR 0 ± 1 ) and the ionised (NMR + ± 1 ) case. The ± 1 subscript indicates that such transitions change the nuclear spin projection by one quantum of angular momentum, i.e., Δm I = ± 1. ...
Efficient scaling and flexible control are key aspects of useful quantum computing hardware. Spins in semiconductors combine quantum information processing with electrons, holes or nuclei, control with electric or magnetic fields, and scalable coupling via exchange or dipole interaction. However, accessing large Hilbert space dimensions has remained challenging, due to the short-distance nature of the interactions. Here, we present an atom-based semiconductor platform where a 16-dimensional Hilbert space is built by the combined electron-nuclear states of a single antimony donor in silicon. We demonstrate the ability to navigate this large Hilbert space using both electric and magnetic fields, with gate fidelity exceeding 99.8% on the nuclear spin, and unveil fine details of the system Hamiltonian and its susceptibility to control and noise fields. These results establish high-spin donors as a rich platform for practical quantum information and to explore quantum foundations.
... Quantum bits encoded into the spin of individual electrons in silicon have shown rapid progress in the past few years 1 . Phosphorus atom qubits in silicon (Si:P), in particular, have allowed for single qubit gates using both electron spin resonance (ESR) 2 and nuclear spin resonance (NMR) 3 with some of the highest fidelities and longest coherence times in the solid state to date [4][5][6][7][8] (Table 1). One of the unique control mechanisms in these atom-based systems is the hyperfine coupling between the electron and nuclear spins, which has been utilized to demonstrate violation of Bell inequalities 6 and a high-fidelity two-qubit gate 8 . ...
Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit $$\sqrt{\mathrm{SWAP}}$$ SWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( $$F=10{0}_{-6}^{+0}$$ F = 10 0 − 6 + 0 %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to $$\left\vert \Downarrow \Downarrow \Downarrow \right\rangle$$ ⇓ ⇓ ⇓ , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of $${T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}$$ T 2 * = 12 μ s .
... Then, the electrostatic potential is increased to ionize the donor atom by removing the electron and only the nuclear spin is manipulated using RF pulses [39]. The readout process using electron spin resonance can be made dependent on the nuclear spin state, thus achieving nuclear readout via spin dependent tunneling of the electron [33,40]. ...
... Thus, our approach, using two MT pulses and OAT, can yield highly coherent SCSs in less than 9 ms-within the dephasing time on current hardware. Faster Rabi frequencies are easily achieved for nuclear magnetic resonance (NMR) methods [34,40], which could reduce the time needed for MT pulses and lead to faster generation and detection of nuclear SCSs. ...
We propose a scheme to generate spin cat states, i.e., superpositions of maximally separated quasiclassical states on a single high-dimensional nuclear spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to drive the nucleus significantly faster than usual gate sequences, achieving collapses and revivals two orders of magnitude faster than the dephasing timescale. Furthermore, these states are engineered without entanglement with an ancilla, hence, are robust against error propagation. With our multitone control, we can realize arbitrary high-spin rotations within an experimentally feasible regime, as well as transform a spin coherent state to a spin cat state using only phase modulation, opening the possibility of storing and manipulating high-fidelity cat states.
... Experimental advancements in the past decades have enabled the precision placement of phosphorus donors in silicon [4][5][6][7][8]. The platform of phosphorus donor-based quantum computing has been bolstered by key milestone achievements over the last decade, including singleshot spin readout [9], the realization of single-electronspin and single-nuclear-spin qubits [10,11], and, more recently, two-qubit SWAP gates [12] and a three-qubitdonor quantum processor with universal logic operation [13]. Exchange coupling between the electronic spins of donors remains a key mechanism for fast coupling of two qubits [12,14]. ...
Atomic engineering in a solid-state material has the potential to functionalize the host with novel phenomena. STM-based lithographic techniques have enabled the placement of individual phosphorus atoms at selective lattice sites of silicon with atomic precision. Here we show that by placing four phosphorus donors spaced 10–15 nm apart from their neighbors in a linear chain, one can realize coherent spin coupling between the end dopants of the chain, analogous to the superexchange interaction in magnetic materials. Since phosphorus atoms are a promising building block of a silicon quantum computer, this enables spin coupling between their bound electrons beyond nearest neighbors, allowing the qubits to be separated by 30–45 nm. The added flexibility in architecture brought about by this long-range coupling not only reduces gate densities but can also reduce correlated noise between qubits from local noise sources that are detrimental to error-correction codes. We base our calculations on a full-configuration-interaction technique in the atomistic tight-binding basis, solving the four-electron problem exactly, over a domain of a million silicon atoms. Our calculations show that superexchange can be tuned electrically through gate voltages where it is less sensitive to charge noise and donor-placement errors.
... On the classical engineering side, they offer compatibility with standard semiconductor microelectronics manufacturing processes; on the quantum side they have recently crossed the threshold of one-and two-qubit logic gate fidelities exceeding 99%. [3][4][5][6] Among the possible physical qubit implementations in semiconductors, donor (also referred to as 'dopant' or 'impurity') atoms in silicon were the first to be proposed [7] and experimentally demonstrated [8,9] as spin qubits. With the introduction of an isotopically enriched 28 Si host matrix, which possesses a significantly reduced residual 29 Si content (< 0.1% [10] ), donor spin qubits have achieved extraordinary values of spin coherence times, both in bulk [11,12] and in single-atom nanoscale devices. ...
... splitting of the electronic and nuclear spin states. The Hamiltonian of the donor system can then be written as [8,9] ...
... [34] Nanoelectronic structures on the surface of the chip provide electrostatic control of the donors, create a single-electron transistor (SET) charge sensor, and deliver microwave and radiofrequency signals through a broadband antenna (Figure 1). With this set-up, we can perform single-shot electron spin readout, [53] and high fidelity (approximately 99.9%) single-shot quantum nondemolition readout of the nuclear spins, [9] as well as nuclear magnetic resonance (NMR) and ESR [8] on all spins involved. ...
Donor spins in silicon‐28 are among the best performing qubits in the solid state, offering unmatched coherence times, gate fidelities beyond 99% and the ability to fabricate arrays using deterministic ion implantation. Donor placement precision is improved upon, advantageous for qubit readout and coupling, by implanting molecule ions that carry bystander atoms to boost the detection confidence. Here, the suitability of phosphorus difluoride (PF2$\rm{PF}_2$) molecule ions is demonstrated to fabricate donor qubits. Using secondary ion mass spectrometry, it is confirmed that (nuclear spin I=1/2$I=1/2$) diffuses away from the implant site while remains close to its original location during a donor activation anneal. Electron spin resonance measurements are then performed on PF2$\rm{PF}_2$‐implanted qubit devices. A pure dephasing time of T2∗=20.5±0.5μs$T_2^*= 20.5\pm 0.5 \mu\rm{s}$ and a coherence time of T2Hahn=424±5μs$T_2^{\text{Hahn}}=424\pm 5 \mu\rm{s}$ are extracted for the P donor electron‐ values comparable to those found in conventional atomic ‐implanted qubit devices. Additionally, the P donor electron is not found to hyperfine couple to any nuclear spins in its vicinity. Molecule ions therefore show great promise for producing high‐precision deterministically‐implanted arrays of long‐lived donor spin qubits.
