Distance measurements via the dipolar interaction are fundamental to the application of nuclear magnetic resonance (NMR) to molecular structure determination, but they only provide information on the absolute distance $r$ and polar angle $θ$ between spins. In this Letter, we present a protocol to also retrieve the azimuth angle $ϕ$. Our method relies on measuring the nuclear precession phase after application of a control pulse with a calibrated external radio-frequency coil. We experimentally demonstrate three-dimensional positioning of individual carbon-13 nuclear spins in a diamond host crystal relative to the central electronic spin of a single nitrogen-vacancy center. The ability to pinpoint three-dimensional nuclear locations is central for realizing a nanoscale NMR technique that can image the structure of single molecules with atomic resolution.
We propose a method to measure the hyperfine vectors between a nitrogen-vacancy (NV) center and an environment of interacting nuclear spins. Our protocol enables the generation of tunable electron-nuclear coupling Hamiltonians while suppressing unwanted inter-nuclear interactions. In this manner, each nucleus can be addressed and controlled individually thereby permitting the reconstruction of the individual hyperfine vectors. With this ability the 3D-structure of spin ensembles and spins in bio-molecules can be identified without the necessity of varying the direction of applied magnetic fiel…
We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio-frequency pulses. Moreover, the multi-level structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.
The measurement of single quanta in a collection of coherently interacting objects is transformative in the investigations of emergent quantum phenomena. An isolated nuclear-spin ensemble is a remarkable platform owing to its coherence, but detecting its single spin excitations has remained elusive. Here, we use an electron spin qubit in a semiconductor quantum dot to sense a single nuclear-spin excitation (a nuclear magnon) with 1.9-ppm precision via the 200-kHz hyperfine shift on the 28-GHz qubit frequency. We demonstrate this single-magnon precision across multiple modes identified by nucle…
Detecting and controlling nuclear spin nano-ensembles is crucial for the further development of nuclear magnetic resonance (NMR) spectroscopy and for the emerging solid state quantum technology. Here we present the fabrication of a $\approx$ 1 nanometre thick diamond layer consisting of $^{13}$C nuclear spins doped with Nitrogen-Vacancy centres (NV) embedded in a spin-free $^{12}$C crystal matrix. A single NV in the vicinity of the layer is used for polarization of the $^{13}$C spins and the readout of their magnetization. We demonstrate a method for coherent control of few tens of nuclear spi…
Hyperfine interactions with a nuclear spin environment fundamentally limit the coherence properties of confined electron spins in the solid-state. Here, we show that a quantum interference effect in optical absorption from two electronic spin states of a solid-state emitter can be used to prepare the surrounding environment of nuclear spins in well-defined states, thereby suppressing electronic spin dephasing. The evolution of the coupled electron-nuclei system into a coherent population trapping state by optical excitation induced nuclear spin diffusion can be described in terms of Levy fligh…
We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system suitable to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds an electronic spin 1/2 coupled through hyperfine interaction to a nuclear spin 7/2, both characterized by remarkable coherence. We demonstrate this by an extensive broadband nuclear magnetic resonance study, which allow us to characterize the nuclear spin-Hamiltonian and to measure the spin dephasing time as a function of the magnetic field. In addition, we combine targeted measurements …
Future communication and computation technologies that exploit quantum information require robust and well-isolated qubits. Electron spins in III-V semiconductor quantum dots, while promising candidates, see their dynamics limited by undesirable hysteresis and decohering effects of the nuclear spin bath. Replacing electrons with holes should suppress the hyperfine interaction and consequently eliminate strong nuclear effects. Using picosecond optical pulses, we demonstrate coherent control of a single hole qubit and examine both free-induction and spin-echo decay. In moving from electrons to h…
Magnetic fluctuations caused by the nuclear spins of a host crystal are often the leading source of decoherence for many types of solid-state spin qubit. In group-IV materials, the spin-bearing nuclei are sufficiently rare that it is possible to identify and control individual host nuclear spins. This work presents the first experimental detection and manipulation of a single $^{29}$Si nuclear spin. The quantum non-demolition (QND) single-shot readout of the spin is demonstrated, and a Hahn echo measurement reveals a coherence time of $T_2 = 6.3(7)$ ms - in excellent agreement with bulk experi…
Coherent population trapping (CPT) provides a highly sensitive means for probing the energy level structure of an atomic system. For a nitrogen vacancy center in diamond, the CPT offers an alternative to the standard optically-detected magnetic resonance method for measuring the hyperfine structure of the electronic ground states. We show that the nuclear spin dependent CPT measures directly the hyperfine splitting of these states due to the 14N nuclear spin. The CPT spectral response obtained in the presence of a strong microwave field, resonant or nearly resonant with a ground state spin tra…
The understanding of weak measurements and interaction-free measurements has greatly expanded the conceptual and experimental toolbox to explore the quantum world. Here we demonstrate single-shot variable-strength weak measurements of the electron and the nuclear spin states of a single $^{31}$P donor in silicon. We first show how the partial collapse of the nuclear spin due to measurement can be used to coherently rotate the spin to a desired pure state. We explicitly demonstrate that phase coherence is preserved throughout multiple sequential single-shot weak measurements, and that the parti…
Coherent excitation of an ensemble of quantum objects underpins quantum many-body phenomena, and offers the opportunity to realize a quantum memory to store information from a qubit. Thus far, a deterministic and coherent interface between a single quantum system, e.g. a qubit, and such an ensemble has remained elusive. We first use an electron to cool the mesoscopic nuclear-spin ensemble of a semiconductor quantum dot to the nuclear sideband-resolved regime. We then implement an all-optical approach to access these individual quantized electronic-nuclear spin transitions. Finally, we perform …
Phase locking nuclear spins in silicon with spin-orbit coupling
Department of Physics and Astronomy, University of Rochester（罗切斯特大学物理与天文系）；University of Rochester Center for Coherence and Quantum Science（罗切斯特大学相干性与量子科学中心）
Nuclear spins interact weakly with their environment. In particular, they are generally insensitive to mechanical vibrations. Here, we successfully demonstrate the coherent coupling of mechanics to a single nuclear spin. This coupling is mediated by a silicon vacancy (SiV) centre in diamond, taking advantage of its large strain susceptibility and hyperfine interaction with nuclear spins. Importantly, we demonstrate that the nuclear spin retains its excellent coherence properties even in the presence of this coupling. This provides a way to leverage nuclear spins as quantum memories for mechani…
We show that detuned optical pulse trains with a modest spectral width can polarize nuclear spins in InAs quantum dots. The pulse bandwidth is large enough to excite a coherent superposition of both electron spin eigenstates in these negatively charged dots but narrow enough to give partial spectral selectivity between the eigenstates. The coherent precession of electron spin states and periodic excitation focuses the nuclear spin distribution, producing a discrete set of precession modes. The spectral selectivity generates a net nuclear polarization, through a mechanism that relies on optical…
We have demonstrated electron-electron and electron-nuclear spin manipulations of Gd3+ ion in CaWO4 crystal. The results suggest that the studied system is perspective for multiqubit implementation in quantum computing.
Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, e.g. in chemistry, medicine, materials science and mining. Nuclear spins also featured in early ideas and demonstrations of quantum information processing. Scaling up these ideas requires controlling individual nuclei, which can be detected when coupled to an electron. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. C…
We demonstrate coherent control of two nuclear spins mediated by the magnetic resonance of a hyperfine-coupled electron spin. This control is used to create a double nuclear coherence in one of the two electron spin manifolds, starting from an initial thermal state, in direct analogy to the creation of an entangled (Bell) state from an initially pure unentangled state. We identify challenges and potential solutions to obtaining experimental gate fidelities useful for quantum information processing in this type of system.
Coherent population transfer between nuclear states using x-ray laser pulses is studied. The laser pulses drive two nuclear transitions between three nuclear states in a setup reminding of stimulated Raman adiabatic passage used for atomic coherent population transfer. To compensate for the lack of $γ$-ray laser sources, we envisage accelerated nuclei interacting with two copropagating or crossed x-ray laser pulses. The parameter regime for nuclear coherent population transfer using fully coherent light generated by future X-Ray Free-Electron Laser facilities and moderate or strong acceleratio…
Electron spins in quantum dots under coherent control exhibit a number of novel feedback processes. Here, we present experimental and theoretical evidence of a feedback process between nuclear spins and a single electron spin in a single charged InAs quantum dot, controlled by the coherently modified probability of exciting a trion state. We present a mathematical model describing competition between optical nuclear pumping and nuclear spin-diffusion inside the quantum dot. The model correctly postdicts the observation of a hysteretic sawtooth pattern in the free-induction-decay of the single …
Collective Nuclear Polaritons with Coherent and Tunable Excitation Dynamics
Zhejiang Normal University（浙江师范大学）；Zhejiang Institute of Photoelectronics（浙江省光电子研究所）；Abrikosov Center for Theoretical Physics, Moscow Center for Advanced Studies（莫斯科高级研究中心阿布里科索夫理论物理中心）；School of Science, Westlake University（西湖大学理学院）
We use nominally forbidden electron-nuclear spin transitions in nitrogen-vacancy (NV) centers in diamond to demonstrate coherent manipulation of a nuclear spin ensemble using microwave fields at room temperature. We show that employing an off-axis magnetic field with a modest amplitude($\approx$ 0.01 T) at an angle with respect to the NV natural quantization axes is enough to tilt the direction of the electronic spins, and enable efficient spin exchange with the nitrogen nuclei of the NV center. We could then demonstrate fast Rabi oscillations on electron-nuclear spin exchanging transitions, c…
We report the detection and polarization of nuclear spins in diamond at room temperature by using a single nitrogen-vacancy (NV) center. We use Hartmann-Hahn double resonance to coherently enhance the signal from a single nuclear spin while decoupling from the noisy spin-bath, which otherwise limits the detection sensitivity. As a proof-of-principle we: (I) observe coherent oscillations between the NV center and a weakly coupled nuclear spin, (II) demonstrate nuclear bath cooling which prolongs the coherence time of the NV sensor by more than a factor of five. Our results provide a route to na…
The possibility to control the coherent decay of resonant excitations in nuclear forward scattering is investigated. By changing abruptly the direction of the nuclear hyperfine magnetic field, the coherent scattering of photons can be manipulated and even completely suppressed via quantum interference effects between the nuclear transition currents. The efficiency of the coherent decay suppression and the dependence of the scattered light polarization on the specific switching parameters is analyzed in detail. Using a sophisticated magnetic switching sequence involving four rotations of the hy…
Individually addressed Er$^{3+}$ ions in solid-state hosts are promising resources for quantum repeaters, because of their direct emission in the telecom band and compatibility with silicon photonic devices. While the Er$^{3+}$ electron spin provides a spin-photon interface, ancilla nuclear spins could enable multi-qubit registers with longer storage times. In this work, we demonstrate coherent coupling between the electron spin of a single Er$^{3+}$ ion and a single $I=1/2$ nuclear spin in the solid-state host crystal, which is a fortuitously located proton ($^1$H). We control the nuclear spi…
Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications alike. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool to control electron dynamics. Recently, coherent control in the extreme-ultraviolet range was demonstrated, with timing stability of the applied light fields in the few-attosecond range. At hard x-ray energies, Mössbauer nuclei feature narrow nuclear resonances, and spectroscopy of these resonances is a widespread tool to study magnetic, structural and dynamical properties of matter. It has…
A practical source of high fidelity entangled photons is desirable for quantum information applications and exploring quantum physics. Semiconductor quantum dots have recently been shown to conveniently emit entangled light when driven electrically, however the fidelity was not optimal. Here we show that the fidelity is not limited by decoherence, but by coherent interaction with nuclei. Furthermore we predict that on 100μs timescales, strongly enhanced fidelities could be achieved. This insight could allow tailoring of quantum logic to operate using quantum dots in the fault tolerant regime.
Nuclear spins of noble-gas atoms are exceptionally isolated from the environment and can maintain their quantum properties for hours at room temperature. Here we develop a mechanism for entangling two such distant macroscopic ensembles by using coherent light input. The interaction between the light and the noble-gas spins in each ensemble is mediated by spin-exchange collisions with alkali-metal spins, which are only virtually excited. The relevant conditions for experimental realizations with ^{3}\text{He} or ^{129}\text{Xe} are outlined.
Coherent control of nuclear pumping in a three level system driven by x-ray light is investigated. In single nuclei, the pumping performance is determined by the branching ratio of the excited state populated by the x-ray pulse. Our results are based on the observation that in ensembles of nuclei, cooperative excitation and decay leads to a greatly modified nuclear dynamics, which we characterize by a time-dependent cooperative branching ratio. We discuss prospects of steering the x-ray pumping by coherently controlling the cooperative decay. First, we study an ideal case with purely superradi…
Electron spin qubits in molecular systems offer high reproducibility and the ability to self assemble into larger architectures. However, interactions between neighbouring qubits are 'always-on' and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both controllably turn on/off dipolar interactions between neighbouring spins and benefit from the long nucl…
Generation of single-photon entanglement is discussed in nuclear forward scattering. Using successive switchings of the direction of the nuclear hyperfine magnetic field, the coherent scattering of photons on nuclei is controlled such that two signal pulses are generated out of one initial pump pulse. The two time-resolved correlated signal pulses have different polarizations and energy in the keV regime. Spatial separation of the entangled field modes and extraction of the signal from the background can be achieved with the help of state-of-the-art x-ray polarizers and piezoelectric fast stee…
Interfacing between various elements of a computer - from memory to processors to long range communication - will be as critical for quantum computers as it is for classical computers today. Paramagnetic rare earth doped crystals, such as Nd$^{3+}$:Y$_2$SiO$_5$ (YSO), are excellent candidates for such a quantum interface: they are known to exhibit long optical coherence lifetimes (for communication via optical photons), possess a nuclear spin (memory) and have in addition an electron spin that can offer hybrid coupling with superconducting qubits (processing). Here we study two of these three …
We theoretically demonstrate that nuclear spins can be harnessed to coherently control two-electron spin states in a double quantum dot. Hyperfine interactions lead to an avoided crossing between the spin singlet state and the ms = +1 triplet state, T_+ . We show that a coherent superposition of singlet and triplet states can be achieved using finite-time Landau-Zener-Stückelberg interferometry. In this system the coherent rotation rate is set by the Zeeman energy, resulting in ~1 nanosecond single spin rotations. We analyze the coherence of this spin qubit by considering the coupling to the n…
The interaction between super-intense coherent x-ray light and nuclei is studied theoretically. One of the main difficulties with driving nuclear transitions arises from the very narrow nuclear excited state widths which limit the coupling between laser and nuclei. In the context of direct laser-nucleus interaction, we consider the nuclear width broadening that occurs when in solid targets, the excitation caused by a single photon is shared by a large number of nuclei, forming a collective excited state. Our results show that for certain isotopes, cooperative effects may lead to an enhancement…
Coherent control of quantum systems has far-reaching implications in quantum engineering. In this context, coherent population trapping (CPT) involving dark resonances has played a prominent role, leading to a wealth of major applications including laser cooling of atoms and molecules, optical magnetometry, light storage and highly precise atomic clocks. Extending CPT methods to individual solid-state quantum systems has been only achieved in cryogenic environments for electron spin impurities and superconducting circuits. Here, we demonstrate efficient CPT of a single nuclear spin in a room t…
An experimental platform of ultralow-temperature pulsed ENDOR (electron-nuclear double resonance) spectroscopy is constructed for the bulk materials. Coherent property of the coupled electron and nuclear spins of the rare-earth (RE) dopants in a crystal (143Nd3+:Y2SiO5) is investigated from 100 mK to 6 K. At the lowest working temperatures, two-pulse-echo coherence time exceeding 2 ms and 40 ms are achieved for the electron and nuclear spins, while the electronic Zeeman and hyperfine population lifetimes are more than 15 s and 10 min. With the aid of the near-unity electron spin polarization a…
Coherent storage and phase modulation of x-ray single-photon wave packets in resonant scattering of light off nuclei is investigated theoretically. We show that by switching off and on again the magnetic field in the nuclear sample, phase-sensitive storage of photons in the keV regime can be achieved. Corresponding $π$ phase modulation of the stored photon can be accomplished if the retrieving magnetic field is rotated by $180^{\circ}$. The development of such x-ray single-photon control techniques is a first step towards forwarding quantum optics and quantum information to shorter wavelengths…
Optimizing the frequency positioning of tunable couplers in a circuit QED processor to mitigate spectator effects on quantum operations
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克与卡弗里纳米科学研究所）；Orange Quantum Systems（橙量子系统）；Quantware B.V.（Quantware有限公司）
Localization and coherent control of 25 nuclear spins in Silicon Carbide
University of Stuttgart（斯图加特大学）；Eötvös Loránd University（罗兰大学）；MTA–ELTE Lendület “Momentum” NewQubit Research Group（匈牙利科学院-罗兰大学Lendulet“动量”NewQubit研究组）；Leibniz-Institute of Surface Engineering (IOM)（莱布尼兹表面工程研究所）；Linköping University（林雪平大学）；Max Planck Institute for solid state physics（马克斯·普朗克固体物理研究所）
Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudo-nuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo-NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: $ i) $ the free evolution of the NMR quadrupolar system and, by analogy with the e…
The controlled transfer of nuclear state population using two x-ray laser pulses is investigated theoretically. The laser pulses drive two nuclear transitions in a nuclear three-level system facilitating coherent population transfer via the quantum optics technique of stimulated Raman adiabatic passage. To overcome present limitations of the x-ray laser frequency, we envisage accelerated nuclei interacting with two copropagating or crossed x-ray laser pulses in a three-beam setup. We present a systematic study of this setup providing both pulse temporal sequence and laser pulse intensity for o…
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of the potential energy surfaces between wavepackets therefore usually have to be approximated. It is shown, that if a modified form of valence bond theory is used instead of the usual MO-based theories, the matrix elements can be obtained exactly. This is so because the molecular Hamiltonian only contains the Coulomb potential, for which matrix elements between …
We introduce an optical tweezer platform for assembling and individually manipulating a two-dimensional register of nuclear spin qubits. Each nuclear spin qubit is encoded in the ground $^{1}S_{0}$ manifold of $^{87}$Sr and is individually manipulated by site-selective addressing beams. We observe that spin relaxation is negligible after 5 seconds, indicating that $T_1\gg5$ s. Furthermore, utilizing simultaneous manipulation of subsets of qubits, we demonstrate significant phase coherence over the entire register, estimating $T_2^\star = \left(21\pm7\right)$ s and measuring $T_2^\text{echo}=\l…
We investigate the electron and nuclear spin coherence properties of ytterbium ($\mathrm{Yb}^{3+}$) ions with non-zero nuclear spin, within an yttrium orthosilicate (Y$_2$SiO$_5$) crystal, with a view to their potential application in quantum memories or repeaters. We find electron spin-lattice relaxation times are maximised at low magnetic field ($<100$ mT) where $g~\sim6$, reaching 5 s at 2.5 K, while coherence times are maximised when addressing ESR transitions at higher fields where $g\sim0.7$ where a Hahn echo measurement yields $T_2$ up to 73 $μ$s. Dynamical decoupling (XY16) can be used…
We investigate the Smith-Purcell emission produced by electron- or ion-beam-driven coherent excitation of nuclei arranged in periodic crystal lattices. The excitation and subsequent radiative decay of the nuclei can leave the target in the initial ground state after $γ$-ray emission, thus generating a coherent superposition of the far-field photon amplitude emanating from different nuclei that results in sharp angular patterns at spectrally narrow nuclear transition energies. We focus on Fe-57 as an example of two-level nuclear lossy system giving rise to Smith-Purcell emission at 14.4\,keV wi…
