We simulate the dynamics of varying density quasi-two-dimensional spin ensembles in solid-state systems, focusing on the nitrogen-vacancy centers in diamond. We consider the effects of various control sequences on the averaged dynamics of large ensembles of spins, under a realistic "spin-bath" environment. We reveal that spin locking is efficient for decoupling spins initialized along the driving axis, both from coherent dipolar interactions and from the external spin-bath environment, when the driving is two orders of magnitude stronger than the relevant coupling energies. Since the application of standard pulsed dynamical decoupling sequences leads to strong decoupling from the environment, while other specialized pulse sequences can decouple coherent dipolar interactions, such sequences can be used to identify the dominant interaction type. Moreover, a proper combination of pulsed decoupling sequences could lead to the suppression of both interaction types, allowing additional spin manipulations. Finally, we consider the effect of finite-width pulses on these control protocols and identify improved decoupling efficiency with increased pulse duration, resulting from the interplay of dephasing and coherent dynamics.
New magnetometry techniques based on Nitrogen Vacancy (NV) defects in diamond have received much attention of late as a means to probe nanoscale magnetic environments. The sensitivity of a single NV magnetometer is primarily determined by the transverse spin relaxation time, $T_2$. Current approaches to improving the sensitivity employ crystals with a high NV density at the cost of spatial resolution, or extend $T_2$ via the manufacture of novel isotopically pure diamond crystals. We adopt a complementary approach, in which optimal dynamic decoupling techniques extend coherence times out to th…
Ultimate sensitivity for quantum magnetometry using nitrogen-vacancy (NV) centers in diamond is limited by number of NV centers and coherence time. Microwave irradiation with a high and homogeneous power density for a large detection volume is necessary to achieve highly sensitive magnetometer. Here, we demonstrate a microwave resonator to enhance the power density of the microwave field and an optical system with a detection volume of 1.4e-3 mm$^3$. The strong microwave field enables us to achieve 48 ns Rabi oscillation which is sufficiently faster than the phase relaxation time of NV centers…
Dynamical decoupling is a powerful technique for extending the coherence time (T$_2$) of qubits. We apply this technique to the electron spin qubit of a single nitrogen-vacancy center in type IIa diamond. In a crystal with natural abundance of $^{13}$C nuclear spins, we extend the decoherence time up to 2.2 ms. This is close to the T$_1$ value of this NV center (4 ms). Since dynamical decoupling must perform well for arbitrary initial conditions, we measured the dependence on the initial state and compared the performance of different sequences with respect to initial state dependence and robu…
We perform a detailed theoretical-experimental study of the dynamical decoupling (DD) of the nitrogen-vacancy (NV) center in diamond. We investigate the DD sequences applied to suppress the dephasing of the electron spin of the NV center induced by the coupling to a spin bath composed of the substitutional nitrogen atoms. The decoupling efficiency of various DD schemes is studied, including both periodic and periodic pulse sequences. For ideal control pulses, we find that the DD protocols with the Carr-Purcell-Meiboom-Gill (CPMG) timing of the pulses provides best performance. We show that, as…
Single-molecule nuclear magnetic resonance (NMR) is a crown-jewel challenge in the field of magnetic resonance spectroscopy and has important applications in chemical analysis and in quantum computing. Recently, it becomes possible to tackle this grand challenge thanks to experimental advances in preserving quantum coherence of nitrogen-vacancy (NV) center spins in diamond as a sensitive probe and theoretical proposals on atomic-scale magnetometry via dynamical decoupling control. Through decoherence measurement of NV centers under dynamical decoupling control, sensing of single $^{13}\textbf{…
We use multi-pulse dynamical decoupling to increase the coherence lifetime (T2) of large numbers of nitrogen-vacancy (NV) electronic spins in room temperature diamond, thus enabling scalable applications of multi-spin quantum information processing and metrology. We realize an order-of-magnitude extension of the NV multi-spin T2 for diamond samples with widely differing spin environments. For samples with nitrogen impurity concentration <~1 ppm, we find T2 > 2 ms, comparable to the longest coherence time reported for single NV centers, and demonstrate a ten-fold enhancement in NV multi-spin se…
To implement reliable quantum information processing, quantum gates have to be protected together with the qubits from decoherence. Here we demonstrate experimentally on nitrogen-vacancy system that by using continuous wave dynamical decoupling method, not only the coherence time is prolonged by about 20 times, but also the quantum gates is protected for the duration of controlling time. This protocol shares the merits of retaining the superiority of prolonging the coherence time and at the same time easily combining with quantum logic tasks. It is expected to be useful in task where duration …
We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to $77$ K suppresses longitudinal spin relaxation $T_1$ effects and DD microwave pulses are used to increase the transverse coherence time $T_2$ from $\sim 0.7$ ms up to $\sim 30$ ms. We extend previous work of single-axis (CPMG) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance o…
Identifying weakly coupled nuclear spins around single electron spins is a key step of implementing quantum information processing using coupled electron-nuclei spin systems or sensing like single spin nuclear magnetic resonance detection using diamond defect spins. Dynamical decoupling control of the center electron spin with periodic pulse sequences [e.g., the Carre-Purcell-Meiboom-Gill (CPMG) sequence] has been successfully used to identify single nuclear spins and to resolve structure of nuclear spin clusters. Here, we design a new type of pulse sequences by replacing the repetition unit (…
Inhomogeneous dephasing from uncontrolled environmental noise can limit the coherence of a quantum sensor or qubit. For solid state spin qubits such as the nitrogen-vacancy (NV) center in diamond, a dominant source of environmental noise is magnetic field fluctuations due to nearby paramagnetic impurities and instabilities in a magnetic bias field. In this work, we use ac stress generated by a diamond mechanical resonator to engineer a dressed spin basis in which a single NV center qubit is less sensitive to its magnetic environment. For a qubit in the thermally isolated subspace of this prote…
Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center. We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits. We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of C…
We study the parametric interaction between a single Nitrogen-Vacancy electronic spin and a diamond mechanical resonator in which the spin is embedded. Coupling between spin and oscillator is achieved by crystal strain, which is generated upon actuation of the oscillator and which parametrically modulates the spins' energy splitting. Under coherent microwave driving of the spin, this parametric drive leads to a locking of the spin Rabi frequency to the oscillator mode in the megahertz range. Both the Rabi oscillation decay time and the inhomogeneous spin dephasing time increase by two orders o…
We experimentally demonstrate over two orders of magnitude increase in the coherence time of nitrogen vacancy centres in diamond by implementing decoupling techniques. We show that equal pulse spacing decoupling performs just as well as non-periodic Uhrig decoupling and has the additional benefit that it allows us to take advantage of "revivals" in the echo (due to the coherent nature of the bath) to explore the longest coherence times. At short times, we can extend the coherence of particular quantum states out from T_2*=2.7 us out to an effective T_2 > 340 us. For preserving arbitrary states…
Robust gigahertz-range ac magnetometry with an ensemble of NV centers in diamond using concatenated continuous dynamical decoupling
Ulm University（乌尔姆大学）；Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Advanced Materials Laboratory, Sumitomo Electric Industries Ltd.（住友电工株式会社先进材料实验室）；Quantum Materials and Applications Research Center, National Institutes for Quantum Science and Technology（量子科学和技术研究院量子材料与应用程序研究中心）；Faculty of Pure and Applied Sciences, University of Tsukuba（筑波大学理工学部）
The charge degree of freedom in solid-state defects fundamentally underpins the electronic spin degree of freedom, a workhorse of quantum technologies. Here we study charge state properties of individual near-surface nitrogen-vacancy (NV) centers in diamond, where NV$^{-}$ hosts the metrologically relevant electron spin. We find that NV$^{-}$ initialization fidelity varies between individual centers and over time, and we alleviate the deleterious effects of reduced NV$^{-}$ initialization fidelity via logic-based initialization. We also find that NV$^{-}$ can ionize in the dark, which compromi…
Sensing the internal dynamics of individual nuclear spins or clusters of nuclear spins has recently become possible by observing the coherence decay of a nearby electronic spin: the weak magnetic noise is amplified by a periodic, multi-pulse decoupling sequence. However, it remains challenging to robustly infer underlying atomic-scale structure from decoherence traces in all but the simplest cases. We introduce Floquet spectroscopy as a versatile paradigm for analysis of these experiments, and argue it offers a number of general advantages. In particular, this technique generalises to more com…
We theoretically study the decoherence and the dynamical decoupling control of nitrogen-vacancy center electron spins in high-purity diamond, where the hyperfine interaction with $^{13}$C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flip-flops. The importance of different elementary processes…
Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers (${\text{NV}}^{-}$) have been proposed as a platform to generate macroscopic spatial superpositions. Requirements for this include having a long ${\text{NV}}^{-}$ spin coherence time, which necessitates formulating a dynamical decoupling strategy in which the regular spin flips do not cancel the growth of the superposition through the Stern-Gerlach effect in an inhomogeneous magnetic field. Here, we propose a scheme to place a $250$-nm-diameter diamond in a superposition with spatial separation of over $250$ nm, whil…
Nitrogen-vacancy centres (NVs) in diamond are attractive for research straddling quantum information science and nanoscale magnetometry and thermometry. While ultrapure bulk diamond NVs sustain the longest spin coherence times among optically accessible spins, nanodiamond NVs display persistently poor spin coherence. Here we introduce high-purity nanodiamonds accommodating record-long NV coherence times, >60 us, observed via universal dynamical decoupling. We show that the main contribution to decoherence comes from nearby nitrogen impurities rather than surface states. We protect the NV spin …
Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We dramatically suppress the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence is preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement is found to follow a general scaling with the number of decoupling pulses. No limit is observed for the decoupling action up to 136 pulses, for which the coherence time is enhanced …
We report on the noise spectrum experienced by few nanometer deep nitrogen-vacancy centers in diamond as a function of depth, surface coating, magnetic field and temperature. Analysis reveals a double-Lorentzian noise spectra consistent with a surface electronic spin bath, with slower dynamics due to spin-spin interactions and faster dynamics related to phononic coupling. These results shed new light on the mechanisms responsible for surface noise affecting shallow spins at semiconductor interfaces, and suggests possible directions for further studies. We demonstrate dynamical decoupling from …
Nitrogen vacancy (NV-) color centers in diamond are a prime candidate for use in quantum information devices, owing to their spin-1 ground state, straightforward optical initialization and readout, and long intrinsic coherence times in a room-temperature solid. While the 13C nuclear spin is often a dominant source of magnetic noise, we observe transitions between electron-nuclear hyperfine states of NV- centers in 99% 13C diamond that are robust to decoherence. At magnetic field strengths ranging from 550 - 900 G, these transitions are observable by optically detected magnetic resonance (ODMR)…
Arrays of NV centers in the diamond have the potential in the fields of chip-scale quantum information processing and nanoscale quantum sensing. However, determining their orientations one by one is resource intensive and time consuming. Here, in this paper, by combining scanning confocal fluorescence images and optical detected magnetic resonance, we realized a method of identifying single NV centers with the same orientation, which is practicable and high efficiency. In the proof of principle experiment, five single NV centers with the same orientation in a NV center array were identified. A…
We propose a scheme for mixed dynamical decoupling (MDD), where we combine continuous dynamical decoupling with robust sequences of phased pulses. Specifically, we use two fields for decoupling, where the first continuous driving field creates dressed states that are robust to environmental noise. Then, a second field implements a robust sequence of phased pulses to perform inversions of the dressed qubits, thus achieving robustness to amplitude fluctuations of both fields. We show that MDD outperforms standard concatenated continuous dynamical decoupling in realistic numerical simulations for…
Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Fur…
We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences [Physical Review Letters 122, 200403 (2019)] can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to $π$ pulse imperfections and spurious responses due to finite-width $π$ pulses. This enhances selectivity of quantum sensors such as those based on NV centers in diamond.
Realistic quantum computing is subjected to noise. A most important frontier in research of quantum computing is to implement noise-resilient quantum control over qubits. Dynamical decoupling can protect coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which automatically suppresses the noise effect. We designed and implemented a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling cont…
We present a protocol to selectively decouple, recouple, and engineer effective couplings in mesoscopic dipolar spin networks. In particular, we develop a versatile protocol that relies upon magic angle spinning to perform Hamiltonian engineering. By using global control fields in conjunction with a local actuator, such as a diamond Nitrogen Vacancy center located in the vicinity of a nuclear spin network, both global and local control over the effective couplings can be achieved. We show that the resulting effective Hamiltonian can be well understood within a simple, intuitive geometric pictu…
We demonstrate fluorescence thermometry techniques with sensitivities approaching 10 mK Hz^(-1/2) based on the spin-dependent photoluminescence of nitrogen vacancy (NV) centers in diamond. These techniques use dynamical decoupling protocols to convert thermally induced shifts in the NV center's spin resonance frequencies into large changes in its fluorescence. By mitigating interactions with nearby nuclear spins and facilitating selective thermal measurements, these protocols enhance the spin coherence times accessible for thermometry by 45x, corresponding to a 7x improvement in the NV center'…
Coupled spin chains are promising candidates for 'wiring up' qubits in solid-state quantum computing (QC). In particular, two nitrogen-vacancy centers in diamond can be connected by a chain of implanted nitrogen impurities; when driven by a suitable global fields the chain can potentially enable quantum state transfer at room temperature. However, our detailed analysis of error effects suggests that foreseeable systems may fall far short of the fidelities required for QC. Fortunately the chain can function in the more modest role as a mediator of noisy entanglement, enabling QC provided that w…
It was recently demonstrated that bulk nuclear polarization can be obtained using Nitrogen Vacancy (NV) color centers in diamonds, even at ambient conditions. This is based on the optical polarization of the NV electron spin, and using several polarization transfer methods. One such method is the NOVEL sequence, where a spin-locked sequence is applied on the NV spin, with a microwave power equal to the nuclear precession frequency. This was performed at relatively high fields, to allow for both polarization transfer and noise decoupling. As a result, this scheme requires accurate magnetic fiel…
Ensembles of nitrogen-vacancy (NV) centers in diamond are widely used as AC magnetometers. While such measurements are usually performed using standard (XY) dynamical decoupling (DD) protocols at room temperature, we study the sensitivities achieved by utilizing various DD protocols, for measuring magnetic AC fields at frequencies in the 10-250 kHz range, at room temperature and 77 K. By performing measurements on an isotopically pure $^{12}$C sample, we find that the Carr-Purcell-Meiboom-Gill (CPMG) protocol, which is not robust against pulse imperfections, is less efficient for magnetometry …
Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling (DD) attenuates the destructive effect of the environmental noise, but so far it has been used primarily in the context of quantum memories. Here, we present a general scheme for combining DD with quantum logical gate operations and demonstrate its performance on the example of an electron spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than…
Although a nuclear spin is weakly coupled to its environment, due to its small gyromagnetic ratio, its coherence time is limited by the hyperfine coupling to a nearby noisy electron. Here, we propose to utilize continuous dynamical decoupling to refocus the coupling to the electron. If the random phase accumulated by the nuclear spin through the reduced coupling terms is sufficient small, we can increase the nuclear coherence time. Initially, we demonstrate this on a simple case with a two-level electron spin, while taking all relevant hyperfine coupling terms and noise terms into account. We …
We propose a protocol that achieves arbitrary N-qubit interactions between nuclear spins and that can measure directly nuclear many-body correlators by appropriately making the nuclear spins interact with a nitrogen vacancy (NV) center electron spin. The method takes advantage of recently introduced dynamical decoupling techniques and demonstrates that action on the electron spin is sufficient to fully exploit nuclear spins as robust quantum registers. Our protocol is general, being applicable to other nuclear spin based platforms with electronic spin defects acting as mediators as the case of…
We experimentally resolve several weakly coupled nuclear spins in diamond using a series of novelly designed dynamical decoupling controls. Some nuclear spin signals, hidden by decoherence under ordinary dynamical decoupling controls, are shifted forward in time domain to the coherence time range and thus rescued from the fate of being submerged by the noisy spin bath. In this way, more and remoter single nuclear spins are resolved. Additionally, the field of detection can be continuously tuned on sub-nanoscale. This method extends the capacity of nanoscale magnetometry and may be applicable i…
The studies of many-body dynamics of interacting spin ensembles, as well as quantum sensing in solid state systems, are often limited by the need for high spin concentrations, along with efficient decoupling of the spin ensemble of interest from its spin-bath environment. In particular, for an ensemble of nitrogen-vacancy (NV) centers in diamond, high conversion efficiencies between nitrogen (P1) defects and NV centers are essential, while maintaining long coherence times of an NV ensemble. In this work, we study the effect of electron irradiation on the conversion efficiency and the coherence…
Group-IV color centers in diamond are a promising light-matter interface for quantum networking devices. The negatively charged tin-vacancy center (SnV) is particularly interesting, as its large spin-orbit coupling offers strong protection against phonon dephasing and robust cyclicity of its optical transitions towards spin-photon entanglement schemes. Here, we demonstrate multi-axis coherent control of the SnV spin qubit via an all-optical stimulated Raman drive between the ground and excited states. We use coherent population trapping and optically driven electronic spin resonance to confirm…
Spin qubits with long dephasing times are an essential requirement for the development of new quantum technologies and have many potential applications ranging from quantum information processing to quantum memories and quantum networking. Here we report a theoretical study and the calculation of the spin dephasing time of defect color centers for the negatively charged nitrogen vacancy center in diamond. We employ ab initio density functional theory to compute the electronic structure, and extract the dephasing time using a cumulant expansion approach. We find that phonon-induced dephasing is…
Quantum bits or qubits naturally decohere by becoming entangled with uncontrollable environments. Dynamical decoupling is thereby required to disentangle qubits from an environment by periodically reversing the qubit bases, but this causes rotation error to accumulate. Whereas a conventional qubit is rotated within the SU(2) two-level system, a geometric qubit defined in the degenerate subspace of a V-shaped SU(3) three-level system is geometrically rotated via the third ancillary level to acquire a geometric phase. We here demonstrate that, simply by introducing detuning, the dynamical decoup…
Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen vacancy (NV) center in diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC field can be generally obtained…
Quantum probes can measure time-varying fields with high sensitivity and spatial resolution, enabling the study of biological, material, and physical phenomena at the nanometer scale. In particular, nitrogen-vacancy centers in diamond have recently emerged as promising sensors of magnetic and electric fields. Although coherent control techniques have measured the amplitude of constant or oscillating fields, these techniques are not suitable for measuring time-varying fields with unknown dynamics. Here we introduce a coherent acquisition method to accurately reconstruct the temporal profile of …
Nuclear spins in certain solids couple weakly to their environment, making them attractive candidates for quantum information processing and inertial sensing. When coupled to the spin of an optically-active electron, nuclear spins can be rapidly polarized, controlled and read via lasers and radiofrequency fields. Possessing coherence times of several milliseconds at room temperature, nuclear spins hosted by a nitrogen-vacancy center in diamond are thus intriguing systems to observe how classical physical rotation at quantum timescales affects a quantum system. Unlocking this potential is hampe…
The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins aro…
Shallow nitrogen-vacancy (NV) centers in diamond are promising for nano-magnetometry for they can be placed proximate to targets. To study the intrinsic magnetic properties, zero-field magnetometry is desirable. However, for shallow NV centers under zero field, the strain near diamond surfaces would cause level anti-crossing between the spin states, leading to clock transitions whose frequencies are insensitive to magnetic signals. Furthermore, the charge noises from the surfaces would induce extra spin decoherence and hence reduce the magnetic sensitivity. Here we demonstrate that the relativ…
