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Quantum metrology with single spins in diamond under ambient conditions

Quantum metrology with single spins in diamond under ambient conditions Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 National Science Review 5: 346–355, 2018 REVIEW doi: 10.1093/nsr/nwx121 Advance access publication 11 October 2017 PHYSICS Quantum metrology with single spins in diamond under ambient conditions Ming Chen, Chao Meng, Qi Zhang, Changkui Duan, Fazhan Shi and Jiangfeng Du ABSTRACT The detection of single quantum systems can reveal information that would be averaged out in traditional techniques based on ensemble measurements. The nitrogen-vacancy (NV) centers in diamond have shown brilliant prospects of performance as quantum bits and atomic sensors under ambient conditions, such as ultra-long coherence time, high fidelity control and readout of the spin state. In particular, the sensitivity of the NV center spin levels to external environmental changes makes it a versatile detector capable of measuring various physical quantities, such as temperature, strain, electric fields and magnetic fields. In this paper, we review recent progress in NV-based quantum metrology, and speculate on its future. Keywords: diamond, nitrogen-vacancy centers, quantum metrology, quantum sensing, quantum information process This review is organized as follows. In the first sec- INTRODUCTION tion (NV CENTER) we recapitulate the structure Magnetic resonance is an established technique to and Hamiltonian of the NV center. In the second obtain non-destructively information about molec- section (MAGNETOMETRY) we give a concise in- ular structure, including biomolecules [1]. On the troduction to the principle and typical sensitivities of other hand, the technique also has wide applica- the detection of magnetic fields using the NV cen- tions in quantum control and imaging. Recently, ter in the first subsection (Nanoscale magnetome- magnetometers based on diamonds [2–5] and try) and then the second subsection (Sensing spins) magnetic resonance force microscopy [6–8]have highlights vital progress on nanoscale electron spin been demonstrated using magnetic resonance on Key Laboratory of resonance (ESR) and nuclear magnetic resonance nanoscale spins with ultra-high sensitivity [9]. Microscale Magnetic (NMR). Other metrology applications such as elec- The nitrogen-vacancy (NV) center in diamond Resonance and trometry and thermometry are discussed in the third is one of the most promising magnetic resonance Department of section (OTHER METROLOGY). systems. The excellent features, including optical Modern Physics, University of Science readout, optical polarization [10] and coherence and Technology of time of milliseconds [11–13], make the system an China, Hefei 230026, important tool in quantum information process- NV CENTER China ing and quantum metrology. Since scientists from Structure the USA and Germany proposed nanoscale mag- Corresponding netic imaging under ambient conditions in 2008 An NV center is composed of a nitrogen impurity author. E-mail: [14–16], NV centers have been rapidly progress- and an adjacent vacancy, as shown in Fig. 1(a). The djf@ustc.edu.cn ing in quantum metrology. NV centers have been structure has C symmetry with the ‘nitrogen– 3v used as interferometers to measure magnetic fields, lattice vacancy’ pair oriented along the axis of Received 21 May electric fields [ 17] and temperatures [18–20]atthe symmetry, normally called the NV axis. The Fermi 2016; Revised 30 nanoscale. In particular, the magnetic-field measur- level of the diamond lattice makes the NV center September 2016; ing precision has been improving to realize external prefer to be negatively charged, NV , or neutral, Accepted 30 single-nuclear-spin readout, which is a prerequisite NV [21,22]. In particular, it is convenient to September 2016 of NMR-based single-molecule imaging. polarize and read out the spin state of an NV by The Author(s) 2017. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For permissions, plea se e-mail: journals.permissions@oup.com Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 REVIEW Chen et al. 347 where the z direction is along the NV axis. Here (a) (b) E 1 D = 2.87 GHz is the zero-field splitting of the -1 electron spin at room temperature but varies linearly with temperature [24], which makes the NV center a temperature sensor [18–20]. The second term is 637 nm the off-diagonal term of the zero-field splitting. In an ideal lattice without an external electric field, E = 0; 2 when a horizon stress or electric field is present, E = 1 0. So the stress and the electric field can be mea- Dark sured by the effect of E [17]. It is noted that E is -1 2.87 GHz also temperature-dependent [24]. The third term is 0 the Zeeman term, describing the interaction of the Bright magnetic field B with the electron spin, which en- ables the NV center for magnetometry. The last term Figure 1. (a) The structure of an NV center; (b) the electronic energy level structure of describes the interaction of the electron spin of the NV [23]. NV with other spins, such as the nitrogen nuclear spin nearby, and the nuclear and electron spins in the applying a 532 nm green laser, due to an intersystem environment. This term can be manipulated to de- crossing process. This makes NV promising in tect and control other spins. The applications of each quantum computation and quantum metrology. term in the Hamiltonian are summarized in Fig. 2. Hereafter, the NV center is denoted as NV without a specific description. The electron energy levels of the NV are shown MAGNETOMETRY in Fig. 1(b) [23]. The ground state A and the first 3 1 excited state E are electron-spin triplet states; A Nanoscale magnetometry and E are electron-spin singlet states. The zero-field As the magnetic field generated by magnetic mo- splitting of A into m = 0 and m =±1 states of 2 S S ments decreases with distance (inverse cubic depen- 2.87 GHz characterizes NV . The fluorescence in- dence), the further away is the probe detector from tensities of NV are spin-dependent on its original the spins that carry the magnetic moments, and the states before the laser illumination, which enables higher is the magnetic field sensitivity required for the readout of its spin state. The principle of the spin- the probe detector. So far, Hall detectors, traditional dependent fluorescence is sketched in Fig. 1(b), NMR, SQUID, atom gas units, magnetic resonance with radiative transitions and non-radiative ones de- force microscopy, NV centers and so on have been noted as solid lines and dotted lines, respectively. used to probe magnetic field signals. Their sensitivi- The m =±1 sublevels in the E excited state have ties and spatial resolutions are schematically shown a higher probability of decaying non-radiatively to −1/2 in Fig. 3 [26]. Normally, a sensitivity of 1 μ /Hz the ground state m = 0 via singlet states, while the (Bohr magneton) is required to probe a single elec- m = 0 sublevels of the excited state are more likely S −1/2 tron spin and ∼1/1000 μ /Hz [27] for a single to experience a spin-conservation process by radiat- proton, which can be hopefully achieved using NV ing a single photon and decaying to the ground state. centers. As a result, the m =±1 spin states have a weaker The idea of the NV center as a magnetic field fluorescence intensity and the population will be probe arose in 2008, when Wrachtrup’s group [14] pumped to m = 0 after repeated pumping, result- and Lukin’s group [15,16] demonstrated initial ex- ing in high spin polarization (92% population on the periments for nanoscale magnetic field imaging with m = 0 state) in a few microseconds even at room NV centers. A general scheme is shown in Fig. 4 temperature. [28]. The NV electron spin is polarized by a laser and then prepared to a superposition state with a π/2mi- crowave pulse. Different base states of the NV spin The Hamiltonian of an NV center will accumulate different phases as a result of inter- The Hamiltonian of the ground state of an NV center acting with the magnetic field or detecting the spin is evolving along different paths. The value of the phase depends on the strength of the interaction and the 2 2 2 accumulation time. The phase information is then H = DS + E S − S z x y transformed, by making the two paths interfere with a π/2 pulse, into the population of an NV spin state, − γ B · S + S · A · I , e i i which can be read out optically. In ideal situations, i Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 Single electron spin Single proton spin 348 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW limited by T , μ the Bohr magneton,  the Planck 2 B 2 2 2 H = D · S + E · (S S ) γ B · S + S · A · I constant and g ≈ 2 the Lande´ factor of the elec- Z x y e i i −1/2 tron spin. In principle, 1 nTHz sensitivity can be achieved given a T value of 0.1 ∼1ms,whichistyp- ical for NV centers in bulk. Moreover, the size of the Spin-coupling Electric-field Magnetic NV center probe can be set to 10 nm, which is not Temperature Spin-sensing stress detection field feasible with traditional methods. In AC magnetic field detection, to improve the Figure 2. The Hamiltonian in the NV center. The physical parameters for each term of signal-to-noise ratio (SNR), dynamical decoupling the Hamiltonian can be deduced from experimental data [25]. technologies are used to prolong the coherence time, which will increase the signal accumulative time. 1/2 Magnetic field sensitivity (per Hz ) However, in DC detection, dynamical decoupling 1pT 1nT 1µT 1mT technologies have no effect, and as a result, the de- 10 µm tection time is limited by T . Conventionally, space ConventionaI SQUID NMR sensors sensors resolution is sacrificed in an ensemble magnetome- (from 1944) tertoimproveSNR [29,30]. In addition, in order (2003) −1/2 to achieve a sensitivity of fTHz with millimeter 1 µm resolution, multi-qubit entanglement schemes have been proposed [31–33]. (2002) Hall Many applications of NV-based magnetic sens- sensors Force 10 µ sensors ing techniques have been proposed and demon- 100 nm strated ever since, such as the magnetic imaging (2008) (2004) 3 using an array of spins in diamond in 2010 [34], 10 µ NV the nanoscale imaging accomplished by combin- sensors 10 nm Magnetic moment ing a single nitrogen vacancy with atomic force mi- 1/2 sensitivity (per Hz ) (2013) 1µ croscopy (AFM) [35], the sensing of a mechanical (2015) resonator in 2012 [36], the sensing of a static vec- (2014) tor magnetic field in 2013 [ 37], and the vector mi- 1 nm -3 10 µ crowave magnetometry based on a single nitrogen- vacancy center in diamond in 2015 [38]. It is Figure 3. Techniques of magnetic field detection. A variety of techniques have been especially worth mentioning that the method can be developed to measure small magnetic moments. The key to nanoscale spin detection is applied to probe oscillating magnetic fields with fre- to combine small tip-sample separations with good magnetic field sensitivity. Reprinted quencies ranging from kHz [15] to GHz [38]. Fur- with permission from [26]. thermore, Du’s group implemented high-resolution vector microwave magnetometry [38] based on the 1 2 3 4 5 Rabi oscillation of NV spins driven by a resonant iΦ/2 e Cos(Φ) microwave magnetic field. The magnetic field vector Φ/2 can be reconstructed by utilizing NV centers of four Φ = ημ μ t Magnetic e n different orientations. 1. Initialization field 2. Superposition μ : n-Magnetic moment -iΦ/2 3. Accumulate phase μ : e-Magnetic moment 4. Interferometer η: Coupling strength Sensing spins 5. Readout t : Coherence time Φ/2 Using nitrogen-vacancy centers to sense near- surface external electron spins began in 2011 Convert weakly magnetic signal (such as nuclear dipolar μ ) n [39]. Its principle has been demonstrated by three to phase Φ which can be detected by quantum interferometer. groups [40–42] and the sensing of an external single electron spin was achieved in 2012 [43]. In Figure 4. Principle of converting a magnetic field signal to the phase  of the quantum 2013, two groups [2,3] simultaneously reported interferometer [28]. the realization of microscopic NMR at nanoscale using an NV center as a probe to detect the proton limited by quantum projection noise, the minimum NMR signal in an organic sample outside of the detecting magnetic field is [ 15]: diamond. Then sensing and atomic-scale structure analysis of single-nuclear-spin clusters in diamond δB ≈ √ (1) were demonstrated [44]. Recently, NMR on four 2πg μ T T B 2 Si spins with single-nuclear-spin sensitivity was where T is the coherence time of the NV’s electron performed [27]. Moreover, detection of electron spin state, T the time of one measurement, which is spin resonance spectra from a single protein was Typical tip–sample separation Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 REVIEW Chen et al. 349 INIT laser repolarizes the NV center; and finally, the (a) (b) π/2 π π/2 detecting sequences confirm the effect of polariza- With RF 1.0 MW τ τ No RF tion (detection part). The microwave and radiofre- RF 0.8 quency used to realize these logic operations are ΔB shown in Fig. 6(b). By decreasing the half-evolution Noises 0.6 π/2 π/2 π time of the SEDOR sequence in Fig. 6(c), a CNOT MW τ 0.4 π operation can be implemented. The problem that RF the CNOT operation time of the dark spin by the 0.2 ΔB NV center exceeds the Hahn echo decay time T 0 20 40 60 80 Noises can be overcome by inserting the XY4 sequence to Free precession time τ (μs) prolong the coherence time. The evolution process Figure 5. The method of detecting dark spins. (a) The Hahn-echo sequence to detect of the NV center under a CNOT operation where dark spins; (b) adding an RF pulse π to flip the dark spin and varying the τ, an oscillation the dark spin controls the NV center is shown in at the coupling strength of the dark spins will appear. Reprinted with permission from Fig. 6(c). The states of the two dark spins are rep- [47]. resented by red and blue arrows. The experimental results of Fig. 6(a) are plotted in Fig. 6(d). The pro- achieved [5], making it possible to extract structure cesses are: (i) polarizing the states of the dark spins and dynamics information [45] from a single to I =−1/2 and I =+1/2 alternatively; (ii) de- z z biomolecule even in living cells. Details of several tecting the difference of polarization of the NV cen- recent works will be discussed below. ters, which is S ; and (iii) using the Rabi oscilla- tion to show that NV center spin polarization has Nano-ESR been transferred to the dark spins and the polariza- In diamond there are numerous defects with elec- tion is 14.3%. The simulation results considering de- tron spins not directly detectable via photolumines- coherence are plotted as black dots. cence, which are called dark spins [46]. Initializing The results above imply that it is possible to ap- and reading out a dark electron spin provides a ver- ply the dark spins around the NV center in scalable ification of the feasibility of sensing an external sin- quantum computation. The directions for further de- gle spin and the possibility of using the dark electron velopments are: (i) increase the dark spins’ polariza- spins as local quantum registers [47]. tion and controlling fidelity; and (ii) couple the NV To detect a single electron spin, two protocols center and the spins outside diamond like N@C60 of spin-echo-detected double electron–electron res- to implement an operational scalable quantum com- onance (known as SEDOR or DEER [3,48–50]) putation. are applied. The basic scheme is shown in Fig. 5(a). The dark spin produces at the NV center a magnetic field B, which superposes the noise magnetic field Single-molecule ESR. Nanoscale ESR outside dia- at the NV center produced by the spin bath. The NV mond has been achieved in recent years. In 2013, de- center spin will accumulate different phases as a re- tection and nanoscale imaging of the magnetic field sult of its interaction with the magnetic field. When produced by a single NV center were achieved [43]. a π operation of the NV center is inserted in the Several groups attempted to sense the nitrogen- middle of the precession time, the phases accumu- oxide spin labels attached to the diamond [ 39,48]. lated during the two τ periods cancel each other. But However, none of them successfully observed the when an RF is inserted in the Hahn echo pulse se- three characteristic hyperfine peaks of the nitrogen- quence to flip the dark spin simultaneously with the oxide label. This indicated that the signal was from NV center spin, the phase induced by the dark spin the surface radicals rather than the nitrogen-oxide will be accumulated for the whole time. As a result spin labels. we can obtain information on the dark spins. Fig- 3D imaging and structure analysis of single ure 5(b) shows that tuning frequencies equal to the biomolecules have been pursued by several re- coupling strengths appear when we fix the RF pulse searchers [39,43,48,51]. One critical step was as a π operation and change the time τ gradually. achieved in 2015 by Du’s group [5]. They chose the MAD2 (mitotic arrest deficient-2) protein as Single electron spin resonance. The process of polariz- the sample. This protein was easily site-specifically ing a dark spin through quantum logic operations is modified with a single nitroxide spin label and shown in Fig. 6 [47]. As the sequence network dia- immobilized on the diamond surface by embedding gram shows in Fig. 6(a): firstly, two cascade CNOT it in a polylysine layer. The detection was based on operations transfer the polarization from the NV the magnetic dipole interaction between the spin center to the dark spin (cooling part); secondly, an label and a single NV center [52]. The individual S (NV) Z Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 350 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW and to increase its sensitivity in the magnetic field, (a) U U X INIT + - while RF pulses were applied on the nitroxide spin NV labels to flip the electron spins synchronously. The ESR spectrum of a single spin label is shown in Fig. 8(a). The three peaks mark the hyperfine COOL DETECT interaction between the spin label’s electron spin (b) (S = 1/2) and the nitrogen nuclear spin (I = 1) e-CNOT NV-CNOT π π/2 π π π at an external magnetic field B = 153.0G. The en- π/2 π/2 π/2 0 ×2 τ τ τ X X Y X X X τ Y semble ESR spectrums in fluid (Fig. 8(b), upper MW 0 0 0 0 π π/2 π τ π/2 panel) and frozen (Fig. 8(b), lower panel) solutions τ τ 0 0 XX X Y Y X RF 4 2 are shown in Fig. 8(b). In principle, the spectrum XY4 of a single spin label is closer to the solid-state spin (c) 0.2 ensemble (Fig. 9(b), lower panel) in which the ran- l 0> (d) COOL + DETECT DETECT dom orientation of the molecular spin principal axis Simulation causes the broadening of the spectral peaks [53]. This reveals that the anisotropic hyperfine coupling can be determined reliably through single-spin ESR. The significance of obtaining the structural and dy- namical information is shown below. 0.0 Close analysis of the spectra (Fig. 9) reveals the molecular dynamics. Figure 9(b) shows that the 0 100 200 300 -1> transition frequencies depend on . The molecular Pulse duration time τ (ns) motion specifically changes the angle between the Figure 6. Quantum logic cooling of the dark spin. (a) Cooling sequence. (b) Gates im- nitrogen p orbitals (ZM in Fig. 9(a)) and B ,which z 0 plemented by a modification of the SEDOR sequence. (c) Evolution of the NV center causes the broadening of the peaks (Fig. 9(c)). over the e-CNOT gate in (b). (d) Result of sequence (a). Reprinted with permission from The asymmetric peaks become more obvious as [47]. the external magnetic field increases (Fig. 9(d)). Figure 9(e) shows that the electron g-factor is con- (a) (b) sistent with the reported values [54]. Figure 10(a) shows the DEER sequence for de- Polylysine layer riving the relaxation time of the spin label and its cou- MAD2 pling strength to the NV center. Figure 10(b) shows ~10 nm NV center the simulations for different spin relaxations and NV center coupling strengths. The possible sites of spin labels in Diamond the transverse cross section constrained by the cou- pling strength are denoted by red lines in Fig. 10(c). (c) τ τ X Y × 2 0 0 As a result, they derive a coupling strength of 90 kHz corresponding to a distance between the spin label NV center ππ π π π π π and the NV spin of ∼9 nm. The size of the spin la- bel is much smaller than a single MAD2 molecule τ ττ τ τ τ τ τ (∼5 nm), which is important for single protein de- Spin label tection. Addressing single-electron spin labels on pro- Figure 7. Diagram of the setup, experimental method and pulses for the single- molecule ESR experiment [5]. (a) On the surface of diamond, MAD2 proteins labeled teins enables ultra-precise structure determination with nitroxide spin labels; under the surface of diamond, NV centers were implanted. based on NV centers. It extends the sensing range to Microwaves were applied by a coplanar wave guide. (b) AFM image for freeze-dried dozens of nanometers, while diamond-sensor-based proteins on the diamond surface. (c) Pulse sequence to measure the coupling of an NV NMR [2,3,27,44] can only sense nuclear spins in sensor to the protein. Reprinted with permission from [5]. very close proximity. NV centers were about 5 nm below the surface of Nano-NMR the diamond and the size of the spin label was much Single-nuclear-spin MR. Detecting a single Chas smaller than a single MAD2 molecule (∼5nm), been implemented through measuring the de- which was ensured by AFM as shown in Fig. 7(b). coherence of NV centers by applying dynamical The experimental pulses to measure the coupling decoupling [40–43]. In 2012, Du’s group detected 13 13 between an NV center and the protein are shown in a single C– C pair about 1 nm away from the NV Fig. 7(c). Periodic XY8-N pulses on the NV center sensor by using the multiple dynamical decoupling were used to preserve the NV sensor’s coherence sequences on the NV center and obtained the ΔS (NV) z Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 ΔΦ REVIEW Chen et al. 351 ω is the Zeeman frequency of the nuclear spins, (a) (b) T = 300 K A are coupling between nuclear spins and NV 1,2 Liquid With protein center spin state |+ 1, D is the dipolar coupling Acid cleaned tensor between nuclear spins I and I . The dynam- 1 2 ical evolution of the dimer can be described by the T = 127 K pseudo-spin model. Two spin states of the dimer Solid |↑↓ and |↓↑ map to the pseudo-spin states |⇑ and |⇓; the other two states of the dimer |↑↑ 0 0 and |↓↓ can be ignored due to the fact that their 3400 3450 3500 300 400 500 Zeeman splittings are much larger than the coupling Frequency (MHz) Magnetic field B (G) strengths under a high magnetic field, which will not induce evolution in coupling interaction. The Figure 8. Spectrum of electron spin resonance of nitroxide spin labels. (a) ESR spectra Hamiltonian of pseudo spins is described [55]: of single spin under ambient conditions (black line) compared with the background spectra by removing the protein by acid cleaning (red line). (b) ESR spectrum of an 1 1 ensemble of protein molecules in a buffer solution at room temperature (upper panel) (m ) (m ) (m ) S S S H = h · σ = (X σ + Z σ ) x z ps and in a frozen buffer solution (lower panel). Reprinted with permission from [5]. 2 2 Here, the pseudo spin affected by the effective field (a) (b) B (d) Simulation 0 (α) (m ) 3 S 180 h decomposes to X and Z , which are the M Experiment coupling strengths between the two spins and the B = 153.0 G Protein motion difference of coupling with the NV, respectively. (overall) Under the effective field, the dimer begins to 4 6 evolve between the two pseudo-spin states period- B = 110.7 G ically, which will induce a periodic magnetic field on 300 400 500 Peak position (MHz) the NV center. By applying dynamical decoupling (c) 0 0 m = -1 0 +1 sequence pulses, the dimer’s information can be ob- tained through measuring the accumulated phase B = 76.0 G generated by the effective magnetic field. ΔΦ=0° Nanoscale proton MR. In 2013, scientists from China 150 300 450 ΔΦ=5° Frequency (MHz) and Germany worked together to perform an exper- (e) iment to detect proton signals in liquid and solid or- ΔΦ=15° 400 ganic samples with a volume of (5 nm) [2]. In this g= 2.008 ± 0.006 work, the proton signals from the liquid and solid on the surface of diamond were achieved by using an ΔΦ=25° NV center as a sensor. The Larmor precession of the 200 300 400 500 75 150 Frequency (MHz) Magnetic field (G) protons under an external magnetic field would gen- erate fluctuation signals of amplitude and phase. The Figure 9. Dynamical behavior of the spin label. (a) Spin-label-attached protein. (b) The dynamical decoupling pulses XY8-N were used to angle  versus transition frequencies, corresponding to m =−1, 0, +1 transitions detect the spin noise. A Ramsey interferometer con- (B = 153G). (c) Simulation of the single-protein ESR spectrum. (d) The spectra of sin- sisting of a π/2 pulse at the beginning and the end of gle spin labels at various external magnetic fields. (e) Resonance frequency of the cen- the sequences was used to detect the magnetic noise. tral peak in (d) versus external magnetic field. Reprinted with permission from [ 5]. The N π pulse amplified the noise at some specific frequencies while suppressing it at others frequen- coupling strength between two nuclear spins by cies; i.e. it acted like a filter. The spin noise spectrum analyzing the experimental data [44]. Based on the can be measured by modifying the pulse evolution coupling strength, the orientation of the spin pair in time τ. atomic-scale resolution can be resolved. In the NV Combined with the scanning NV probe technol- center’s eigenstates |m = 0, +1, the Hamiltonian ogy, it is hoped that nanoscale-NMR imaging appli- of the system containing the NV center and the cations will be implemented [14,35]. NMR detec- 13 13 C– C dimer is [55,56]: tion can be achieved at a low, even zero, magnetic field as the signals come from statistical polarized H = ω |0 0|+ ω |+ 1 +1|+|+ 1 +1| 0 1 nuclear spins instead of traditional thermal polar- ized signals [57]. In this principle, instead of rotating ⊗ (A · I (I + I ) 1 1,z 2,z 1+A ·I )+I ·D ·I +ω 2 2 1 12 2 C the sample in the normal magic angle spinning tech- (2) nique, we can actually rotate the external magnetic Fluor. contrast (%, arb.unit) Φ (°) Central peak Fluor. contrast (%, arb. unit) (MHz) Intensity (arb. unit) Population difference (%) Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 –1 0.8 G nm Permanent magnet –1 0.1 G nm Microwave wire 352 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW (a) × 2 Initialization 0 Readout τ τ ππ ππ ππ ππ NV center 0 0 ππ ππ π π Spin label 532 nm laser 0 1 , X 0 1 , Y NV NV e e NV NV (b) (c) With SL π pulse With SL π pulse Possible site Without SL π pulse Without SL π pulse 1.0 4 μs 90 kHz 10 μs 110 kHz 1 μs 70 kHz Diamond θ L 0.5 NV center 020 40 60 020 40 60 -5 0 5 10 X (nm) 16τ (μs) 0 16τ (μs) Figure 10. Sequence and distance between the NV center and the spin label. (a) DEER sequence between an NV center and a spin label. (b) Simulations of different spin label relaxations and coupling strengths. (c) The possible sites of the spin label in the transverse cross section containing the NV center vector illustrated by red lines. Reprinted with permission from [5]. (b) (a) (c) 0.21 –1 Si: 0.847 kHz G 0.20 0.19 <100 Hz (d) 1,894 G 1,951 G1,993 G 2,044 G 0.80 ~3 kHz 0.75 0.70 0.65 NV center 1.60 1.65 1.70 1.75 Larmor frequency (MHz) Figure 11. Si nuclei NMR with a strongly coupled sensor. (a) Schematic of the setup. (b) Schematic of the strong coupling regime. (c) Using the XY8-K decoupling sequence to measure the Si NMR signal as a function of the applied magnetic field. Reprinted with permission from [ 27]. field, which means that it is easier to achieve higher exploiting the field gradient generated by the rotating speeds. This has important applications in diamond. The scheme of the experiment is shown solid NMR. It can also be extended to hyperpolar- in Fig. 11(a). Amorphous silica was deposited on ization applications via coherent transferring of the the diamond surface, which had shallow NV centers polarization from the NV center to nuclear spins. of 2–3 nm in depth. Strong coupling was obtained by using a diluted spin sample as Si nuclear spins at the surface experience a dipolar magnetic field Single-spin-sensitivity NMR. In 2015, scientists from from nearby NV centers; this was stronger than Germany and China performed the detection and imaging of near-single nuclear spin outside the the inter-nuclear coupling, exceeding even the diamond. In their reports, four silicon nuclei were coupling between Si dimers (Fig. 11(b)). The detected on the diamond. They realized strong signal measured by the XY8 spin-echo sequence is coupling between the NV sensor and nuclei by plotted in Fig. 11(c, d). The clear dip near the Si SiO diamond –1 0.25 G nm B field –1 0.5 G nm –1 1.2 G nm Population of |0> 2.1 nm Y(nm) Fluorescence signal B field (T) Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 REVIEW Chen et al. 353 (a) (b) 10-s acquisition Experimental NMR signal 100-s acquisition 0.54 Unbroadened linewidth Single nuclear spin Fit (basis pursuit) 0.8 2 σ 0.52 0.6 0.5 0.4 2 σ 6 kHz 0.2 0.48 10 kHz 0.46 –0.2 0.44 1.725 1.73 1.735 1.74 1.745 –0.4 1.718 1.72 1.722 1.724 1.726 1.728 1.73 Frequency (MHz) Larmor frequency (MHz) Figure 12. Individual Si nuclei’s NV center gradient separation. (a) The NV center magnetic gradient induced inhomogeneous broadening of the Si NMR line can be observed (XY8-512 pulse sequence). (b) Expected NMR signal for the case of a single Si nuclear spin on the surface. Reprinted with permission from [27]. Larmor frequency resulted from the relative phase field will be detected by the NV center as a result of acquired by the NV center. The NMR signal with the large gradient field. In this method, the Brown inhomogeneous broadening became apparent, as motion of the cantilever can be measured. By further shown in Fig. 12(a). The spectral decomposition of developing the techniques, the zero-point oscillation the contributing nuclear spins and their hyperfine might be detectable by the NV center and so strong coupling parameters implied that four nuclei ac- coupling between single phonons and spins might be count for more than 50% of the signal. Basis pursuit realized. de-noising (BPDN) recovered the best fit locations of the silicon nuclei to present how structural infor- mation and imaging may be obtained. The ultimate Electrical field sensitivity limit of NMR spectroscopy was achieved Detecting a single charge is significant in many re- there by the signal-to-noise ratio of the experiments, search fields and applications. In contrast to other as shown in Fig. 12(b). This work showed that the methods of detecting a weak electric field, the NV sensitivity of NMR and imaging can be extended to center electric field transducer works in ambient single nuclear spins in the strong coupling regime. conditions with atomic spatial resolution [17]. Be- cause of the spin–orbit coupling between the ground state and the excited state, the NV center has an OTHER METROLOGY electric dipole moment at the orbital ground state. The energy difference of the m = 0 and m =±1 S S Vibration states is sensitive to the electric field when the static As described above, by applying the dynamical de- magnetic field is perpendicular to the NV center axis. coupling pulse sequence, sensing of the AC mag- The AC electric field sensitivity has reached 202 ± netic field signal can be achieved by detuning the −1 −1 6V cm Hz , corresponding to the electric field coherent curve. The signal also results from spin pre- produced by a single charge about 150 nm away. Al- cession or other vibration of the magnetic material. though this value is two orders of magnitude off rel- For instance, the vibration of the mechanical res- ative to the most sensitive method, the nanoscale onator can be detected by measuring the vibration sensor can be much closer to the detected charges. of the magnetic field at the NV center nearby. This Thus the possibility to image individual charges with was done by a group in the USA in 2012 [36]. nanometer spatial resolution under ambient condi- When the resonator is far from the NV center, the tions is opened up. field gradient at the NV center is so small that it is not enough to generate an obvious signal by the Brown- ian motion of the resonator. Driving the cantilever Temperature strongly will induce magnetic field oscillations, so that the frequency and average displacement can be In 2010, the dependence of the zero-field split- analyzed. When the distance between the cantilever ting and temperature of NV centers was obtained and the NV center is short enough, the oscillating as dD /dT =−74.2(7)kHz/K[24]. This makes Fluorescence signal Effective NMR signal Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 354 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW NV centers highly sensitive temperature probes of FUNDING nanometer spatial resolution. This work was supported by the National Basic Research Pro- The sensitivity of NV-center-based thermome- gram of China (973 Program) (2013CB921800), the National √ √ try reached 25 mK/ Hz[19] and 5 mK/ Hz[18]. Natural Science Foundation of China (11227901, 31470835 The signal was only related to D and the phase- and 61635012), the China Postdoctoral Science Foundation accumulating time. This was achieved by state swap (XDB01030400) and the Fundamental Research Funds for the Central Universities (WK2340000064). between m =+1 and m =−1 during the phase- S S accumulating period, thus eliminating the low- frequency magnetic noise. 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Quantum metrology with single spins in diamond under ambient conditions

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Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 National Science Review 5: 346–355, 2018 REVIEW doi: 10.1093/nsr/nwx121 Advance access publication 11 October 2017 PHYSICS Quantum metrology with single spins in diamond under ambient conditions Ming Chen, Chao Meng, Qi Zhang, Changkui Duan, Fazhan Shi and Jiangfeng Du ABSTRACT The detection of single quantum systems can reveal information that would be averaged out in traditional techniques based on ensemble measurements. The nitrogen-vacancy (NV) centers in diamond have shown brilliant prospects of performance as quantum bits and atomic sensors under ambient conditions, such as ultra-long coherence time, high fidelity control and readout of the spin state. In particular, the sensitivity of the NV center spin levels to external environmental changes makes it a versatile detector capable of measuring various physical quantities, such as temperature, strain, electric fields and magnetic fields. In this paper, we review recent progress in NV-based quantum metrology, and speculate on its future. Keywords: diamond, nitrogen-vacancy centers, quantum metrology, quantum sensing, quantum information process This review is organized as follows. In the first sec- INTRODUCTION tion (NV CENTER) we recapitulate the structure Magnetic resonance is an established technique to and Hamiltonian of the NV center. In the second obtain non-destructively information about molec- section (MAGNETOMETRY) we give a concise in- ular structure, including biomolecules [1]. On the troduction to the principle and typical sensitivities of other hand, the technique also has wide applica- the detection of magnetic fields using the NV cen- tions in quantum control and imaging. Recently, ter in the first subsection (Nanoscale magnetome- magnetometers based on diamonds [2–5] and try) and then the second subsection (Sensing spins) magnetic resonance force microscopy [6–8]have highlights vital progress on nanoscale electron spin been demonstrated using magnetic resonance on Key Laboratory of resonance (ESR) and nuclear magnetic resonance nanoscale spins with ultra-high sensitivity [9]. Microscale Magnetic (NMR). Other metrology applications such as elec- The nitrogen-vacancy (NV) center in diamond Resonance and trometry and thermometry are discussed in the third is one of the most promising magnetic resonance Department of section (OTHER METROLOGY). systems. The excellent features, including optical Modern Physics, University of Science readout, optical polarization [10] and coherence and Technology of time of milliseconds [11–13], make the system an China, Hefei 230026, important tool in quantum information process- NV CENTER China ing and quantum metrology. Since scientists from Structure the USA and Germany proposed nanoscale mag- Corresponding netic imaging under ambient conditions in 2008 An NV center is composed of a nitrogen impurity author. E-mail: [14–16], NV centers have been rapidly progress- and an adjacent vacancy, as shown in Fig. 1(a). The djf@ustc.edu.cn ing in quantum metrology. NV centers have been structure has C symmetry with the ‘nitrogen– 3v used as interferometers to measure magnetic fields, lattice vacancy’ pair oriented along the axis of Received 21 May electric fields [ 17] and temperatures [18–20]atthe symmetry, normally called the NV axis. The Fermi 2016; Revised 30 nanoscale. In particular, the magnetic-field measur- level of the diamond lattice makes the NV center September 2016; ing precision has been improving to realize external prefer to be negatively charged, NV , or neutral, Accepted 30 single-nuclear-spin readout, which is a prerequisite NV [21,22]. In particular, it is convenient to September 2016 of NMR-based single-molecule imaging. polarize and read out the spin state of an NV by The Author(s) 2017. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For permissions, plea se e-mail: journals.permissions@oup.com Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 REVIEW Chen et al. 347 where the z direction is along the NV axis. Here (a) (b) E 1 D = 2.87 GHz is the zero-field splitting of the -1 electron spin at room temperature but varies linearly with temperature [24], which makes the NV center a temperature sensor [18–20]. The second term is 637 nm the off-diagonal term of the zero-field splitting. In an ideal lattice without an external electric field, E = 0; 2 when a horizon stress or electric field is present, E = 1 0. So the stress and the electric field can be mea- Dark sured by the effect of E [17]. It is noted that E is -1 2.87 GHz also temperature-dependent [24]. The third term is 0 the Zeeman term, describing the interaction of the Bright magnetic field B with the electron spin, which en- ables the NV center for magnetometry. The last term Figure 1. (a) The structure of an NV center; (b) the electronic energy level structure of describes the interaction of the electron spin of the NV [23]. NV with other spins, such as the nitrogen nuclear spin nearby, and the nuclear and electron spins in the applying a 532 nm green laser, due to an intersystem environment. This term can be manipulated to de- crossing process. This makes NV promising in tect and control other spins. The applications of each quantum computation and quantum metrology. term in the Hamiltonian are summarized in Fig. 2. Hereafter, the NV center is denoted as NV without a specific description. The electron energy levels of the NV are shown MAGNETOMETRY in Fig. 1(b) [23]. The ground state A and the first 3 1 excited state E are electron-spin triplet states; A Nanoscale magnetometry and E are electron-spin singlet states. The zero-field As the magnetic field generated by magnetic mo- splitting of A into m = 0 and m =±1 states of 2 S S ments decreases with distance (inverse cubic depen- 2.87 GHz characterizes NV . The fluorescence in- dence), the further away is the probe detector from tensities of NV are spin-dependent on its original the spins that carry the magnetic moments, and the states before the laser illumination, which enables higher is the magnetic field sensitivity required for the readout of its spin state. The principle of the spin- the probe detector. So far, Hall detectors, traditional dependent fluorescence is sketched in Fig. 1(b), NMR, SQUID, atom gas units, magnetic resonance with radiative transitions and non-radiative ones de- force microscopy, NV centers and so on have been noted as solid lines and dotted lines, respectively. used to probe magnetic field signals. Their sensitivi- The m =±1 sublevels in the E excited state have ties and spatial resolutions are schematically shown a higher probability of decaying non-radiatively to −1/2 in Fig. 3 [26]. Normally, a sensitivity of 1 μ /Hz the ground state m = 0 via singlet states, while the (Bohr magneton) is required to probe a single elec- m = 0 sublevels of the excited state are more likely S −1/2 tron spin and ∼1/1000 μ /Hz [27] for a single to experience a spin-conservation process by radiat- proton, which can be hopefully achieved using NV ing a single photon and decaying to the ground state. centers. As a result, the m =±1 spin states have a weaker The idea of the NV center as a magnetic field fluorescence intensity and the population will be probe arose in 2008, when Wrachtrup’s group [14] pumped to m = 0 after repeated pumping, result- and Lukin’s group [15,16] demonstrated initial ex- ing in high spin polarization (92% population on the periments for nanoscale magnetic field imaging with m = 0 state) in a few microseconds even at room NV centers. A general scheme is shown in Fig. 4 temperature. [28]. The NV electron spin is polarized by a laser and then prepared to a superposition state with a π/2mi- crowave pulse. Different base states of the NV spin The Hamiltonian of an NV center will accumulate different phases as a result of inter- The Hamiltonian of the ground state of an NV center acting with the magnetic field or detecting the spin is evolving along different paths. The value of the phase depends on the strength of the interaction and the 2 2 2 accumulation time. The phase information is then H = DS + E S − S z x y transformed, by making the two paths interfere with a π/2 pulse, into the population of an NV spin state, − γ B · S + S · A · I , e i i which can be read out optically. In ideal situations, i Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 Single electron spin Single proton spin 348 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW limited by T , μ the Bohr magneton,  the Planck 2 B 2 2 2 H = D · S + E · (S S ) γ B · S + S · A · I constant and g ≈ 2 the Lande´ factor of the elec- Z x y e i i −1/2 tron spin. In principle, 1 nTHz sensitivity can be achieved given a T value of 0.1 ∼1ms,whichistyp- ical for NV centers in bulk. Moreover, the size of the Spin-coupling Electric-field Magnetic NV center probe can be set to 10 nm, which is not Temperature Spin-sensing stress detection field feasible with traditional methods. In AC magnetic field detection, to improve the Figure 2. The Hamiltonian in the NV center. The physical parameters for each term of signal-to-noise ratio (SNR), dynamical decoupling the Hamiltonian can be deduced from experimental data [25]. technologies are used to prolong the coherence time, which will increase the signal accumulative time. 1/2 Magnetic field sensitivity (per Hz ) However, in DC detection, dynamical decoupling 1pT 1nT 1µT 1mT technologies have no effect, and as a result, the de- 10 µm tection time is limited by T . Conventionally, space ConventionaI SQUID NMR sensors sensors resolution is sacrificed in an ensemble magnetome- (from 1944) tertoimproveSNR [29,30]. In addition, in order (2003) −1/2 to achieve a sensitivity of fTHz with millimeter 1 µm resolution, multi-qubit entanglement schemes have been proposed [31–33]. (2002) Hall Many applications of NV-based magnetic sens- sensors Force 10 µ sensors ing techniques have been proposed and demon- 100 nm strated ever since, such as the magnetic imaging (2008) (2004) 3 using an array of spins in diamond in 2010 [34], 10 µ NV the nanoscale imaging accomplished by combin- sensors 10 nm Magnetic moment ing a single nitrogen vacancy with atomic force mi- 1/2 sensitivity (per Hz ) (2013) 1µ croscopy (AFM) [35], the sensing of a mechanical (2015) resonator in 2012 [36], the sensing of a static vec- (2014) tor magnetic field in 2013 [ 37], and the vector mi- 1 nm -3 10 µ crowave magnetometry based on a single nitrogen- vacancy center in diamond in 2015 [38]. It is Figure 3. Techniques of magnetic field detection. A variety of techniques have been especially worth mentioning that the method can be developed to measure small magnetic moments. The key to nanoscale spin detection is applied to probe oscillating magnetic fields with fre- to combine small tip-sample separations with good magnetic field sensitivity. Reprinted quencies ranging from kHz [15] to GHz [38]. Fur- with permission from [26]. thermore, Du’s group implemented high-resolution vector microwave magnetometry [38] based on the 1 2 3 4 5 Rabi oscillation of NV spins driven by a resonant iΦ/2 e Cos(Φ) microwave magnetic field. The magnetic field vector Φ/2 can be reconstructed by utilizing NV centers of four Φ = ημ μ t Magnetic e n different orientations. 1. Initialization field 2. Superposition μ : n-Magnetic moment -iΦ/2 3. Accumulate phase μ : e-Magnetic moment 4. Interferometer η: Coupling strength Sensing spins 5. Readout t : Coherence time Φ/2 Using nitrogen-vacancy centers to sense near- surface external electron spins began in 2011 Convert weakly magnetic signal (such as nuclear dipolar μ ) n [39]. Its principle has been demonstrated by three to phase Φ which can be detected by quantum interferometer. groups [40–42] and the sensing of an external single electron spin was achieved in 2012 [43]. In Figure 4. Principle of converting a magnetic field signal to the phase  of the quantum 2013, two groups [2,3] simultaneously reported interferometer [28]. the realization of microscopic NMR at nanoscale using an NV center as a probe to detect the proton limited by quantum projection noise, the minimum NMR signal in an organic sample outside of the detecting magnetic field is [ 15]: diamond. Then sensing and atomic-scale structure analysis of single-nuclear-spin clusters in diamond δB ≈ √ (1) were demonstrated [44]. Recently, NMR on four 2πg μ T T B 2 Si spins with single-nuclear-spin sensitivity was where T is the coherence time of the NV’s electron performed [27]. Moreover, detection of electron spin state, T the time of one measurement, which is spin resonance spectra from a single protein was Typical tip–sample separation Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 REVIEW Chen et al. 349 INIT laser repolarizes the NV center; and finally, the (a) (b) π/2 π π/2 detecting sequences confirm the effect of polariza- With RF 1.0 MW τ τ No RF tion (detection part). The microwave and radiofre- RF 0.8 quency used to realize these logic operations are ΔB shown in Fig. 6(b). By decreasing the half-evolution Noises 0.6 π/2 π/2 π time of the SEDOR sequence in Fig. 6(c), a CNOT MW τ 0.4 π operation can be implemented. The problem that RF the CNOT operation time of the dark spin by the 0.2 ΔB NV center exceeds the Hahn echo decay time T 0 20 40 60 80 Noises can be overcome by inserting the XY4 sequence to Free precession time τ (μs) prolong the coherence time. The evolution process Figure 5. The method of detecting dark spins. (a) The Hahn-echo sequence to detect of the NV center under a CNOT operation where dark spins; (b) adding an RF pulse π to flip the dark spin and varying the τ, an oscillation the dark spin controls the NV center is shown in at the coupling strength of the dark spins will appear. Reprinted with permission from Fig. 6(c). The states of the two dark spins are rep- [47]. resented by red and blue arrows. The experimental results of Fig. 6(a) are plotted in Fig. 6(d). The pro- achieved [5], making it possible to extract structure cesses are: (i) polarizing the states of the dark spins and dynamics information [45] from a single to I =−1/2 and I =+1/2 alternatively; (ii) de- z z biomolecule even in living cells. Details of several tecting the difference of polarization of the NV cen- recent works will be discussed below. ters, which is S ; and (iii) using the Rabi oscilla- tion to show that NV center spin polarization has Nano-ESR been transferred to the dark spins and the polariza- In diamond there are numerous defects with elec- tion is 14.3%. The simulation results considering de- tron spins not directly detectable via photolumines- coherence are plotted as black dots. cence, which are called dark spins [46]. Initializing The results above imply that it is possible to ap- and reading out a dark electron spin provides a ver- ply the dark spins around the NV center in scalable ification of the feasibility of sensing an external sin- quantum computation. The directions for further de- gle spin and the possibility of using the dark electron velopments are: (i) increase the dark spins’ polariza- spins as local quantum registers [47]. tion and controlling fidelity; and (ii) couple the NV To detect a single electron spin, two protocols center and the spins outside diamond like N@C60 of spin-echo-detected double electron–electron res- to implement an operational scalable quantum com- onance (known as SEDOR or DEER [3,48–50]) putation. are applied. The basic scheme is shown in Fig. 5(a). The dark spin produces at the NV center a magnetic field B, which superposes the noise magnetic field Single-molecule ESR. Nanoscale ESR outside dia- at the NV center produced by the spin bath. The NV mond has been achieved in recent years. In 2013, de- center spin will accumulate different phases as a re- tection and nanoscale imaging of the magnetic field sult of its interaction with the magnetic field. When produced by a single NV center were achieved [43]. a π operation of the NV center is inserted in the Several groups attempted to sense the nitrogen- middle of the precession time, the phases accumu- oxide spin labels attached to the diamond [ 39,48]. lated during the two τ periods cancel each other. But However, none of them successfully observed the when an RF is inserted in the Hahn echo pulse se- three characteristic hyperfine peaks of the nitrogen- quence to flip the dark spin simultaneously with the oxide label. This indicated that the signal was from NV center spin, the phase induced by the dark spin the surface radicals rather than the nitrogen-oxide will be accumulated for the whole time. As a result spin labels. we can obtain information on the dark spins. Fig- 3D imaging and structure analysis of single ure 5(b) shows that tuning frequencies equal to the biomolecules have been pursued by several re- coupling strengths appear when we fix the RF pulse searchers [39,43,48,51]. One critical step was as a π operation and change the time τ gradually. achieved in 2015 by Du’s group [5]. They chose the MAD2 (mitotic arrest deficient-2) protein as Single electron spin resonance. The process of polariz- the sample. This protein was easily site-specifically ing a dark spin through quantum logic operations is modified with a single nitroxide spin label and shown in Fig. 6 [47]. As the sequence network dia- immobilized on the diamond surface by embedding gram shows in Fig. 6(a): firstly, two cascade CNOT it in a polylysine layer. The detection was based on operations transfer the polarization from the NV the magnetic dipole interaction between the spin center to the dark spin (cooling part); secondly, an label and a single NV center [52]. The individual S (NV) Z Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 350 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW and to increase its sensitivity in the magnetic field, (a) U U X INIT + - while RF pulses were applied on the nitroxide spin NV labels to flip the electron spins synchronously. The ESR spectrum of a single spin label is shown in Fig. 8(a). The three peaks mark the hyperfine COOL DETECT interaction between the spin label’s electron spin (b) (S = 1/2) and the nitrogen nuclear spin (I = 1) e-CNOT NV-CNOT π π/2 π π π at an external magnetic field B = 153.0G. The en- π/2 π/2 π/2 0 ×2 τ τ τ X X Y X X X τ Y semble ESR spectrums in fluid (Fig. 8(b), upper MW 0 0 0 0 π π/2 π τ π/2 panel) and frozen (Fig. 8(b), lower panel) solutions τ τ 0 0 XX X Y Y X RF 4 2 are shown in Fig. 8(b). In principle, the spectrum XY4 of a single spin label is closer to the solid-state spin (c) 0.2 ensemble (Fig. 9(b), lower panel) in which the ran- l 0> (d) COOL + DETECT DETECT dom orientation of the molecular spin principal axis Simulation causes the broadening of the spectral peaks [53]. This reveals that the anisotropic hyperfine coupling can be determined reliably through single-spin ESR. The significance of obtaining the structural and dy- namical information is shown below. 0.0 Close analysis of the spectra (Fig. 9) reveals the molecular dynamics. Figure 9(b) shows that the 0 100 200 300 -1> transition frequencies depend on . The molecular Pulse duration time τ (ns) motion specifically changes the angle between the Figure 6. Quantum logic cooling of the dark spin. (a) Cooling sequence. (b) Gates im- nitrogen p orbitals (ZM in Fig. 9(a)) and B ,which z 0 plemented by a modification of the SEDOR sequence. (c) Evolution of the NV center causes the broadening of the peaks (Fig. 9(c)). over the e-CNOT gate in (b). (d) Result of sequence (a). Reprinted with permission from The asymmetric peaks become more obvious as [47]. the external magnetic field increases (Fig. 9(d)). Figure 9(e) shows that the electron g-factor is con- (a) (b) sistent with the reported values [54]. Figure 10(a) shows the DEER sequence for de- Polylysine layer riving the relaxation time of the spin label and its cou- MAD2 pling strength to the NV center. Figure 10(b) shows ~10 nm NV center the simulations for different spin relaxations and NV center coupling strengths. The possible sites of spin labels in Diamond the transverse cross section constrained by the cou- pling strength are denoted by red lines in Fig. 10(c). (c) τ τ X Y × 2 0 0 As a result, they derive a coupling strength of 90 kHz corresponding to a distance between the spin label NV center ππ π π π π π and the NV spin of ∼9 nm. The size of the spin la- bel is much smaller than a single MAD2 molecule τ ττ τ τ τ τ τ (∼5 nm), which is important for single protein de- Spin label tection. Addressing single-electron spin labels on pro- Figure 7. Diagram of the setup, experimental method and pulses for the single- molecule ESR experiment [5]. (a) On the surface of diamond, MAD2 proteins labeled teins enables ultra-precise structure determination with nitroxide spin labels; under the surface of diamond, NV centers were implanted. based on NV centers. It extends the sensing range to Microwaves were applied by a coplanar wave guide. (b) AFM image for freeze-dried dozens of nanometers, while diamond-sensor-based proteins on the diamond surface. (c) Pulse sequence to measure the coupling of an NV NMR [2,3,27,44] can only sense nuclear spins in sensor to the protein. Reprinted with permission from [5]. very close proximity. NV centers were about 5 nm below the surface of Nano-NMR the diamond and the size of the spin label was much Single-nuclear-spin MR. Detecting a single Chas smaller than a single MAD2 molecule (∼5nm), been implemented through measuring the de- which was ensured by AFM as shown in Fig. 7(b). coherence of NV centers by applying dynamical The experimental pulses to measure the coupling decoupling [40–43]. In 2012, Du’s group detected 13 13 between an NV center and the protein are shown in a single C– C pair about 1 nm away from the NV Fig. 7(c). Periodic XY8-N pulses on the NV center sensor by using the multiple dynamical decoupling were used to preserve the NV sensor’s coherence sequences on the NV center and obtained the ΔS (NV) z Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 ΔΦ REVIEW Chen et al. 351 ω is the Zeeman frequency of the nuclear spins, (a) (b) T = 300 K A are coupling between nuclear spins and NV 1,2 Liquid With protein center spin state |+ 1, D is the dipolar coupling Acid cleaned tensor between nuclear spins I and I . The dynam- 1 2 ical evolution of the dimer can be described by the T = 127 K pseudo-spin model. Two spin states of the dimer Solid |↑↓ and |↓↑ map to the pseudo-spin states |⇑ and |⇓; the other two states of the dimer |↑↑ 0 0 and |↓↓ can be ignored due to the fact that their 3400 3450 3500 300 400 500 Zeeman splittings are much larger than the coupling Frequency (MHz) Magnetic field B (G) strengths under a high magnetic field, which will not induce evolution in coupling interaction. The Figure 8. Spectrum of electron spin resonance of nitroxide spin labels. (a) ESR spectra Hamiltonian of pseudo spins is described [55]: of single spin under ambient conditions (black line) compared with the background spectra by removing the protein by acid cleaning (red line). (b) ESR spectrum of an 1 1 ensemble of protein molecules in a buffer solution at room temperature (upper panel) (m ) (m ) (m ) S S S H = h · σ = (X σ + Z σ ) x z ps and in a frozen buffer solution (lower panel). Reprinted with permission from [5]. 2 2 Here, the pseudo spin affected by the effective field (a) (b) B (d) Simulation 0 (α) (m ) 3 S 180 h decomposes to X and Z , which are the M Experiment coupling strengths between the two spins and the B = 153.0 G Protein motion difference of coupling with the NV, respectively. (overall) Under the effective field, the dimer begins to 4 6 evolve between the two pseudo-spin states period- B = 110.7 G ically, which will induce a periodic magnetic field on 300 400 500 Peak position (MHz) the NV center. By applying dynamical decoupling (c) 0 0 m = -1 0 +1 sequence pulses, the dimer’s information can be ob- tained through measuring the accumulated phase B = 76.0 G generated by the effective magnetic field. ΔΦ=0° Nanoscale proton MR. In 2013, scientists from China 150 300 450 ΔΦ=5° Frequency (MHz) and Germany worked together to perform an exper- (e) iment to detect proton signals in liquid and solid or- ΔΦ=15° 400 ganic samples with a volume of (5 nm) [2]. In this g= 2.008 ± 0.006 work, the proton signals from the liquid and solid on the surface of diamond were achieved by using an ΔΦ=25° NV center as a sensor. The Larmor precession of the 200 300 400 500 75 150 Frequency (MHz) Magnetic field (G) protons under an external magnetic field would gen- erate fluctuation signals of amplitude and phase. The Figure 9. Dynamical behavior of the spin label. (a) Spin-label-attached protein. (b) The dynamical decoupling pulses XY8-N were used to angle  versus transition frequencies, corresponding to m =−1, 0, +1 transitions detect the spin noise. A Ramsey interferometer con- (B = 153G). (c) Simulation of the single-protein ESR spectrum. (d) The spectra of sin- sisting of a π/2 pulse at the beginning and the end of gle spin labels at various external magnetic fields. (e) Resonance frequency of the cen- the sequences was used to detect the magnetic noise. tral peak in (d) versus external magnetic field. Reprinted with permission from [ 5]. The N π pulse amplified the noise at some specific frequencies while suppressing it at others frequen- coupling strength between two nuclear spins by cies; i.e. it acted like a filter. The spin noise spectrum analyzing the experimental data [44]. Based on the can be measured by modifying the pulse evolution coupling strength, the orientation of the spin pair in time τ. atomic-scale resolution can be resolved. In the NV Combined with the scanning NV probe technol- center’s eigenstates |m = 0, +1, the Hamiltonian ogy, it is hoped that nanoscale-NMR imaging appli- of the system containing the NV center and the cations will be implemented [14,35]. NMR detec- 13 13 C– C dimer is [55,56]: tion can be achieved at a low, even zero, magnetic field as the signals come from statistical polarized H = ω |0 0|+ ω |+ 1 +1|+|+ 1 +1| 0 1 nuclear spins instead of traditional thermal polar- ized signals [57]. In this principle, instead of rotating ⊗ (A · I (I + I ) 1 1,z 2,z 1+A ·I )+I ·D ·I +ω 2 2 1 12 2 C the sample in the normal magic angle spinning tech- (2) nique, we can actually rotate the external magnetic Fluor. contrast (%, arb.unit) Φ (°) Central peak Fluor. contrast (%, arb. unit) (MHz) Intensity (arb. unit) Population difference (%) Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 –1 0.8 G nm Permanent magnet –1 0.1 G nm Microwave wire 352 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW (a) × 2 Initialization 0 Readout τ τ ππ ππ ππ ππ NV center 0 0 ππ ππ π π Spin label 532 nm laser 0 1 , X 0 1 , Y NV NV e e NV NV (b) (c) With SL π pulse With SL π pulse Possible site Without SL π pulse Without SL π pulse 1.0 4 μs 90 kHz 10 μs 110 kHz 1 μs 70 kHz Diamond θ L 0.5 NV center 020 40 60 020 40 60 -5 0 5 10 X (nm) 16τ (μs) 0 16τ (μs) Figure 10. Sequence and distance between the NV center and the spin label. (a) DEER sequence between an NV center and a spin label. (b) Simulations of different spin label relaxations and coupling strengths. (c) The possible sites of the spin label in the transverse cross section containing the NV center vector illustrated by red lines. Reprinted with permission from [5]. (b) (a) (c) 0.21 –1 Si: 0.847 kHz G 0.20 0.19 <100 Hz (d) 1,894 G 1,951 G1,993 G 2,044 G 0.80 ~3 kHz 0.75 0.70 0.65 NV center 1.60 1.65 1.70 1.75 Larmor frequency (MHz) Figure 11. Si nuclei NMR with a strongly coupled sensor. (a) Schematic of the setup. (b) Schematic of the strong coupling regime. (c) Using the XY8-K decoupling sequence to measure the Si NMR signal as a function of the applied magnetic field. Reprinted with permission from [ 27]. field, which means that it is easier to achieve higher exploiting the field gradient generated by the rotating speeds. This has important applications in diamond. The scheme of the experiment is shown solid NMR. It can also be extended to hyperpolar- in Fig. 11(a). Amorphous silica was deposited on ization applications via coherent transferring of the the diamond surface, which had shallow NV centers polarization from the NV center to nuclear spins. of 2–3 nm in depth. Strong coupling was obtained by using a diluted spin sample as Si nuclear spins at the surface experience a dipolar magnetic field Single-spin-sensitivity NMR. In 2015, scientists from from nearby NV centers; this was stronger than Germany and China performed the detection and imaging of near-single nuclear spin outside the the inter-nuclear coupling, exceeding even the diamond. In their reports, four silicon nuclei were coupling between Si dimers (Fig. 11(b)). The detected on the diamond. They realized strong signal measured by the XY8 spin-echo sequence is coupling between the NV sensor and nuclei by plotted in Fig. 11(c, d). The clear dip near the Si SiO diamond –1 0.25 G nm B field –1 0.5 G nm –1 1.2 G nm Population of |0> 2.1 nm Y(nm) Fluorescence signal B field (T) Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 REVIEW Chen et al. 353 (a) (b) 10-s acquisition Experimental NMR signal 100-s acquisition 0.54 Unbroadened linewidth Single nuclear spin Fit (basis pursuit) 0.8 2 σ 0.52 0.6 0.5 0.4 2 σ 6 kHz 0.2 0.48 10 kHz 0.46 –0.2 0.44 1.725 1.73 1.735 1.74 1.745 –0.4 1.718 1.72 1.722 1.724 1.726 1.728 1.73 Frequency (MHz) Larmor frequency (MHz) Figure 12. Individual Si nuclei’s NV center gradient separation. (a) The NV center magnetic gradient induced inhomogeneous broadening of the Si NMR line can be observed (XY8-512 pulse sequence). (b) Expected NMR signal for the case of a single Si nuclear spin on the surface. Reprinted with permission from [27]. Larmor frequency resulted from the relative phase field will be detected by the NV center as a result of acquired by the NV center. The NMR signal with the large gradient field. In this method, the Brown inhomogeneous broadening became apparent, as motion of the cantilever can be measured. By further shown in Fig. 12(a). The spectral decomposition of developing the techniques, the zero-point oscillation the contributing nuclear spins and their hyperfine might be detectable by the NV center and so strong coupling parameters implied that four nuclei ac- coupling between single phonons and spins might be count for more than 50% of the signal. Basis pursuit realized. de-noising (BPDN) recovered the best fit locations of the silicon nuclei to present how structural infor- mation and imaging may be obtained. The ultimate Electrical field sensitivity limit of NMR spectroscopy was achieved Detecting a single charge is significant in many re- there by the signal-to-noise ratio of the experiments, search fields and applications. In contrast to other as shown in Fig. 12(b). This work showed that the methods of detecting a weak electric field, the NV sensitivity of NMR and imaging can be extended to center electric field transducer works in ambient single nuclear spins in the strong coupling regime. conditions with atomic spatial resolution [17]. Be- cause of the spin–orbit coupling between the ground state and the excited state, the NV center has an OTHER METROLOGY electric dipole moment at the orbital ground state. The energy difference of the m = 0 and m =±1 S S Vibration states is sensitive to the electric field when the static As described above, by applying the dynamical de- magnetic field is perpendicular to the NV center axis. coupling pulse sequence, sensing of the AC mag- The AC electric field sensitivity has reached 202 ± netic field signal can be achieved by detuning the −1 −1 6V cm Hz , corresponding to the electric field coherent curve. The signal also results from spin pre- produced by a single charge about 150 nm away. Al- cession or other vibration of the magnetic material. though this value is two orders of magnitude off rel- For instance, the vibration of the mechanical res- ative to the most sensitive method, the nanoscale onator can be detected by measuring the vibration sensor can be much closer to the detected charges. of the magnetic field at the NV center nearby. This Thus the possibility to image individual charges with was done by a group in the USA in 2012 [36]. nanometer spatial resolution under ambient condi- When the resonator is far from the NV center, the tions is opened up. field gradient at the NV center is so small that it is not enough to generate an obvious signal by the Brown- ian motion of the resonator. Driving the cantilever Temperature strongly will induce magnetic field oscillations, so that the frequency and average displacement can be In 2010, the dependence of the zero-field split- analyzed. When the distance between the cantilever ting and temperature of NV centers was obtained and the NV center is short enough, the oscillating as dD /dT =−74.2(7)kHz/K[24]. This makes Fluorescence signal Effective NMR signal Downloaded from https://academic.oup.com/nsr/article/5/3/346/4430770 by DeepDyve user on 13 July 2022 354 Natl Sci Rev, 2018, Vol. 5, No. 3 REVIEW NV centers highly sensitive temperature probes of FUNDING nanometer spatial resolution. This work was supported by the National Basic Research Pro- The sensitivity of NV-center-based thermome- gram of China (973 Program) (2013CB921800), the National √ √ try reached 25 mK/ Hz[19] and 5 mK/ Hz[18]. Natural Science Foundation of China (11227901, 31470835 The signal was only related to D and the phase- and 61635012), the China Postdoctoral Science Foundation accumulating time. This was achieved by state swap (XDB01030400) and the Fundamental Research Funds for the Central Universities (WK2340000064). between m =+1 and m =−1 during the phase- S S accumulating period, thus eliminating the low- frequency magnetic noise. 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Published: May 1, 2018

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