Single-molecule scale magnetic resonance spectroscopy using quantum diamond sensors

Single-molecule technology stands as a powerful tool, enabling the characterization of intricate structural and dynamic information that would otherwise remain concealed within the averaged behaviors of numerous molecules. This technology finds extensive application across diverse fields including physics, chemistry, biology, and medicine. Quantum sensing, particularly leveraging nitrogen-vacancy (NV) centers within diamond structures, presents a promising avenue for single-molecule magnetic resonance, offering prospects for sensing and imaging technology at the single-molecule level. Notably, while significant strides have been made in single-molecule scale magnetic resonance using NV centers over the past two decades, current approaches still exhibit limitations in magnetic sensitivity, spectral resolution, and spatial resolution. In particular, the full reconstruction of three-dimensional positions of nuclear spins within single molecules remains an unattained goal. This review provides a comprehensive overview of the current state of the art in single-molecule scale magnetic resonance encompassing an analysis of various relevant techniques involving NV centers. Additionally, it explores the optimization of technical parameters associated with these methods. This detailed analysis serves as a foundation for the development of new technologies and the exploration of potential applications.

Figure 1

The NV center is a point defect in diamond comprising a substitutional nitrogen atom adjacent to a vacancy. It exhibits sensitivity to various physical quantities, especially to magnetic fields. As a solid-state quantum sensor operating under ambient temperature, the NV center can leverage quantum sensing protocols to enhance sensitivity, spectral resolution, and spatial resolution. This versatile quantum sensor finds applications in single-molecule studies, including magnetic spectroscopy of single proteins ([362]; [247]) and single DNA molecules ([363]), detection of single qubits in spin networks ([355]) and doped fullerenes ([325]), characterization of atomic-thin materials like monolayer hexagonal boron nitride ($h$-BN) ([248]) and graphene ([158]), and diagnosis of HIV-1 RNA ([276]).

Figure 2

The breakthrough of single-molecule techniques has allowed access to unprecedented physical, chemical, and biological details of molecules, ranging from tracking the movement of individual molecules to observing the vibrational and conformational changes of single bonds within them. These measurements yield a single-molecule scale view of chemical reactions, physical processes, and intermolecular interactions, offering insight into the behavior and properties of individual molecules and offering novel understanding for interdisciplinary fields. This overview of various types of single-molecule measurements is categorized based on the principles employed in the techniques; moreover, several of these techniques combine multiple principles, which are also addressed herein. The first column of color blocks corresponds to the four major physical principles: optics, electricity, mechanics, and magnetism. The second column corresponds to single-molecule techniques, connected by lines to their associated underlying principles. The last column highlights the applications of single-molecule techniques. The solid-state quantum sensor, which is linked to all four fundamental physical principles and boasts high sensitivity, spectral resolution, and spatial resolution, finds widespread applications (“future” marks potential applications).

Figure 3

NV center. (a) NV center in a hexoctahedral diamond lattice. The NV center comprises a nitrogen atom (the purple ball labeled N) and an adjacent lattice vacancy (gray ball labeled V). The principal axis lies along the connection line between nitrogen and the vacancy. (b) Scanning optical confocal imaging of the NV centers. (c),(d) Energy-level configurations of the ${\mathrm{N}\mathrm{V}}^{-}$ and ${\mathrm{N}\mathrm{V}}^0$ centers in diamond. The NV center is situated within the conduction and valence bands of the diamond lattice. (c) Negatively charged ${\mathrm{N}\mathrm{V}}^{-}$ center energy level. The energy difference between the excited state and the ground state is 1.945 eV, which corresponds to a 637-nm zero phonon line. The orange box indicates the energy level of the ground state. The ground state of ${\mathrm{N}\mathrm{V}}^{-}$ is a triplet spin-1 system, with a zero-field splitting $D=2.87\mathrm{GHz}$ between the electronic spin levels $m_s=0$ and $\pm 1$. Furthermore, applying a magnetic field $B$ causes an energy splitting between the $|m_s=\pm 1⟩$ levels. The spin state can be detected through fluorescence intensity due to a spin-dependent transition, which results from an intersystem crossing between the excited state and metastable level. (d) Neutrally charged ${\mathrm{N}\mathrm{V}}^0$ center energy level. The energy difference between the excited state and the ground state is 2.15 eV, which corresponds to the 575-nm zero phonon line and the 575–750-nm sideband.

Figure 4

ODMR methods. (a) cwODMR spectra of a single NV center. The spectrum is observed by sweeping the applied cw microwave frequency while laser pumping is applied. The fluorescence decreases at the resonant frequency. The upper curve is obtained under zero external field where the $m_s=\pm 1$ states are degenerate. The lower curve is obtained under the $B_0$ field with $2{\gamma }_e{B}_0/2\pi$ splitting. (b) Rabi oscillation of single NV center. By resonant microwave pulse, the NV center spin oscillates between the $m_s=0$ and 1 spin states.

Figure 5

Control protocols for quantum sensing for dc and ac target magnetic field. (a) Pulse sequence for the dc magnetometry using a Ramsey fringe with a sequence of $\pi /2-\tau -\pi /2$. (b) Pulse sequence $\pi /2-\tau -\pi -\tau -\pi /2$ for the ac magnetometry. $\pi$ is inserted in the middle of the sequence to eliminate unwanted environmental noise and accumulate the desired magnetic field with the right frequency $\omega =\pi /\tau$.

Figure 6

Quantum sensing. (a) Concept of quantum sensing illustrated through an interferometer with two beam splitters (corresponding to a $\pi /2$ pulse) and a phase accumulation operation ($\varphi$). (b) Spin evolution in the Bloch sphere. The spin is initially rotated by a $\pi /2$ pulse along the $x$ axis to establish coherence on the $x\text{−}y$ plane. Subsequently a second $\pi /2$ pulse along the $y$ axis is used to project the real component of the spin coherence onto the $z$ axis. (c) Measurement of the signal for the real component of spin coherence vs the magnetic field $B$. (d) Similar to (b) but with the second $\pi /2$ pulse along the $x$ axis. The signal measurement for the imaginary component of the coherence is shown. (e) Signal measurement for the imaginary component of the spin coherence vs the magnetic field $B$.

Figure 7

Measurements of macroscopic spin and nanoscale spin systems. (a) Fluctuation of the macroscopic ensemble spin system characterized by $\delta N/N\sim 1/\sqrt{N}$. It is always smaller than the polarization. The real-component readout signal, which detects the fluctuation $\sim ⟨\delta \varphi {⟩}^2$, is smaller than the imaginary-component readout signal $\sim {\varphi }_{\mathrm{pola}}=⟨\varphi ⟩$, which is proportional to the polarization. (b) Conversely, the fluctuation in the few-spin system, which is characterized by $\delta N/N\sim 1/\sqrt{N}$, can be larger than the polarization. In such cases, the fluctuation signal $⟨\delta \varphi {⟩}^2$ can surpass the polarization signal. Further details are reported in Fig. 13.

Figure 8

Reported spin number detection sensitivity ${\eta }_{\mathrm{spin}}$ by different magnetic resonance technologies vs the sensor-sample distance. The spin detection sensitivity ${\eta }_{\mathrm{spin}}$ represents the minimum detectable spin number (standard deviation) per ${\mathrm{Hz}}^{1/2}$. For the works without specific reported values, we estimated the spin sensitivity of electrons or protons per ${\mathrm{Hz}}^{1/2}$ for different detection methods by estimating the magnetic field generated by spins or by comparing the signal standard deviation with the experimental time. The applications of SSMR are restricted to two regions, one that has high spin number sensitivity at short sensor-sample distances and the other that has low spin number sensitivity at long sensor-sample distances. Our ultimate research goal is to achieve single spin sensitivity under long sensor-sample distance conditions. Details are presented in Table 1.

Figure 9

Single-molecule EPR realized by the DEER method. (a) DEER pulse control sequence to probe the coupling between the NV spin and the labeled electron spin on a single protein. The pulse sequence indicates the timing and order of pulses applied to the spins. The microwave frequency is resonant with the NV spin, and the radio frequency is resonant with the labeled electron spins. A DD sequence is applied on the NV spin while synchronous series $\pi$ pulses are applied simultaneously with the microwave $\pi$ pulses. Synchronously driving the NV electron spin and the target spin allows for preservation of the coupling between the NV spin and the target spin while eliminating most nonsynchronous magnetic noise. (b) The protein is labeled using nitroxide spin labels. Moreover, the protein is reliably immobilized on the diamond surface close to the NV center by embedding it in a polylysine layer. Microwave radiation is delivered through a coplanar waveguide, and the fluorescence is collected using a confocal system. (c) Single spin EPR spectra under ambient conditions. The spectrum disappears after removing the protein via acid cleaning. (d) The ensemble ESR spectrum of protein molecules in a frozen buffer solution with glycerine at 127 K. Adapted from [362].

Figure 10

Single-molecule EPR. (a) Single-molecule EPR in liquid. The diamond is attached with DNA on the diamond pillar surface. The surface-tethered DNA strand (indicated by a dashed red line) hybridizes with a strand (indicated by a solid blue line) that contains a spin label (indicated by an orange arrow), leading to the localization of a spin-labeled duplex within the detection volume of an NV center (indicated by a dark red arrow). (b) Top panel: single-electron spin EPR. The splitting has the ${}^{14}\mathrm{N}\text{−}R5$ spin label. Bottom panel: ${}^{14}\mathrm{N}\text{−}R5$ spin label electron spin quenched in the detected spectrum after the laser irradiation. (a),(b) Adapted from [363]. (c) EPR spectra of multiple electron spins measured at $T=4.2\mathrm{K}$ in ultrahigh vacuum. The target sample, doubly spin-labeled polyprolines, is coupled with a shallow, implanted NV center. The hemisphere shown represents the sensing range of the NV sensor and is approximately the same size as the depth of the NV sensor. (d) Measured spectra on the sensor. From top to bottom: blank spectrum without spin-labeled peptides on surface, spectrum of diluted polyproline labels on diamond surface (labeled and unlabeled ratios $1:10$), and spectrum of the cleaned diamond surface after the aforementioned measurement. (c),(d) Adapted from [355]. (e) $\mathrm{N}@{\mathrm{C}}_{60}$ diluted with empty ${\mathrm{C}}_{60}$ cages detected by the NV sensor. (f) Top panel: EPR spectrum of $\mathrm{N}@{\mathrm{C}}_{60}$ on a diamond surface at low temperatures. The solid blue line indicates the simulation of single $\mathrm{N}@{\mathrm{C}}_{60}$ electron spin EPR spectrum. The dashed vertical lines are the positions of ensemble EPR hyperfine components. Middle panel: spectrum under ambient temperature. The linewidth is largely broadening. Bottom panel: ensemble EPR. (e),(f) Adapted from [325].

Figure 11

Single-molecule quantum relaxometry. (a) Single shallow NV center used as an SQS. A single molecule labeled as an ion (${\mathrm{Gd}}^{3+}$) is attached on the surface of the diamond with a shallow NV center. The NV center is shed with a laser, and fluorescence is observed using a confocal microscope. Adapted from [387]. (b) Noise spectral density for ions (${\mathrm{Gd}}^{3+}$) shown with different concentrations (red curves) and demonstrating the broadening effect of coupling ($f_{\text{dip}}$) at higher concentrations. Although the filter function of DD (blue curve, $F_2$) is limited to megahertz fluctuations, $T_1$ relaxometry can probe a wide frequency range up to gigahertz with two sensitivity windows ($F_1^{+}$ and $F_1^{-}$ for the $m_s=\pm 1$ transition) shown as black lines. $F_1^{\pm }$ can be Zeeman shifted via $B_0$, thereby enabling the experimental detection of $S_{\mathrm{ion}}(\omega )$. (c) Quantum relaxometry measurement protocols. The fluorescence is measured after initialization and a waiting time of $\tau$. The presence of a nearby target molecule can increase the relaxation of the NV sensor, which is represented by the red line. (b),(c) Adapted from [384].

Figure 12

Three types of EPR spectroscopic methods based on electron relaxometry. (a) Sweeping magnetic field. Resonance occurs at the energy-level crossover. Adapted from [156]. (b) Energy levels of dressed states tuned by continuous driving. Resonance occurs when the two driving powers match. Adapted from [33]. (c) SQS driven to the dressed states. Resonance occurs when the Rabi frequency matches the energy splitting of the bare states. Adapted from [206].

Figure 13

Polarization-dependent and fluctuation-dependent NMR. (a) Statistical fluctuations (indicated by effective polarization in figure) may exceed the thermal or enhanced nuclear spin polarization depending on the sample size. The typical polarization levels reached by ONP ([393]), DNP ([15]), and quantum rotor polarization ([347]) are shown as light green, green, and dark green lines, respectively. The Boltzmann polarization (BP) of proton under 0.1 and 1 T are displayed as dark blue and blue lines, respectively. The estimated effective polarization of liquid (1 M proton concentration) and solid samples (proton density of $50{\mathrm{nm}}^{-3}$) are shown as dark red and red dashed curves, respectively, depending on the sample size $l$. (b) Polarization-dependent NMR. For ensembles with large spins (nuclear spins $\gtrsim {10}^{12}$), the signal $S$, which corresponds to the time-averaged nuclear induction magnetic field, is proportional to the sample polarization. Under high-temperature conditions, the sample magnetization can be calculated as $N{\gamma }_n{B}_0/k_{B}T$, where $N$ is the number of spins, $B_0$ is the external magnetic field, $T$ is the temperature, and $k_B$ is the Boltzmann constant. (c) For detection of small ensembles, the signal $S$ is proportional to the statistical fluctuation. The effective sample magnetization is $\propto \sqrt{N}$ if the statistical fluctuations exceed polarization. The signal is observed by the real-component readout; thus, $S\propto N{g}_s^2{t}^2$. (d) Detection of individual nuclear. The optimal strength signal $S$ depends on the nuclear spin relaxation time $T_{1,\mathrm{tar}}$.

Figure 14

NV-based DD sensing protocol. (a) DD sequence. The pulse sequence involves two green laser pulses that perform the initialization and readout of the NV spin state (green blocks) and resonant microwave pulses (gray blocks) that start and end with $\pi /2$ pulses. In between, periodic $\pi$ pulses (gray blocks) are introduced with elements that repeat as $\tau /2-\pi -\tau -\pi -\tau /2$. (b) Schematic for the single-molecule NMR with an NV sensor. The single proteins covalently bond on the diamond surface. (c) ${}^2\mathrm{H}$ NMR spectrum of an isotopically enriched ubiquitin protein (${}^2\mathrm{H}$ at $>98\%$ abundance) at an external magnetic field of 247.3 mT using the XY8-507 sequence and Gaussian fit (solid black line). (b),(c) Adapted from [247].

Figure 15

ENODR sequence. The sequence is based on the Hahn-echo sequence of the NV center spin. At the midpoint of the sequence, a resonant $\pi$ pulse is applied to both the nuclear and electron spins.

Figure 16

Detection and polarization of nuclear spins using HH. (a) Energy-level configuration involving the NV center electron spin and a single spin-$1/2$ nuclear spin. The hyperfine coupling between the electron spin and the nuclear spin is suppressed due to the energy mismatch between the electron spin (${\omega }_e$, in blue) and the nuclear spin (${\omega }_L$, in red). When the electron spin driving frequency ${\mathrm{\Omega }}_e$ aligns with the nuclear spin frequency ${\omega }_L$, the energy-level diagram is described using dressed states $|\pm ⟩$ (shown on the right. This removal of the energy mismatch allows the flip-flop transition between $|+,\downarrow ⟩$ and $|-,\uparrow ⟩$. (b) Demonstration of the HH sequence. A 532-nm laser polarizes the NV electron spin (in green), with a microwave application in between where the $x$ pulse is denoted in blue and the $y$ pulse is shown in pink. (c) Illustration of the alternating HH sequence designed to avoid polarization of nuclear spins. (d) Experimentally observed population of the $|0⟩$ state concerning the electron spin driving frequency $\mathrm{\Omega }$ and sensing time $\tau$. Both the isolating nuclear spin and the nuclear spin bath are observed and are labeled with dashed lines. Adapted from [242].

Figure 17

Resolved interaction between nuclear spin pairs. (a) Depiction of the DD pulse sequence designed for detecting ${}^{13}\mathrm{C}\text{−}{}^{13}\mathrm{C}$ nuclear spin pairs. (b) Dip features in the coherence of the NV sensor under DD control with varying numbers of $\pi$ pulses. Notably as the number of $\pi$ pulses ($N$) increases from 2 (top curve) to 18 (bottom curve), the dips induced by a pair of nuclear spins emerge and become increasingly prominent. (c) Configurations employed for detecting ${}^{13}\mathrm{C}\text{−}{}^{13}\mathrm{C}$ pairs using the NV center. Adapted from [361].

Figure 18

Two-dimensional NMR. (a) Experimental pulse sequence of two-dimensional NMR along with the structural analysis of the coupled nuclear spin system. This sequence represents an experimental implementation of nanoscale homonuclear correlation spectroscopy two-dimensional NMR on the NV center. (b) Interrogation times $t_1$ and $t_2$ swept from $4\mathrm{\mu }\mathrm{s}$ to 0.9 ms with 50 samplings. The time-domain spectroscopy is transformed into frequency-domain spectroscopy in (c) through a two-dimensional FFT transformation. (c) Two-dimensional NMR spectrum revealing cross peaks between the third and fourth peaks in the one-dimensional spectrum (upper inset), indicating that they belong to a coupled spin system. (a)–(c) Adapted from [449]. (d) MRI of nuclear spins, with the three-dimensional structure resolved by detecting the distance between each nuclear spin, depending on the dipolar coupling strength. (e) Depiction of the three-dimensional structure of the nuclear spins within the diamond using the diamond-lattice method. The blue lines indicate couplings greater than 3 Hz, thereby illustrating the connectivity of the cluster. (d),(e) Adapted from [2].

Figure 19

Level diagrams and PL of the NV center. (a) PL spectrum of the NV center, where the laser wavelength for spin initialization is typically 532 nm. The peak at 575 nm (638 nm) corresponds to the ZPL of the ${\mathrm{N}\mathrm{V}}^0$ (${\mathrm{N}\mathrm{V}}^{-}$) charge state. The range 630–800 nm corresponds to the phonon sideband of the ${\mathrm{N}\mathrm{V}}^{-}$ charge state. (b) The ${\mathrm{N}\mathrm{V}}^{-}$ spin states exhibit spin-dependent fluorescence wherein ${\mathrm{N}\mathrm{V}}^{-}$ spins prepared in the $m_s=0$ state emit a higher rate of photons than those prepared in the $m_s=\pm 1$ state.

Figure 20

Photonic structures designed to enhance fluorescence collection efficiency. (a) SIL, a half-ball structure created on the diamond with the NV center situated at its center. (b) Array of diamond nanopillars utilized as photonic waveguides guiding fluorescence photons from top to bottom. (c) Immersion metalens structures fabricated on the diamond surface to collimate fluorescence emitted by the NV center. Adapted from [177]. (d) Photonic crystal cavity produced on a thin diamond membrane. Adapted from [335].

Figure 21

Resonant detection protocol. (a) Level structure of the NV center under cryogenic temperatures. The red arrow represents the resonant readout, and the dark red arrow indicates the population pumping. (b) Energy levels used to prepare and measure the NV electron spin state. The transitions are labeled according to the symmetry of the excited states. Dashed lines indicate spin-nonconserving decay paths. (c) PL excitation spectrum of the NV center (the wavelength is given relative to 637.2 nm).

Figure 22

(a) An example of a photon number histogram of projective measurement for an adjacent nuclear spin with the fidelity $\sim 0.99$. Adapted from [438]. (b) Fidelity improves with the number of repetitive readout [the last element in (c)]. (c) Complete ancilla-assisted sensing protocol for detecting a small magnetic field with subnanotesla sensitivity. It consists of four parts: ${\mathrm{N}\mathrm{V}}^{-}$ charge and spin-state initialization by real-time feedback, phase accumulation by dynamical decoupling sequences, swap gates, and repetitive readout. Adapted from [464].

Figure 23

SCC techniques. (a) Schematics illustrating the SCC method at ambient temperature. Left sketch: singlet SCC. Right sketch: triplet SCC. The solid lines depict the laser pump, and the dashed lines indicate decay transitions. Adapted from [174]. (b) Control protocol for the SCC. (c) Left panel: SCC measurement results that are contingent on the initial electron spin state. Right panel: comparison of the signal-to-noise ratio (SNR) between the SCC method and conventional fluorescence measurements across repeat times. (b),(c) Adapted from [171]. (d) Pulse sequence and diagram depicting the SCC readout method under low temperatures where resonant transitions are feasible. (e) Distribution of photon numbers in charge readout using the SCC method, acquired from $2\times {10}^4$ measurement repetitions with NV spin initially prepared in the $m_s=0$ state (blue bar) and the $m_s=1$ state (orange bars). Inset: photon distribution for the resonant fluorescence method under helium temperature.

Figure 24

(a) Surface electron detection utilizing the NV sensor. The green line represents the coherence decay curve observed when the NV sensor is positioned close to another diamond surface, while the blue line shows the decay curve when the NV sensor is positioned farther from the diamond surface. Oscillations in the curves stem from the ${}^{13}\mathrm{C}$ nuclear spin bath within the diamond. Adapted from [249]. (b) Comparison of nuclear spin sensitivities (${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}$ nuclear spins) against NV center depth before (blue) and after (red) surface treatment. Adapted from [247].

Figure 25

Dynamical decoupling. (a) Control pulse sequences for different control methods. (b) Filter function for each control method. The details for the sequence are listed in Table 3.

Figure 26

Coherence elongation by modulating the surface spins. (a) The shallow NV center is affected by the fluctuating field from the surface electronic spin bath, which can cause decoherence and depolarization of the shallow NV center. (b) Modulating the electronic spin bath alters the noise spectrum, creating a mismatch with the filter function, thereby elongating the decoherence time of the NV centers. (c) Control sequence of pulsed control of the bath spin. (d) Control sequence of continuous driving of the bath spin.

Figure 27

Single nuclear spin detection enabled by the reporter electron spins. (a) Measurement of a nuclear spin bath through the reporter spins on the diamond surface. It exhibits the spin-echo modulation induced by a proton spin bath. Inset: control pulse sequence applied to the reporter and the NV center. (b) Spin-echo modulation of the reporter measured with the NV center. It is estimated by the best fit that the reporter is coupled to two proton spins. (c) Schematic diagram of the hyperfine interaction between the reporter spin and the proton spins (the gold arrows). (d) Energy-level diagram for the coupled system of the reporter spin and the proximal proton spin. (e) Localization of the two nearby proton spins with respect to the reporter spin, which is extracted from a fit to the data shown in (b). Adapted from [386].

Figure 28

Zero-field EPR. (a) Power-sweeping sequence for zero-field measurements. (b) Energy levels of the coupling system involving an $S_e=1/2$ electron spin and $I=1/2$ nuclear spin at zero field. (c) Dependence of EPR spectra on the orientations of target spins. The spectra are simulations of an ${}^{15}\mathrm{N}$ nitroxide spin label. (d) Correlation sequence for zero-field measurements. (e) Comparison between normal (${ST}_{\pm 1}$) and clock (${ST}_0$) transitions. Left panel: Ramsey measurements. Right panel: Fourier transform of the Ramsey measurements. Adapted from [206], and [207].

Figure 29

Correlation spectroscopy utilizing the NV sensor, ancilla quantum memory, and Qdyne. (a) Oscillating magnetic field $B(t)=B_{\mathrm{a}\text{c}}\sin (\omega t+\phi )$ probed using a quantum NV sensor employing a dynamical decoupling sequence $U_{\mathrm{img}}$ that is aligned with the resonant condition. The intervals between the $\pi$ pulses are $\tau =\pi /\omega$, and the accumulated phase ${\mathrm{\Phi }}_n=2{\gamma }_e{B}_{\mathrm{a}\mathrm{c}}{t}_s\cos {\phi }_n/\pi$ relies on the initial oscillating field phase ${\phi }_n$ for each sample. (b) Control procedure for correlation spectroscopy that involves detection of two phases $\phi$ and ${\phi }^{\prime }$ using two sensing protocols and culminates in a final measurement recording a correlation signal $⟨\sin \mathrm{\Phi }\sin {\mathrm{\Phi }}^{\prime }⟩$. (c) Correlation spectroscopy integrates a quantum memory such as an adjacent nitrogen nuclear spin and can be combined with the ENDOR sequence. (d) Qdyne sequence involving the repetitive accumulation and measurement of phases ${\mathrm{\Phi }}_n$ over the entire measurement time $T_{\exp }$. (e) Heterodyning with an external clock that records the NV population series $\sin {\mathrm{\Phi }}_n$ and, consequently, the corresponding photon numbers. Through FFT, the time evolution is transformed into the spectrum, enabling the resolution of signal frequency concerning the local oscillator frequency. (f) Spectral resolution comparison of correlation spectroscopy, ancilla quantum memory, and the Qdyne method. Adapted from [356].

Figure 30

(a) Comparison of the Qdyne spectral resolution with the XY8 technique. The resolution of the XY8 technique is determined by the interrogation time and remains constant at 300 kHz. The resolution of the Qdyne method improves with the experiment time $T^{-1}$ until the limit of clock stability is reached. (b) Comparison of the Qdyne spectral precision and the XY8 technique. The frequency precision is fitted by least-squares estimation and thus is always better than the spectral resolution. The XY8 technique has a measurement precision approximating the standard quantum limit. In contrast, the spectral accuracy of Qdyne exceeds and scales as $T^{-3/2}$ until reaching the clock stability limit. Adapted from [356].

Figure 31

Combination of the high-resolution method with the nuclear spin detection. (a) Overall correlation pulse sequence. The spin operations are inserted in the free evolution interval of the correlation sequence. (b) Spin operation of the free effective Hamiltonian $H_0={\omega }_0{I}_z+a_{\parallel }(S_z+1/2)I_z$. (c) Spin operation of the effective Hamiltonian $H_{\mathrm{eff}}={\omega }_0{I}_z+a_{\parallel }{I}_z/2$. (b),(c) Adapted from [48]. (d) Spin operation of the effective Hamiltonian $H_{\mathrm{eff}}=2a_{\perp }/\pi S_z{I}_x$. (e) Two-dimensional NMR COSY sequence.

Figure 32

Tracking the precession of single nuclear spins using weak measurements. (a) Bloch sphere representation of the spin evolution of the measured spin. (b) Signal amplitude depending on the measurement strength $\sin \beta$. (c) Measurement-induced decoherence suppressed quadratically with the measurement strength while performing the weak measurements. Adapted from [81].

Figure 33

Dynamics of the sample near the diamond surface. The layered model in the detection volume (green semisphere) consists of a static adsorption film (below the dashed red line) where translational diffusion of the molecules (light blue arrows) is restricted. In contrast, the outer section behaves as a bulk liquid, where the molecules self-diffuse. Adapted from [380].

Figure 34

Schematics of NV scanning probe microscopy. (a) Target sample attached to the cantilever of the conventional AFM probe. The sample scans above the diamond, which contains a shallow NV center. The NV sensor is read out by the confocal microscope. (b) The NV sensor is fabricated at the end of a diamond nanopillar (as shown in the inset). The diamond nanopillar is utilized as a magnetic probe to scan over the target sample.

Figure 35

Nanoscale MRI of fluorine (${}^{19}\mathrm{F}$) and protons (${}^1\mathrm{H}$). (a) Single shallow NV center (red spin). Nuclear spins are detected within a nanoscale sensing volume above the diamond surface (red hemisphere). Imaging involves scanning the target sample through this sensing volume. (b) A calibration grating is etched into the sample (green sphere representing ${}^{19}\mathrm{F}$-rich Teflon) using the AFM tip. (c) ${}^{19}\mathrm{F}$ NMR imaging of the sample (calibration grating). (d) Accumulated signals obtained through $4\times 3$ binning of the linescan in (c). Adapted from [153].

Figure 36

(a) Nanopillar embedding an NV center employed to scan the target sample. (b) The NV sensor observes the magnetic field imaging of a single-electron spin. A substantial decrease in fluorescence near the center signifies the detection of a single-electron spin. Adapted from [140].

Figure 37

Gradient-based MRI with NV sensor. (a) MRI of dark spins in a diamond utilizing a scanning gradient and a single NV sensor. A scanning magnetic tip is positioned 100 nm above the diamond surface, thereby enabling the measurement of the spatial distribution of the dark spin density by the NV sensor. (b) 0.8 nm resolution NV MRI of a single dark spin. (a),(b) Adapted from [142]. (c) Schematic of Fourier magnetic imaging. An adjustable magnetic field gradient for phase encoding is established by passing an electric current through a pair of gradient microcoils. Currents of 1 A through two gradient microcoil pairs generate magnetic field gradients up to $0.2\mathrm{\mu }\mathrm{T}{\mathrm{nm}}^{-1}$. (d) Nanoscale resolution MRI of the NV center. Top panel: cross section depicting two distinct peaks along the direction indicated by the dashed white line in the two-dimensional image. These peaks correspond to two separate NV centers spaced $121(9)\mathrm{nm}$ apart. Bottom panel: two-dimensional real-space images of the Fourier transform of these two NV centers. (c),(d) Adapted from [14].

Figure 38

Nanoscale resolution MRI of single nuclear spins using the gradient magnetic field of the NV center. (a) Shallow NV center in diamond (2 nm from the surface) coupled with nearby nuclear spins due to hyperfine interaction. The contour lines depict the strength of the effective magnetic gradient experienced by the nuclear spins. (b) Optimal locations of the four most significant contributing nuclear spins (illustrated as colored arcs), as determined through basis pursuit. Each spin’s representative position is marked with a filled ball, and the positional uncertainty in the $x$ and $z$ directions is indicated by the ball’s size. The $y$-axis resolution ranges from 0.1 nm for the nearest spin to 0.5 nm for the farthest spin. Adapted from [286].

Figure 39

(a) Process for creating an NV center via ion implantation. NV centers are formed through nitrogen ion implantation (with energies ranging from 2 to 50 keV and a density of ${10}^8–{10}^{11}{\mathrm{cm}}^{-2}$), followed by high-temperature annealing (ranging from 600 to $1200°\mathrm{C}$). (b) Delta-doping procedure. A thin nitrogen-doped layer (light red) is produced by introducing ${\mathrm{N}}_2$ gas during the diamond growth process. Subsequently, irradiation via laser, ions, or electrons induces vacancies. Annealing is then performed to generate NV centers.

Figure 40

(a) Depth of the implanted ions vs the implantation energy. The blue shadow indicates ion straggling. (b) Yield of the NV centers vs the implantation energy. (b) Adapted from [317].

Figure 41

The electron affinity (in eV) and the stability of an NV charge state depend on the diamond surface termination for a shallow NV center. Adapted from [200].

Figure 42

Energy band schematic of diamond. (a) Diamond surface with positive electron affinity. The conduction band $E_{\mathrm{C}}$ is below $E_{\mathrm{vac}}$ (O termination, for example). The negatively charged ${\mathrm{N}\mathrm{V}}^{-}$ center lies beneath the Fermi level $E_{\mathrm{F}}$. (b) Diamond surface with negative electron affinity. The band levels are shifted up, and the electron in diamond can transfer into the acceptor states on the surface. (c) The band bends due to the effect of electron transfer. The NV center prefers an ${\mathrm{N}\mathrm{V}}^0$ charge state near the surface. (d) A voltage is applied to lift the Fermi energy to control the NV charge state.

Figure 43

(a) Diamond fabrication process without alignment. NV centers are created through maskless ion implantation followed by annealing. Subsequently, nanopillar photonic structures are fashioned using EBL and RIE techniques. (b) Illustration of the self-alignment process employed for fabricating photonic structures. A double-layer mask comprising polydimethylglutarimide (PMGI) and PMMA, produced via a single-step EBL process, confines the positions of both the etching resist and the ion implantation region. Nitrogen ions are implanted in the diamond through the PMMA layer mask. Subsequently, the PMGI layer masks are transferred to the etching resist through a lift-off process. This is followed using RIE techniques to produce the photonic structures, which are then annealed to convert the implanted nitrogen ions into NV centers. Adapted from [417].

Figure 44

Various sensing protocols exhibit differing compatibility levels. This evaluation categorizes the compatibility between diverse technologies into three tiers: high, medium, and low. High compatibility signifies technologies that can enhance one other’s performance, while medium compatibility indicates the absence of conflict. Low compatibility suggests either an inability to coexist or a severe compromise in performance when the protocols are combined. A comprehensive assessment of the compatibility of different technologies is given in Table 5.

Figure 45

There has been significant advancement in microscale and nanoscale magnetic resonance spectroscopy through the utilization of SQS. Despite these strides, the single-molecule field’s progress remains constrained, thus necessitating further development. The primary hindrances impeding advancement revolve around technical gaps that require resolution to enable substantial applications. By amalgamating various SQS technologies, potential solutions arise for addressing several of these technical gaps. The figure delineates the current SQS technologies in the first column, which is organized by color into distinct groups representing different technology categories. Each technology within these categories is discernible by a unique shade corresponding to its color group. Specifically, the red group encompasses quantum sensing technologies such as DEER (Sec. 2a1), quantum relaxometry (Sec. 2a2), and NMR methods (Sec. 2b). Green indicates sensitivity enhancement technologies like PL enhancement (Sec. 3c1), ancilla-assisted readout (Sec. 3c3), and SCC or photoelectric readout (Sec. 3c4). The orange group signifies spectral resolution enhancement technologies encompassing ZFEPR (Sec. 4b1), Qdyne, or weak measurement (Secs. 4b2 and 4b3), along with confined-space techniques (Sec. 4b4). In addition, blue denotes spatial resolution enhancement technology (Sec. 5b), while purple signifies probe fabrication technology Sec. 6). The second column illustrates the technical gaps within single-molecule technology that can potentially be addressed by combining various SQS techniques. The third column outlines the applications that will potentially be achievable when these technical gaps are overcome.

Figure 46

The effective evolution for nuclear spins under dynamical decoupling controlling. (a) Pulse sequence for a typical dynamical decoupling sequence. The basic unit $\tau /2-\pi -\tau -\pi -\tau /2$ repeats for a longer sequence. Complicated sequences are reported in Fig. 25. (b) Pulse sequence for manipulating nuclear spins. (c) Nuclear spin evolution for DD under the resonant condition $\tau ={\tau }_0$ shown in the Bloch sphere. Consequently, the nuclear spin will rotate around antiparallel axes ${\widehat{\mathbf{n}}}_0$ and ${\widehat{\mathbf{n}}}_1$ for different initial ${\mathrm{N}\mathrm{V}}^{-}$ electron spin states $m_s=0$ and 1.