Atomic-Scale Nuclear Spin Imaging Using Quantum-Assisted Sensors in Diamond

Nuclear spin imaging at the atomic level is essential for the understanding of fundamental biological phenomena and for applications such as drug discovery. The advent of novel nanoscale sensors promises to achieve the long-standing goal of single-protein, high spatial-resolution structure determination under ambient conditions. In particular, quantum sensors based on the spin-dependent photoluminescence of nitrogen-vacancy (NV) centers in diamond have recently been used to detect nanoscale ensembles of external nuclear spins. While NV sensitivity is approaching single-spin levels, extracting relevant information from a very complex structure is a further challenge since it requires not only the ability to sense the magnetic field of an isolated nuclear spin but also to achieve atomic-scale spatial resolution. Here, we propose a method that, by exploiting the coupling of the NV center to an intrinsic quantum memory associated with the nitrogen nuclear spin, can reach a tenfold improvement in spatial resolution, down to atomic scales. The spatial resolution enhancement is achieved through coherent control of the sensor spin, which creates a dynamic frequency filter selecting only a few nuclear spins at a time. We propose and analyze a protocol that would allow not only sensing individual spins in a complex biomolecule, but also unraveling couplings among them, thus elucidating local characteristics of the molecule structure.

Popular Summary

Novel magnetic-field quantum sensors have recently detected extrinsic nuclear spins with a sensitivity approaching the single-atom level. These sensors are based on the quantum properties of electronic spins associated with shallow nitrogen-vacancy (NV) defect centers in diamond. An outstanding challenge is to resolve the contributions arising from distinct nuclear spins in a dense sample and use the acquired signal to reconstruct the positions of the spins. We propose a strategy combining the use of a quantum memory intrinsic to the NV system with quantum control to boost the spatial resolution of NV-based magnetic resonance imaging.

Investigating the molecular structure of proteins is critical to designing drugs to bind to specific protein receptor sites. Techniques used thus far for probing molecular structure, including x-ray crystallography and nuclear magnetic resonance imaging, have several drawbacks, such as the requirement that proteins be synthesized in sizable amounts and crystallized. We present a new technique for imaging single proteins in their natural surroundings, and we conduct simulations with the chemokine receptor CXCR4, which is associated with cancer metastasis. We employ NV electronic spins in diamond to conduct magnetic imaging, in which the polarization of the NV spin is transferred to the surrounding nuclear spins via magnetic dipole interactions, spreading via diffusion. The polarization is then returned to the NV spin and the linked nuclear spins are imaged. Thanks to long coherence times provided by a quantum memory and the filtering effect of pulsed microwave control, we achieve a tenfold improvement in spatial resolution over other NV-based methods.

Our strategy, which yields subangstrom spatial resolution, promises to make diamond-based quantum sensors an invaluable technology for bioimaging, as they could reconstruct the local structure of biomolecules, without the need to synthesize large ensembles or alter their natural environment.

Figure 1

(a) Nuclear spin imaging with a shallow NV center in diamond. A single NV spin (purple) at 1–2 nm from the diamond surface can sense single nuclear spins in a molecule (the chemokine receptor CXCR4 [29], ribbon diagram) anchored to the diamond. The magnetic field produced by individual ${}^{13}\mathrm{C}$ (spheres with color scale given by $B_{\perp }^j/{\gamma }_e$) is in the range of nT, within reach of NV sensitivity. In the inset, we show the binding site of interest [atoms other than ${}^{13}\mathrm{C}$ are blue (O) and red (N)]. (b) A shallow NV center (2 nm from the surface) creates a magnetic field gradient [$A(\overrightarrow{r})/{\gamma }_n$] above the [111] surface of the diamond. Note the azimuthal symmetry of the field, which causes degeneracy of the frequency shift at many spatial locations.

Figure 2

(a) Control scheme for filtered cross-polarization nuclear spin sensing. Polarization is transferred from the NV electronic spin to the target nuclear spins in the biomolecule for a time $t/F$. To increase spatial resolution, the nuclear spins are allowed to evolve under a magnetic field gradient for a time $t_g=T_g/F$, while the NV state is stored in the nuclear ${}^{15}\mathrm{N}$ spin. The scheme is repeated $F$ times to create a sharp filter. For reverse sensing, the two $\pi /2$ pulses are omitted. (b) The filter created by the control scheme as a function of the normalized time $2\pi t_g({\omega }_L+A)$. The filter peaks are sharper for higher $F$ (dark line, $F=30$; red line, $F^{\prime }=6$), yielding a smaller linewidth $\delta A$. While it is possible to achieve sharper peaks at longer times (dashed line, $F^{\prime \prime }=6$, $t_g^{\prime \prime }=5t_g$), this results in a smaller bandwidth $\mathrm{\Delta }{A}^{\prime \prime }$.

Figure 3

Protocol for quantum-enhanced nuclear spin imaging. First the NV measures a 1D NMR spectrum (sense). During this step, polarization is selectively transferred from the NV to a particular nuclear spin in the protein (polarize). Polarization is then allowed to spread (diffusion), driven by the nuclear spin-spin dipolar coupling. The polarization now localized on a different nuclear spin is transferred back to the NV spin and measured optically (reverse-sense).

Figure 4

Simulated 1D and 2D NMR spectra for the binding site in CXCR4, obtained with the NV-based filtered sensing protocol. (a) Simulated normalized spin-dependent NV photoluminescence (PL) after the filtered cross-polarization sequence. The $x$ axis shows the on-resonance dipolar frequency $A$ at each measurement point, while the driving frequency is $\mathrm{\Omega }=A/2/\sqrt{3}+{\omega }_L$ (with Larmor frequency ${\omega }_L=2\mathrm{MHz}$) and the gradient time $t_g=2\pi /(A/\sqrt{3}+{\omega }_L)$. A homonuclear decoupling sequence was applied to the ${}^{13}\mathrm{C}$ spins to narrow their intrinsic linewidth. The PL shows dips when $A$ and the inverse gradient time (simultaneously swept) match the longitudinal dipolar coupling $A^j$ of one nuclear ${}^{13}\mathrm{C}$ spin in the protein. We simulated the 12 ${}^{13}\mathrm{C}$ spins in the ARG and ILE active site and a NV center 1.75 nm below the diamond surface, with the [111] axis aligned around the vertical direction. The gradient time was varied from 201.68 to $201.84\mu \mathrm{s}$ (for a maximum total gradient time of $T_g\approx 6\mathrm{ms}$ in $F=30$ steps). The total polarization time was $t=720\mu \mathrm{s}$. The dip height is a measure of the transverse dipolar coupling $B_{\perp }^j$. The spectrum shows eight dips, with the height indicating overlapping contributions from almost equivalent spins. The dashed line is the spectrum one would obtain with a DD-based protocol distorted by the spin-spin couplings (Ref. [34]). (b) Simulated 2D NMR spectra from the proposed protocol. After polarization (obtained with the same parameters as for the 1D spectrum), the nuclear spins evolve freely for $t_d=300\mu \mathrm{s}$, allowing polarization diffusion. The polarization is then mapped back to the NV center and measured via its spin-dependent PL. The left plot is the 2D NMR spectrum for no diffusion $t_d=0$, while the right plot shows the spreading of polarization in the nuclear spin network, as indicated from off-diagonal nonzero terms.

Figure 5

Accuracy of the position assignment obtained from our proposed sensing method for the ${}^{13}\mathrm{C}$ nuclear spins in the 183 and 185 residues of CXCR4 [29]. The spatial reconstruction uncertainty for the positions of ${}^{13}\mathrm{C}$ nuclear spins [34] is shown as scatter plots in the three planes, where the color defines the nuclear spin it refers to. We assumed a constant error $\mathrm{\Delta }{A}_j=\mathrm{\Delta }{B}_j=300\mathrm{Hz}$ and a relative error $\mathrm{\Delta }{D}_{ij}=0.5D_{ij}$.