Abstract
Hyperpolarisation of nuclear spins is important in overcoming sensitivity and resolution limitations of magnetic resonance imaging and nuclear magnetic resonance spectroscopy. Current hyperpolarisation techniques require high magnetic fields, low temperatures, or catalysts. Alternatively, the emergence of room temperature spin qubits has opened new pathways to achieve direct nuclear spin hyperpolarisation. Employing a microwavefree crossrelaxation induced polarisation protocol applied to a nitrogen vacancy qubit, we demonstrate quantum probe hyperpolarisation of external molecular nuclear spins to ~50% under ambient conditions, showing a single qubit increasing the polarisation of ~10^{6} nuclear spins by six orders of magnitude over the thermal background. Results are verified against a detailed theoretical treatment, which also describes how the system can be scaled up to a universal quantum hyperpolarisation platform for macroscopic samples. Our results demonstrate the prospects for this approach to nuclear spin hyperpolarisation for molecular imaging and spectroscopy and its potential to extend beyond into other scientific areas.
Introduction
The hyperpolarisation of nuclear spins within target molecules is a critical and complex challenge in magnetic resonance imaging (MRI)^{1} and nuclear magnetic resonance (NMR) spectroscopy^{2}. Hyperpolarisation offers enormous gains in signal and spatial resolution which may ultimately lead to the development of molecular MRI and NMR^{3}, with the prospect of revolutionising many areas of research and clinical applications. Wellknown hyperpolarisation techniques include highfield/low temperature bruteforce methods^{4}, dynamic nuclear polarisation^{6}, optical pumping^{5}, and parahydrogeninduced polarisation^{7}. On the other hand, the rapid advances in semiconductor spin qubit technology for quantum computing^{9,10} and quantum sensing^{11,12,13,14} has opened up the exciting possibility of hyperpolarising nuclear spins at a fundamental level via quantum mechanical protocols^{6,8,17,18,19,20,21,22,23,24}. Despite early progress^{25,26}, the application of quantum probe technology to this problem still faces a number of significant challenges. To be of practical use, a quantum probe must be capable of polarising a relatively large number of remote nuclear spins external to the probe substrate, ideally under ambient conditions.
In the following, we address these challenges using a quantum spin probe in diamond as an entropy pump, and, using a combined experimental and theoretical analysis, demonstrate polarisation of external molecular spin ensembles to about 50% over relatively large volumes at room temperature, with the prospect of scaling up to a universal hyperpolarisation platform suitable for clinical applications. In contrast to existing methods, our quantum polarisation approach is tunable to a range of nuclear species, is inherently free of radiofrequency (RF) or microwave fields and extraneous chemistry, and is carried out at room temperature.
Results
Principle of the technique
For this study, we employ a nitrogen vacancy (NV) quantum spin probe in a diamond substrate (Fig. 1a)^{11}. Existing approaches to NVbased hyperpolarisation involve the use of an external microwave field to tune the NV Rabi frequency to the Larmor frequency of the target spins, thereby enabling rotatingframe crossrelaxation via the A_{z,x} and A_{z,y} components of their hyperfine interaction. Our approach, on the other hand, takes advantage of the greater (A_{x,y;x,y}) NVtarget hyperfine interaction associated with direct labframe crossrelaxation, which allows for an order of magnitude greater target polarisation rate. This is achieved by using an external magnetic field, B, to tune the groundstate spin transition frequency of the NV (ω_{NV}) into resonance with target nuclear spins (ω_{n}) (Fig. 1b). For a given target species, the spin resonance condition is fulfilled at a magnetic field B_{*}(γ_{n}) ≈ 2D/(γ_{NV} − γ_{n})^{27}, where γ_{n}, γ_{NV} are the target and NV gyromagnetic ratios, and D is the NV zerofield splitting (Fig. 1c). Entropy pumping is facilitated by repeated application of the cross relaxation induced polarisation (CRIP) sequence (Fig. 1d), wherein the NV spin is optically initialised into \(\left 0 \right\rangle\) state and the NVtarget hyperfine interaction is allowed to occur for a given period of time, τ (of order microseconds). The transfer of magnetisation caused by this interaction thus polarises the target spins into their \(\left \downarrow \right\rangle\) state (Fig. 1c). For the sake of comparison, depolarisation may be facilitated by interleaving the initialisation of the NV spin into the opposite state \(\left {  1} \right\rangle\) by the application of an RF πpulse (Fig. 1e).
To quantitatively understand the effect of the CRIP protocol on the target spin ensemble, we developed a microscopic theory that explicitly includes the dipole interactions of ensemble spins and their interaction with a single NV quantum probe (see Supplementary Note 1 for details). We define the polarisation of a spin at position R (relative to the NV) and time t to be P(R, t); with the evolution of P(R, t) described by
subject to an initial unpolarised state P(R, t) = 0; where u(R) = A^{2}(R)/2Γ_{2} is the effective cooling coefficient resulting from the hyperfine coupling A(R) with the NV spin, Γ_{2} is the dephasing rate of the NV spin β is the effective polarisation diffusion coefficient related to the intratarget interactions, and Γ_{SL} is the spinlattice relaxation rate of the target spin ensemble. This formulation allows us to predict and describe the spatial extent of polarisation for a given target sample of arbitrary geometry.
To probe the polarisation effect experimentally, we monitor the spindependent photoluminescence (PL) from the NV^{28,29,30} during the laser pulses, which decays as a function of the CRIP sequence time as \(e^{  \Gamma _{{\mathrm{tot}}}\tau }\). Here Γ_{tot} is the NV longitudinal relaxation rate, which can be expressed as the sum Γ_{tot} = Γ_{bg} + Γ_{CR}, where Γ_{bg} is the background rate caused by lattice phonons or surface effects, and Γ_{CR} is due to crossrelaxation. The latter follows a Lorentzian dependence on the detuning between the probe and target transition frequencies^{28},
where \(A_P^2\) is the total effective hyperfine field seen by the NV due to the target ensemble, which is related to the polarisation distribution via
where n_{t} is the density of the target spin ensemble. The key indicator of significant polarisation is therefore a reduction in Γ_{CR}, which manifests as the disappearance of the target ensemble’s spectral feature from the crossrelaxation spectrum (Fig. 1f), and can be quantified by measuring the crossrelaxation curve at resonance (Fig. 1g).
Polarisation of internal ^{13}C spins
Experimentally, we first demonstrate our technique on the inherent 1.1% ^{13}C spin ensemble surrounding a NV probe in the diamond substrate by tuning to the ^{13}C resonant condition at B_{*}(^{13}C) = 1024.9 G. Comparison of the crossrelaxation spectra for CRIP and depolarisation sequences (Fig. 2a) shows the complete removal of the ^{13}C resonance peak for interaction times of τ = 4 µs, indicating efficient polarisation of the nearest spins, as compared with the target prepared using the depolarising sequence. This is confirmed in the crossrelaxation curves as a function of τ (Fig. 2b, inset), where the polarised case shows no evolution of the NV spin state, while the unpolarised case shows coherent flipflops between the NV and the ^{13}C spins.
To investigate the extent of the polarisation effect, we increase the interaction time τ so as to be sensitive to more remote ^{13}C spins, up to the limit set by the NV centre’s intrinsic spinphonon relaxation rate, Γ_{bg} ≈ 200 s^{−1}. The resulting crossrelaxation curves obtained at the ^{13}C resonance using the CRIP and depolarisation sequences are shown in Fig. 2b, from which we extract the total relaxation rate, Γ_{tot}. By subtracting Γ_{bg} obtained from the offresonance relaxation curve (Fig. 2b, green data), we deduce the ^{13}Cinduced relaxation rate Γ_{CR} = Γ_{tot} − Γ_{bg}, which decreases from \(\Gamma _{{\mathrm{C}}\mathrm{R}}^{{\mathrm{u}}\mathrm{npol}} \approx 250\) ms^{−1} with the depolarisation sequence, to below the noise floor of the measurement after 5 h of CRIP, \(\Gamma _{{\mathrm{CR}}}^{{\mathrm{pol}}}\mathop { < }\limits_ \sim 19\) s^{−1}. We use Eq. (1) (with β = 0.0335 nm^{2}s^{−1} corresponding to the given ^{13}C density) to calculate the time dependence of the radial polarisation profile for total polarisation times of 1–10^{6} s, as depicted in Fig. 2c. By relating the spatial polarisation distribution, P(R,t), to the crossrelaxation rate, Γ_{CR}, via Eq. (2), we find the theoretical results are consistent with the experiment for polarisation times in excess of two hours (Fig. 2c, dashed line). Examination of the spatial polarisation distribution (Fig. 2c, inset, and Fig. 2d) implies a polarisation level of more than 99% within 21 nm of the NV, equating to a 6 × 10^{6}fold increase on thermal polarisation for 3 × 10^{5} spins.
Polarisation of external ^{1}H spins
With the basic protocol established, we now move to the polarisation of molecular ^{1}H nuclear spins external to the diamond crystal. A solution of poly(methyl methacrylate), PMMA, was applied directly to a diamond surface^{12} with single NV spin probes located 8–12 nm below the surface with an average density of 10^{8 }cm^{−}^{2}. The initial criteria for finding suitable NVs involved finding a tradeoff between maximising the NVH coupling (shallow), and minimising the coupling to sparse electronic surface defects (deep) which limit the NV linewidth and the background T_{1} time. The surface is also known to retain a 1–2 nm thick layer of protons of density commensurate with that of PMMA^{15}, which we therefore regard as being part of the target proton system to be polarised.
CRIP was applied with the external magnetic field tuned to resonance at B_{*}(^{1}H) = 1026.2 G. With a much higher diffusion constant and spinlattice relaxation rate (β = 781 nm^{2} s^{−1}, Γ_{SL} = 1s^{−1})^{16} relative to the intrinsic ^{13}C case, the ^{1}H system effectively reaches steadystate within a few seconds. Application of the CRIP sequence to NV1 (data for other NVs are shown in the Supplementary Note 2) for τ = 20s (Fig. 3a) shows the removal of the hydrogen spectral feature (blue), as compared with the depolarising sequence (orange). From the crossrelaxation curves after 1 h of CRIP (Fig. 3b), we extract ^{1}Hinduced rates for the unpolarised (\(\Gamma _{{\mathrm{C}}\mathrm{R}}^{{\mathrm{u}}\mathrm{npol}}\)) and polarised (\(\Gamma _{{\mathrm{C}}\mathrm{R}}^{{\mathrm{p}}\mathrm{ol}}\)) PMMA ^{1}H spin ensembles to be 2.71 ms^{−1} and 0.96 ms^{−1}, respectively. The ratio \(\Gamma _{{\mathrm{CR}}}^{{\mathrm{unpol}}}/\Gamma _{{\mathrm{CR}}}^{{\mathrm{pol}}} = 2.8(3)\) (consistent with the value of 2.4(3) obtained using another NV), is in good agreement with the solution to Eq. (1) for the PMMA ensemble, which gives a ratio of 2.2 in the steady state. The corresponding spatial polarisation distribution is shown in Fig. 3c, indicating that the system reaches 50% average polarisation over a volume of ~ (26 nm)^{3}. Thus, we conclude that the single spin quantum probe has increased the average polarisation of roughly a million hydrogen spins by some six orders of magnitude over the room temperature Boltzmann thermal background.
Improvements and scaling up
There is scope for improvement on these proofofconcept results: for example, engineering NV depths to 5 nm would increase the rate of target spin polarisation by an order of magnitude, and improvements in the inherent NV dephasing rate Γ_{2} (e.g. via improved surface properties) will allow for more precise tuning to different nuclear spin species. As the protocol is all optical, scaling up for highvolume production could be achieved by stacking multiple NV arrays (Fig. 4a) and/or increasing the effective interaction area via surface patterning^{31}, however, issues such as the creation and control of homogeneous DC magnetic fields over the spatial extent of the ensemble are ongoing endeavours that are beyond the scope of the work presented here.
The results presented here indicate that the CRIP protocol could produce macroscopic quantities of MRI contrast agents with high polarisation levels. For example, we consider ^{13}C isotopically enriched HEP (hydroxyethylpropionate,^{13}C_{5}H_{10}O_{3}), a wellknown MRI contrast agent^{32}. Using a single hyperpolarisation cell comprised of two NV arrays in diamond membranes separated by 1 μm (see zoomed schematic in Fig. 4a; we assume an NV density of 4 × 10^{11} cm^{−2} over a 4 × 4 mm diamond surface^{33}), the rate of polarisation transfer to a concentrated 1 M precursor HEP solution is 4 μL s^{−1} at a polarisation level of 80%. The polarisation levels for different contrast agents in 1 M precursor solutions are plotted against polarisation time (assuming perfect mixing occurs over these timescales) in Fig. 4b. In Fig. 4c, we plot the final delivery rate after dilution to 1 mM for a stack of 10 cells, showing that delivery rates of order 100 μL s^{−1} for clinical applications^{34} are achievable.
Discussion
In summary, we have experimentally demonstrated hyperpolarisation of molecular nuclear spins under ambient conditions by employing a quantum spin probe entropy pump. The technique works at low magnetic fields and room temperature conditions, requires no RF or microwave fields, and operates directly on the target molecules without the need for catalysts or free radicals. With high polarisation rates and tunability, there are excellent prospects for scaleup of the system to produce macroscopic quantities of a range of contrast agents at polarisation levels required for molecular MRI/NMR. The technique can be extended to other nuclear spin species and may also provide pathways in quantum information for initialisation of quantum simulators, or increasing the fidelity of operations through spinbath neutralisation. Future work will involve external verification of nuclear spin polarisation using conventional NMR techniques.
Methods
Experimental apparatus
The experimental apparatus consists of a custombuilt confocal microscope and a permanent magnet mounted on a scanning stage, the same setup used, and described, in^{29}. In summary, the excitation source is a solidstate laser emitting at a wavelength λ = 532 nm (Laser Quantum Gem 532). The objective lens (Olympus UPlanSApo 100×, NA = 1.4 Oil) is mounted on an XYZ scanning stage (PI P611.3 NanoCube) to allow fast laser scanning. The PL emitted by the diamond sample is separated from the laser light using a dichroic beam splitter and a bandpass filter, and coupled into a multimode fibre connected to a single photon counting module (Excelitas SPCMAQRH14FC). For T_{1} measurements, the laser beam is modulated by an acoustooptic modulator (AA OptoElectronic MQ180A0,25VIS) in a double pass configuration, and the PL signal is analysed by a time digitiser (FastComTec P7889). For optically detected magnetic resonance (ODMR) measurements, a 20μm copper wire is spanned on the surface of the diamond and connected to the output of a microwave generator (Agilent N5181A) modulated by a switch (MiniCircuits ZASWA250DR+). Laser and microwave modulations are controlled by a programmable pulse generator (SpinCore PulseBlasterESRPRO 500 MHz). The magnetic field direction and strength were varied by using a permanent magnet affixed to a set of three linear translation stages (PI M511) allowing XYZ position control. These stages had a resolution of 100 nm which is sufficient to tune the NV into resonance and align along the field along the NV axis, thus avoiding any misalignment issues^{27}.
Diamond samples
The sample (#132) used for the ^{13}C measurements was a \(\left\langle {111} \right\rangle\)oriented single crystal, electronic grade, chemical vapour deposition (CVD), 100 μm thick diamond purchased from Delaware Diamond Knives. For the measurements reported in Fig. 2, we used native (as grown) NV centres located far (several μm) from the surface. The sample (#122) used for the ^{1}H measurements is a \(\left\langle {100} \right\rangle\)oriented single crystal CVD overgrown on a HPHT substrate from Element Six. The overgrowth is roughly 50 μm and electronic grade. The sample has been implanted with ^{15}N and ^{14}N at 3 keV at a density of 5 × 10^{8} cm^{−2} each. The sample was annealed at 950 °C for 2 h and was exposed to a soft O_{2} plasma for 1 minute^{36}. The PMMA was baked onto the surface of the diamond by a heat gun at 85° for 40 min. The diamond has a range of nearsurface NV depths (~3–13 nm) determined by NVNMR spectroscopy using the dynamical decoupling method^{35}.
General acquisition procedure
The spectra shown in Figs. 2 and 3 were obtained as follows. The magnetic field was first aligned along the NV axis by maximising the PL intensity^{30,37,38}. When doing this near the GSLAC, we estimate an alignment to less than 0.1°. The magnet was then stepped along the NV direction to vary the magnetic field strength B_{0}. For each magnet position, an ODMR spectrum was recorded for about 1 minute from which we extract ω_{NV} via a Lorentzian fit, before the CRIP sequence is applied. The latter consists of a series of 3μs laser pulses, sufficient to completely initialise the NV spin state, separated by a wait time τ. The signal plotted in Figs. 2a and 3a corresponds to the PL intensity integrated over the first 300 ns of the laser pulse, normalised by the intensity integrated over the last 300 ns. To compare with the nonpolarised case, we repeated the scan but by interleaving CRIP and CRIP^{−1} pulse sequences, which acts to prevent polarisation build up in either direction. The CRIP^{−1} simply adds a radiofrequency (RF) pulse to flip the NV spin from 0〉 to −1〉. This π pulse was applied 1 μs after the end of the laser pulse, was 300 ns in duration, and was followed by a wait time τ identical to that used in the preceding CRIP sequence. With the interleaved sequence, there are two independent PL readout, one during the laser pulse following the CRIP sequence, the other following the CRIP^{−1} sequence. Note that the interleaved sequence continuously polarises the bath but each pulse flips the direction of this polarisation. As such, because of pulse imperfections it may still partly polarise nearby spins.
For the fulllength T_{1} measurements presented in main text Figs. 2b and 3c, a similar procedure was applied, except that the magnet was not moved throughout the acquisition, and instead the wait time τ was continuously swept. To monitor magnetic field drifts caused by thermal fluctuations, we recorded an ODMR spectrum at regular intervals. We can thus ensure that the NV remains on resonance with the target transition, within the NV linewidth (see details in Supplementary Note 2).
Model Hamiltonian
Given the generality of our approach with respect to the target species of nuclear spin, we refer to a general environmental target spin system, E. Assuming alignment of the external field with the NV axis, the Hamiltonian becomes
where S_{x,y,z} are the Pauli spin matrices of the spin1 system of the NV, D = 2.87 GHz is the corresponding zerofield splitting, B_{0} is the external field strength, γ_{NV} and γ_{n} are the gyromagnetic ratios of the NV and target spins, \(I_{x,y,z}^{(j)}\) are the Pauli spin matrices of nuclear spin j, A_{ j } is the hyperfine tensor describing the spinspin interaction between the NV and spin j, B_{ jk } is the tensor describing the magnetic dipole interaction between spins j and k; and summation over j,k refer to all spins in the environment. In Eq. 4, γ_{NV} is defined positive, while γ_{n} can be positive or negative depending on the species considered.
Continuum description
Solving Eq. 4 for N_{S} spins, each having hyperfine coupling A_{ j } to the NV, mutual dipole couplings B_{ jk }, and initial state of
the population of the NV \(\left 0 \right\rangle\) state is at a minimum when t = τ = 2^{1/2}π/A_{0}, and is given by
where \(A_0^2 \equiv \mathop {\sum}\nolimits_j A_j^2\) is the total hyperfine coupling field, and \(A_j = \sqrt{ \left( A_{xx}^{(j)}A_{yy}^{(j)}\right)^2 + \left(2A_{xy}^{(j)}\right)^2 }\).
The change in probability of spin j is given by
where B_{ jk } is the secular magnetic dipole coupling between spins j and k, and \(C_{jk}^2 \equiv A_j^2A_k^2/A_0^2\) is the effective hyperfinemediated diffusion strength.
In modelling these systems, we typically consider regions of at least 200 nm in size, which means of order \(N_{\mathrm{S}} \sim 10^{10}\) spins and ~10^{20} couplings for the case of PMMA, thereby making modelling of discrete spin states computationally unfeasible. We therefore map Eq. 7 to a temporally and spatially continuous
In the discrete description, the probability of finding spin j in its \(\left \uparrow \right\rangle\) state is monitored at discrete multiples of the optimal dark time, τ. As we are interested in times \(t \gg \tau\), we map changes in p_{ j } over time to
To obtain the continuum description of the spatial evolution, we put \(p_j \mapsto p\left( {{\bf{R}},t} \right)\) and \(p_k \mapsto p\left( {{\bf{R}} + {\bf{r}},t} \right)\), and discretise the Laplacian operator to get an effective diffusion term with constant β
We also map the discrete hyperfine couplings to a continuous field whose strength is determined by its position relative to the NV, R.
The summation over all hyperfine couplings is then mapped to an integral,
Finally, to account for additional sources of environmental spinlattice relaxation, where applicable, we add an additional probability sink in which any probability outside equilibrium decays at a rate Γ_{SL} = 1/T_{SL}, given by
The differential equation describing the evolution of this system is thus given by
where
is the effective source, or cooling, coefficient at position R relative to the NV, Recasting Eq. 14 in terms of the polarisation P(R, t) = 1 − 2p(R, t), we obtain Equation (1) of the main text.
For cases in which the dephasing rate of the NV spin, Γ_{2}, is greater than the hyperfine coupling to the desired target, i.e. \(\Gamma _2 \gg A_0\), the population of \(\left 0 \right\rangle\) state of the NV spin will exhibit an exponential time dependence. As such, for this regime we instead make the replacement
where the details of this process are discussed in the Supplementary Note 1.
Experimentally, Γ_{2} is obtained via the T_{1}relaxometry spectrum (with the interleaved sequence), since Γ_{2} defines the width of the crossrelaxation resonances^{28}. We note that Γ_{2} is expected to decrease upon polarisation of the ^{13}C bath. However, the effect is relatively small (see section Supplementary Note 1), and as such in the calculations shown in main text Fig. 2 Γ_{2} is kept constant and equal to the offresonance value (i.e. unpolarised case). For the ^{1}H case, the dephasing is dominated by surface effects, and is therefore unaffected by the ^{1}H polarisation.
Upon solution of Eq. 14 for the polarisation P(R, t), we may determine the total number of spins polarised at time t:
Data availability
The data that support the findings of this study are available from the corresponding author upon request.
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Acknowledgements
This work was supported in part by the Australian Research Council (ARC) under the Centre of Excellence scheme (project No. CE110001027). This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). L.C.L.H. acknowledges the support of an ARC Laureate Fellowship (project No. FL130100119). J.P.T. acknowledges support from the ARC through the Discovery Early Career Researcher Award scheme (DE170100129) and the University of Melbourne through an Establishment Grant and an Early Career Researcher Grant. D.A.B is supported by an Australian Government Research Training Program Scholarship.
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Contributions
The CRIP protocol was conceived by L.T.H. Experiments were performed by D.A.B. and J.P.T., with input from A.S., D.A.S., J.D.A.W., L.T.H., and L.C.L.H. L.T.H. developed the theory, with input from L.C.L.H. D.A.B., J.P.T., A.S., and D.A.S. prepared the samples. L.C.L.H., D.A.B. and L.T.H. wrote the manuscript with input from all authors. L.C.L.H. supervised the project.
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Broadway, D.A., Tetienne, JP., Stacey, A. et al. Quantum probe hyperpolarisation of molecular nuclear spins. Nat Commun 9, 1246 (2018). https://doi.org/10.1038/s41467018035781
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