Hyperpolarisation of external nuclear spins using nitrogen-vacancy centre ensembles
A. J. Healey, L. T. Hall, G. A. L. White, T. Teraji, M.-A. Sani, F. Separovic, J.-P. Tetienne, L. C. L. Hollenberg
HHyperpolarisation of external nuclear spins using nitrogen-vacancy centre ensembles
A. J. Healey,
1, 2
L. T. Hall, G. A. L. White, T. Teraji, M.-A.Sani, F. Separovic, J.-P. Tetienne,
1, 2, ∗ and L. C. L. Hollenberg
1, 2, † School of Physics, University of Melbourne, VIC 3010, Australia Centre for Quantum Computation and Communication Technology,School of Physics, University of Melbourne, VIC 3010, Australia National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan School of Chemistry, Bio21 Institute, University of Melbourne, VIC 3010, Australia
The nitrogen-vacancy (NV) centre in diamond has emerged as a candidate to non-invasivelyhyperpolarise nuclear spins in molecular systems to improve the sensitivity of nuclear magneticresonance (NMR) experiments. Several promising proof of principle experiments have demonstratedsmall-scale polarisation transfer from single NVs to hydrogen spins outside the diamond. However,the scaling up of these results to the use of a dense NV ensemble, which is a necessary prerequisite forachieving realistic NMR sensitivity enhancement, has not yet been demonstrated. In this work, wepresent evidence for a polarising interaction between a shallow NV ensemble and external nucleartargets over a micrometre scale, and characterise the challenges in achieving useful polarisationenhancement. In the most favourable example of the interaction with hydrogen in a solid state target,a maximum polarisation transfer rate of ≈ NVs. Reduced levels of polarisation efficiency are found for liquid statetargets, where molecular diffusion limits the transfer. Through analysis via a theoretical model, wefind that our results suggest implementation of this technique for NMR sensitivity enhancement isfeasible following realistic diamond material improvements.
I. INTRODUCTION
Nuclear magnetic resonance (NMR) underpins a vari-ety of techniques that find use across the fields of physics,chemistry, and the life sciences. The sensitivity of anNMR measurement is proportional to the degree of nu-clear spin polarisation in the target to be analysed, whichis very low under typical thermal conditions ( P th ≈ − at room temperature and a magnetic field of 3 T). Con-sequently, a number of approaches have been developedto achieve levels of polarisation well in excess of ther-mal levels (“hyperpolarisation”) in nuclear spin ensem-bles. To date, dynamic nuclear polarisation (DNP) [1–4]is the most widely implemented method of achieving hy-perpolarisation, with para-hydrogen induced polarisation(PHIP) [5, 6] and optical pumping [7, 8] based methodsalso finding success. These methods, however, are farfrom being problem-free in their application. Each suf-fers from limitations, such as in their target specificity(PHIP, optical pumping), or in the technically challeng-ing conditions required for optimal operation (e.g. cryo-genic temperatures, large magnetic fields, and strong mi-crowave driving for DNP).For these reasons, it has been proposed that the neg-atively charged nitrogen-vacancy (NV) centre defect indiamond [9] may be a suitable candidate to address someof the shortcomings in other techniques [10–12]. The NVcentre’s electron spin is efficiently polarised ( ≈ ∗ [email protected] † [email protected] room temperature. Promising proof of principle experi-ments have demonstrated polarisation transfer from NVcentres to nuclear targets via the magnetic dipole-dipoleinteraction using a variety of experimental protocols [10–19]. This transfer is non-invasive to the target and gen-eral, avoiding the target specificity limitations of othertechniques. Further, the potential for room tempera-ture and low-field operation raises the prospect of achiev-ing hyperpolarisation with a reduced technical overhead.However, work so far has been limited to either inter-nal C [13–19] or small-scale external polarisation withsingle NV centres [10–12], which are naturally limitedin their scope towards achieving bulk hyperpolarisationover a sample volume useful for NMR. Recent theoreticalwork in Ref. [20] showed that bulk NMR enhancement(as well as for NV-based, micron-scale NMR [21, 22]) ispossible using dense NV ensembles with sufficiently goodquantum coherence properties. However, successful ex-perimental demonstration of polarisation transfer froman NV ensemble to an external nuclear target has notyet been achieved.Although NV ensembles essentially act as many inde-pendent NVs for the purpose of hyperpolarisation [20],extending the previously reported single NV results tothe case of a dense ensemble is not trivial. As the distancebetween NVs and nuclei external to the diamond will beseveral nanometres, the dipole-dipole coupling that gov-erns the polarisation transfer is weak, and thus the NVcoherence time T (which is scheme dependent) emergesas the limiting variable [23]. In increasing the densityof NV centres within the diamond sample, the magneticnoise is increased proportionally, degrading these quan-tum properties. The dominant noise source in a denseensemble is the substitutional nitrogen bath [24] which, a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n with current standard sample production techniques, isat minimum ten times more abundant than the NV den-sity [25]. In addition, the necessity of placing the NVsnear the diamond surface brings another significant con-tribution to NV decoherence: a range of fast-fluctuatingsurface defects that render near-surface NV propertiesmuch worse than those in the bulk and result in bandbending that reduces the charge stability of the negativeNV charge state within a few nanometres of the surface[26–30].Further, while it may be possible to find a single NVlocated within an anomalously calm spin environmentthat exhibits unusually long coherence times, or that issituated anomalously close to the surface and thus cou-ples more strongly to external spins, in dealing with anNV ensemble the resulting dynamics will be governed byaverage NV properties [31]. It is not immediately clear,therefore, whether previous successful single NV resultsare easily extendible to higher NV densities.In this work, we present an experimental study intothe challenges associated with the scaling up of previ-ous single NV results [10–12] to shallow NV ensembles,with the goal of demonstrating polarisation transfer com-patible with the vision of Ref. [20]. We investigate thepolarisation dynamics over a range of parameters usinga robust, pulse-based scheme (PulsePol [18]). Startingwith an ideal room temperature scenario, we polarise asolid target (biphenyl) and analyse our results using atheoretical model. In doing so, we experimentally de-termine an upper bound on the polarisation (or cooling)rate in the current “best case” scenario and discuss theimplications of this. We then probe the extent to whichthe addition of molecular diffusion compromises the po-larisation transfer by repeating experiments using fluidtargets of varying viscosities. We conclude with a discus-sion of the results and an assessment of the prospects forfuture work. II. RESULTSA. Polarising a solid target
We first investigate the interaction between our shallowNV ensemble and hydrogen spins within a solid target.All experiments were carried out over a 50 × µ m fieldof view (FOV) using a widefield NV microscope. Ele-ments of this setup are depicted schematically in Fig. 1(see Appendix A for details), with the FOV denoted bythe red square in the NV photoluminescence (PL) image,chosen to coincide with a region of relative laser inten-sity and microwave driving uniformity. Biphenyl crystalswere formed on the surface of the diamond and encap-sulated with epoxy to prevent subsequent sublimation(details in Appendix B). As our experiment addresses alarge number of NVs simultaneously and a ∼ µ m target volume, it can be considered as a “toy model” for arealistic, NMR-relevant implementation of the technique. d NV MW resonatorROI
20 μm
Bright-field
532 nm laserNV layerN-free diamond MW resonator:spin state control H y d r ogen t a r ge t NV PL sCMOScamera(b)(a) (c)P>P th NV − centre Hydrogen spin FIG. 1. a) Schematic of experimental setup, depicting wide-field NV microscope and polarisation transfer via dipolar cou-pling between an ensemble of NVs at a depth d NV below thediamond surface and a number of nearby nuclear spins. Polar-isation P greater than the thermal background ( P th ) is builtup locally to an NV (dashed semicircle) as its spin polarisa-tion (quantised along external bias field B ) is donated to thenuclear bath, before spin diffusion spreads this polarisationinto the bulk target. b) Bright-field image of a 200 × µ mregion, showing biphenyl crystals on the diamond surface. c) NV photolumiescence (PL) image of the same region in (b),with the 50 × µ m region of interest (ROI) used for thiswork marked by the red square. Achieving polarisation over this scale presents two prin-cipal challenges: the technical, experimental challengeof successfully addressing a large number of NVs overa useful field of view, and the material problem of re-duced coherence times for high density NV ensembles.The PulsePol pulse sequence has been identified as thebest currently accessible approach in addressing theseconcerns due to its robustness to realistic experimentalerrors (see Appendix C) [18]. Its action as a decouplingsequence is also beneficial in addressing our ensemblesas they are subject to broadband noise from the nitro-gen spin bath and surface defects. The ensembles werecreated using a 2.5 keV N implant with a fluence of1-2 × cm − and a 1100 ◦ C ramped anneal, leadingto NVs lying within 10 nm of the surface with an arealdensity σ NV ≈ µ m − (see details in Appendix B).Coherence times in excess of 10 µ s were achieved usingPulsePol which is a considerable extension over low-orderdecoupling sequences in this regime [24, 31].The PulsePol pulse sequence, depicted in Fig. 2(a),sets an average Hamiltonian that approximates a flip-flop Hamiltonian between the NV and a target nuclearspin species when a resonant condition τ = nτ L / n is met, where τ is defined as the durationof the unit sequence, repeated 2 N times, and τ L is thetarget Larmor period.Fig. 2(b) shows a typical PulsePol spectrum obtainedby sweeping τ for fixed N = 30. The y-axis is the nor-malised NV PL averaged over the full FOV, which is aproxy for the population of the m s = 0 NV spin state,referred to as NV spin polarisation in what follows. Thedip at τ ≈
840 ns is the n = 3 hydrogen resonance, whichproduces the strongest interaction [18] and will be the fo-cus of this work. When the resonant condition is met, alarge drop in NV spin polarisation is observed, which isinferred to have been symmetrically donated to the targethydrogen bath by virtue of the PulsePol sequence design[18]. To gain an insight into the dynamics of the appar-ent polarisation transfer, we examine the decay of NVspin polarisation versus total interaction time t = 2 N τ by increasing N for fixed τ , and compare the resonant( τ = τ res ) case with the off-resonant case. Both sets ofdata are shown in Fig. 2(c), where the red points areestimates of the off-resonance decay at τ = τ res made byaveraging data obtained at τ = τ res ±
60 ns, and the bluepoints show the resonant decay. Following the treatmentof Refs. [23, 32, 33], we represent the resonant decaycurve as a product of the background NV decoherence(which is independent of any polarisation dynamics) andthe resonant contribution, P NV ( t ) = P off ( t ) P res ( t ) , (1)where P NV is the population of the NV m s = 0 spin state(assumed to be perfectly initialised at t = 0).For the present experiment, we find that the off-resonance decay is well fit by P off ( t ) = exp( − ( t/T NV ) β )with T NV = 22 µ s and β = 0 .
42. In analysing theshape of the resonant decay curve, it is useful to considerthe extreme cases of the strong and negligible dephasingregimes. In both cases, we assume that there is a di-rect correspondence between extra coherence lost by theNV when the resonant condition is met and that resultingfrom the flip-flop interaction in the effective Hamiltonian.In the ideal case, there is coherent coupling betweenNV and the hydrogen spin bath, and the evolution of thesystem is governed by P res ( t ) = cos (cid:18) A t (cid:19) , (2)where A = (cid:115)(cid:88) j A j is the summed dipolar coupling be-tween the NV and full spin bath, made up of j hydrogen spins [10, 23]. In the absence of decoherence, the flip-floptime τ = π/A corresponds to the full donation of theNV’s spin polarisation to the target bath.Conversely, in the strong dephasing regime Γ tot2 (cid:29) A ,where Γ tot2 = Γ NV + Γ H (with Γ NV = 1 /T NV and Γ H isthe hydrogen spin dephasing rate) is the total dephasingrate of the system under the PulsePol sequence, inco-herent polarisation transfer proceeds via the monotonicevolution [10, 23] P res ( t ) = exp (cid:18) − A Γ tot2 t (cid:19) . (3)With an average NV depth measured at d NV ≈ A and Γ tot2 (whichis affected by a nuclear dephasing gradient due to thepresence of unpaired electron spins on the diamond sur-face [23]) with d NV = 6 nm. Good agreement is foundwith the strong dephasing case, indicating that Eqn. 3gives a good approximation to the polarisation dynamicsin our experiment. It is possible, however, that there aresome target spins that exist in or near the strong coupling( A > Γ tot2 ) regime, implying the existence of a small co-herent component in our data. In order to capture thisinterchange between coherent and incoherent behaviour,as averaged over our measurement ensemble, we intro-duce the following phenomenological adjustment to Eqn.3: P NV ( t ) = exp (cid:0) − (Γ NV t ) β (cid:1) (cid:26) exp( − Γ int t ) cos (cid:18) A t (cid:19) + (1 − exp( − Γ int t )) exp (cid:18) − A Γ tot2 t (cid:19)(cid:27) , (4)where Γ int is a parameter controlling this interchange.Setting Γ int ≈ Γ tot2 ≈
100 kHz makes only a subtle ad-justment to the decay shape, however the influence ofthis factor becomes more apparent in Fig. 2(d). Here, weplot the difference between the experimental off- and on-resonance data, normalised by the difference in PL givenby ensembles initialised in the m s = 0 and m s = − t at each point. This amounts to a direct experimentalmeasurement of the rate of additional NV depolarisationdue to the interaction with the hydrogen bath, which weinfer to correspond directly with the hydrogen coolingrate, defining u ( t ) = 1 t ( P off ( t ) − P NV ( t )) , (5)which is a generalisation of the definition in Refs. [20, 23].Note that this equation is exact when the hydrogen bathpolarisation is given by P H ( t ) = P off ( t ) − P NV ( t ) and an (b)(a)(c)(d) 𝜋 𝑦𝜋2 𝑦 𝜋2 𝑦 𝜋 −𝑥 𝜋2 𝑥𝜋2 𝑥 τ v τ /4 τ /4 τ /4 τ /4 μs) N VP L ( a . u . ) Off-resonance dataOn-resonance dataCoherentStrong dephasingHybrid
CoherentStrong dephasingHybridExperiment N V depo l . r a t e ( s - ) t ( μs) N VP L ( a . u . ) τ (ns) τ = τ res FIG. 2. a) Schematic of the PulsePol pulse sequence. b) N =30 PulsePol spectrum scanning τ , with T ∗ ,n -limited hydrogenresonance visible at τ = 3 τ L /
2. The solid blue line is a fit tothe data (black circles) using a Lorentzian lineshape. c) Off-(red) and on-resonance (dark blue) NV decay with PulsePolsequences of increasing length and total duration t = 2 Nτ .Solid lines give theoretical predictions based on numericallyintegrated values of A , and Γ tot2 for the coherent (green),strong-dephasing (light red), and hybrid (light blue) cases. d) Experimentally determined NV depolarisation rate (greycircles) and comparison to theory (solid curves). overestimate when there is additional resonant coherenceloss that does not contribute to useful polarisation. Thecurrent experiment is unable to make the distinction andso the cooling rates quoted in this work represent upperlimits of the true values.The experimental data peaks at a value of u ≈ − for N = 8, corresponding to an interaction time t ≈ µ s. The strong dephasing approximation vastly over-estimates the NV depolarisation rate for small times be-cause it sees coherence decrease exponentially while co-herent transfer is sinusoidal (sin x ≈ x for small x ),while the fully coherent case predicts an accurate maxi-mum depolarisation rate but for a much longer sequence than the actual N = 8. The modification of Eqn. 4 isrequired to give qualitative agreement with the data, pro-ducing a peak positioned according to the value of Γ int .The good agreement we find with a model that containsonly experimentally determined parameters and one freeparameter Γ int suggests that the assumption that NV de-polarisation corresponds to hydrogen bath polarisationis valid. Additionally, the close correspondence betweenthe magnitude of the maximum experimental cooling rateand that predicted in the coherent case (accounting forbackground NV decay) supports the use of the coherentmodel for general predictions as in Ref. [20].Under continuous application of this optimal sequence,polarisation can be built up within the target bath ac-cording to the differential equation: ∂P ( R , T ) ∂T = u ( R ) [1 − P ( R , T )] − Γ ,n P ( R , T )+ D n ∇ P ( R , T ) , (6)where Γ ,n is the nuclear relaxation rate, D n is thenuclear diffusion constant, and u ( R ) is the position-dependent cooling rate, integrating to the maximumexperimentally determined NV depolarisation rate [20].Approximating the hydrogen spin diffusion in thebiphenyl crystal to that of a spin-1/2 species on a cu-bic lattice, D n ≈ . µ π (cid:126) γ n ρ / n [34], we find D n ≈
571 nm /s. Thus diffusion out of the the NV sensingvolume will happen on a comparable timescale to thepolarisation transfer, leading to efficient polarisation ofthe total bath but only a small buildup of polarisationlocal to the NV. This is not a problem for the ultimateimplementation of the technique but it does make unam-biguously measuring polarisation buildup using the sameshallow NVs difficult.Fig. 3 shows an attempt to evidence polarisationbuildup within the NV sensing volume using the optimalsequence previously identified ( N = 8). This measure-ment is made as per the pulse sequence schematic in Fig.3(a): a resonant PulsePol sequence is repeated for a time t pol > T ,n and polarisation buildup measured throughthe change in NV PL. The NV PL should increase overthe course of the measurement as polarisation builds upwithin the NV sensing volume and the depth of the hy-drogen resonance decreases (due to an effective reductionin A ). The procedure is then repeated with the NV ini-tialised in the m s = − u = 7506 s − and setting T ,n = 1 / Γ ,n = 1 s. T ,n sets the time scale to reach the steady state (herewe use a simple exponential rise with time constant T ,n ).Higher values of T ,n will allow higher levels of polarisa-tion to accumulate but this will result in only a modestincrease in the steady state value as we make a localmeasurement and D n is large compared to u . Biphenyl T ,n has been reported to be as high as ≈
10 min at C hange i n N V depo l a r i s a t i on ( % ) pol (s) DataFitTheory (b)(a) t pol = R(t + t d )PP � N R times ... PP � N PP � N R times ... PP � N FIG. 3. a) Pulse sequence used to demonstrate local polar-isation buildup: a resonant PulsePol sequence is repeated R times to reach a steady state. The bath is then reset with a“depolarisation” sequence of the same length, where polari-sation in the opposite direction is achieved by initialising theNV in the m s = − b) Measured polarisation buildup within NVsensing volume following repeated application of the PulsePolsequence previously identified to give the maximum coolingrate ( N = 8). The blue line is the theoretical predictionbased on the solution of the differential equation Eqn. 6 with T ,n = 1 s and the red line is a fit to the experimental data,finding T ,n ≈ .
88 s. room temperature and ≈ ∼
450 G). The steady statePulsePol dip reduction (the expected measurement con-trast) for an NV 6 nm from the surface was calculated bynumerically integrating over the steady state probabilitydistribution. The predicted contrast change is extremelysmall ( ≈ . π pulse prior to readout to account for com-mon mode noise) and thus represents the cumulative PLgiven by R ≈ µ s), necessary to ensuremaximal and even ensemble initialisation across the fullFOV but reducing the spin readout contrast. This alsoreduces the polarisation duty cycle in the experimentwhich is a major limiting factor in the steady-state po-larisation produced, taking u (cid:55)→ u ( t seq ) t seq t seq + t d F , where t seq is the optimal sequence length and t d is the sequence “dead time”, exceeding 30 µ s in this case, and a finite ini-tialisation fidelity F = 0 . t d to be neg-ligible. The solid red curve in Fig. 3(b) is a fit to theexperimental data (again a single exponential rise), yield-ing a similar total contrast change on the slightly shortertime scale T ,n ≈ . π/ B. Polarisation scaling with NV T Having demonstrated and analysed polarisation trans-fer in a current best case scenario, we now further probethe dependencies of Eqn. 4 by varying the NV and tar-get properties. To see this clearly, we remove the influ-ence of the background NV decay as much as possible by,for every data point, dividing the difference between theon- and off-resonance measurements by the off-resonancevalue at that point, to obtain a normalised polarisationsignal S ( t ) ≡ P H ( t ) /P off ( t ). Taking our earlier defini-tions and Eqn. 4 we find S ( t ) =1 − exp( − Γ int t ) cos (cid:18) A t (cid:19) − (1 − exp( − Γ int t )) exp (cid:18) − A t Γ tot2 (cid:19) , (7)so that we have an exponential rise to unity with the pos-sible appearance of sinusoidal behaviour at short times.Although we consistently observe saturation to a valuebelow one due to the increased influence of decoherenceat long times, this equation well describes our data fortimes ≤ µ s which is well beyond a realistic optimalsequence length ≈ µ s.First we examine the influence of NV T , which still en-ters into Eqn. 7 through the previous definition of Γ tot2 . (b)(a) D1 biphenyl t (μs) P o l a r i s a t i on s i gna l ( no r m . ) D1 PMMAD1 bareD2 bareD2 PMMA N VP L ( no r m . ) D1 biphenylD1 PMMAD1 bareD2 PMMAD2 bare
FIG. 4. a) Comparison of background (off-resonance) Pulse-Pol T decay for different solid targets (biphenyl, PMMA, barediamond surface) and diamond samples (labelled D1 and D2).Solid lines are fits to an exponential decay exp( − ( t/T NV ) β )with β ranging from 0.42 to 0.47. Data normalised to themaximum NV spin contrast for a given diamond. b) Nor-malised polarisation transfer for different solid targets andbare diamond hydrogen signals for two diamond samples.
In Fig. 4 we present the normalised polarisation transfersignal obtained for two solid hydrogen targets, biphenyland poly(methyl methacrylate) (PMMA), and using twodiamond samples with different T - varying between ≈ µ s and 22 µ s (with minimal variation in the exponent β ) as shown in the off-resonance PulsePol decay curvesin Fig. 4(a). T changes between two diamonds, D1 andD2, as D2 was implanted with twice the dose of N ionsas D1 and so features a more dense nitrogen spin bathand possibly more implantation-induced crystal damage(see SI for diamond sample details). Additionally, how-ever, T was also found to vary based on the hydrogentarget present on the diamond surface. This effect wasconfirmed to be a genuine background effect (rather thanoff-resonant polarisation transfer) by the appearance ofsimilar variation in Hahn echo T (see Appendix C) andhas previously been observed in near-surface single NVs,where it was explained in terms of an electronic passiva-tion of surface electron density [36].This shows that, even where the nitrogen spin bath isexpected to be the dominant source of NV decoherence asin our samples, unpaired electron spins on the diamondsurface (or other surface effects) are also significant. Thedielectric properties of PMMA and biphenyl are unlikelyto explain such a large difference but a similar electrical passivation may be possible through a separate mecha-nism such as chemisorption to unpaired electron spins onthe surface through, for example, a target double bond[37, 38]. Regardless, the source of this effect is not im-portant for the current discussion, though it convenientlyallows us to probe the dependence of the polarisation dy-namics on NV T in a controlled way.The effect of the target-specific NV T is evidentthrough comparison of the D1 biphenyl and D1 PMMAcurves in Fig. 4(b). Polarisation transfer to biphenylis observed to be more efficient than to PMMA, despitePMMA’s greater hydrogen density ( ρ PMMA H = 56 nm − versus ρ biph. H = 41 nm − ) and negligible differences in T ∗ ,H (= 1 / Γ H for a solid target) for both targets as mea-sured via XY8 correlation spectroscopy [39]. The differ-ence in NV T is sufficient to explain our data and ismost evident at longer times when the system’s evolu-tion is well described by the strong-dephasing limit. Forshort times ( < µ s), when coherent evolution is preva-lent, PMMA gives a stronger signal than biphenyl as thecoherent polarisation exchange is related only to the cou-pling strength A ∝ √ ρ H .Comparing the PMMA signal from the two diamonds,it is clear that a reduction in NV T reduces per-NVpolarisation transfer efficiency (possibly small differencesin coupling strength too due to depth distribution - seeAppendix B). This results in a 3.5-fold reduction in max-imal experimentally measured per-NV cooling rate. Thisis greater than the difference in estimated NV densitybetween the two samples, although there is room to im-prove the properties of high-density NV ensembles (seeSec. III). A similar difference is also observed in the re-spective bare diamond signals, which is believed to arisefrom an adventitous hydrogen layer on the diamond sur-face [39, 40]. This signal is expected to be present in allour data as it is not removed by any cleaning process.We do not subtract it from the data in this work as inprinciple any polarisation transferred to this layer candiffuse into the target and, regardless, its contribution tothe maximum cooling rates for solid targets is small. C. Effect of target diffusion
The results of Sec. II B demonstrate the impact ofchanging Γ tot2 through varying NV T . Differences in thetarget T will affect polarisation transfer in the same way.While the measured T ∗ ,H values for the two solid tar-gets compared were similar, molecular diffusion of targetspins into and out of the NV sensing volume during thepolarisation transfer will result in a loss of phase coher-ence in the interaction (and thus an effective T , scal-ing as D − n ). When using a pulse-based scheme such asPulsePol this is compounded by an additional loss in po-larisation transfer efficiency, as the requirement for theNV-target interaction to be long enough lived for the av-erage Hamiltonian to accurately approximate a flip-flopHamiltonian introduces an effective reduction in couplingwhich scales as D − n when the diffusion timescale exceedsthe Larmor period [23]. We therefore expect the coolingrate u max ∝ A / Γ tot2 using PulsePol to scale as D − n forfluid targets.This represents a challenge for genuine liquid-state hy-perpolarisation, which is an attractive niche for NV-based techniques to fill as current liquid hyperpolar-isation techniques are less efficient than their solid-state counterparts [41]. Additionally, NV-based micron-scale NMR has recently emerged as having utility foranalysis of liquid samples [21, 22], and has recentlybeen successfully integrated with Overhauser DNP andparahydrogen-based hyerpolarisation techniques [42, 43].It has been proposed that an all-diamond hyperpolari-sation and NMR platform could be competitive in thisregime [20]. The goal of this section, then, is to experi-mentally determine the efficiency of polarisation transferto targets in the liquid state compared to those in thesolid state, with diamond material properties held con-stant.To assess the impact of molecular diffusion on polar-isation transfer, several mixtures of glycerol and waterwere produced with the glycerol volume fraction χ g rang-ing from 0 (pure water) to 1 (pure glycerol). Assumingthe static coupling between bath hydrogen spins and NVis constant (justifiable as ρ H should vary by less than1% under laboratory conditions [44]) and any effect ofchanging background NV decoherence due to target di-electric properties is minimal (see Appendix D : NV T changes minimally), any loss in polarisation transfer ef-ficiency with reduced viscosity can be ascribed to thechanging molecular dynamics.Fig. 5(a) plots the inferred polarisation transfer, withthe background NV decay (diamond D1) normalised outfor clarity. A clear trend is visible, with the growth ofthe pure glycerol resonance comparable to a solid tar-get due to its high viscosity, while diluting with waterdown to χ g = 0 . T , which is consistent with the results of theprevious section.Fig. 5(b) plots the NV depolarisation rates (which weagain take to correspond to the cooling rate) as in Sec.II A. Compared to the biphenyl results, the maximumcooling rate for pure glycerol is roughly a factor of twolower, despite almost identical background NV T . XY8correlation spectroscopy measures only a small reductionin target T which is not enough to explain the full re-duction, especially when considering that glycerol is morehydrogen-dense than biphenyl ( ρ gly H ≈
65 nm − ). Thusour data supports an additional reduction in polarisa-tion transfer as a result of using the PulsePol sequence:assuming again that the maximum experimental coolingrate is proportional to the theoretical strong-dephasing limited rate, this result suggests a reduction in effectivecoupling strength by a factor of ≈
3. However, Fig. 5(b)shows that reducing NV T by using D2 instead of D1made a larger difference than diluting glycerol by 50%by volume in water, which is expected to result in anincrease in D n of over an order of magnitude [45].Fig. 5(c) summarises the cooling rate results for theglycerol mixtures and other targets for comparison. Aswell as the solid targets already discussed, we also includeresults obtained with a highly viscous oil (Sigma-Aldrich1250 cSt I0890 immersion oil). As a figure of merit, wedivide the maximum measured cooling rate by the theo-retical strong-dephasing cooling rate for each data point,normalising to the maximum value obtained (biphenyl).In doing so, we normalise out any differences due to T tot2 , d NV , or ρ H , isolating the effective coupling reduction dueto molecular diffusion [23]. Again we include data ob-tained with diamond D2 as well as D1 for three of thetargets, finding that differences between the diamondsare well normalised out, providing further support forthe model.This quantity is plotted against the inverse of the kine-matic viscosity, a readily available quantity that is pro-portional to D n through the Stokes-Einstein equation (al-though this proportionality will not necessarily be iden-tical for all targets). The remaining trend confirms thatincreasing molecular diffusion makes polarisation transferto liquid targets less efficient than to solid targets usingPulsePol. However, the dependence in the intermediateviscosity regime (glycerol series: χ g = 0 . −
1) is weakerthan expected.This is also true for the variation of measured T H (= 1 / Γ H for a fluid target) for the series of glycerol mix-tures, where a reduction is present but with weaker scal-ing than the expected D − n . Within error, our data is con-sistent with either variation in D n of only approximately20% between χ g = 1 and χ g = 0 .
5, or with the full se-ries exhibiting characteristic diffusion times less than thehydrogen Larmor period ( ≈
550 ns) (see Appendix D).In both cases this contradicts expectation [45]. However,the discrepancy may be explained either in terms of anear-surface adsorption layer where fluid motion is notwell described by bulk viscosity values, or possible near-surface solidification, both of which have previously beensuggested [36, 39].Fig. 5(d) plots the total steady-state nuclear polar-isation predicted to be produced by the maximum ex-perimentally determined cooling rates and taking intoaccount the measured σ NV for the respective samples( σ NV = 1400 µ m − for D1 and 1800 µ m − for D2) andthe area addressed (50 × µ m). As diffusion drivespolarisation away from the NV sensing volume as in Sec.II A in all cases, local saturation effects are negligible andthe simulated steady state hydrogen polarisation per NVtends towards u ( t seq ) t seq t seq + t d F with T ,n = 1 s. Here weplot the limiting case of t d = 0. As this data is not nor-malised against A / Γ tot2 , the effect of NV T can againbe seen here, with the slight increase in NV density in D2 N V depo l a r i s a t i on r a t e ( s - ) P o l a r i s a t i on s i gna l ( no r m . ) (a)(c) (b) u m a x / ( A T t o t )( a . u . ) ν (sm -2 )BiphenylPMMAViscous oil S t ead ys t a t epo l . ( s p i n s ) BiphenylPMMAViscous oil10 ν (sm -2 ) (d) S o li d S o li d χ g = 10.880.750.50D1D2 FIG. 5. a) NV polarisation transfer to glycerol-water mixtures of various compositions denoted by glycerol volume fraction χ g ,normalised to background decoherence. b) Experimental cooling rates from the data in a). c) Plot of maximum cooling rate,normalised with respect to the theoretical no-diffusion value, against the inverse of the kinematic viscosities of the glycerolmixtures and additional liquid and solid state targets for comparison. Error bars extrapolated from the range of cooling ratesobtained within N = N opt ± N opt corresponds to the maximum cooling rate. d) Steady-state nuclear polarisationvalues predicted by a simulation using the measured cooling rates, NV densities, and the addressed field of view of 50 × µ m.Idealised parameters were used, including F = 0.8, t d = 0 µ s, and T ,n = 1 s. insufficient to offset the reduction in T in this sample.These results confirm the difficulty of achieving polar-isation to highly fluid targets, with no evidence found forsignificant interaction with water. However, in the in-termediate viscosity region, the observed dependence isweaker than theoretically predicted. Sufficiently viscousliquids diffuse slowly enough to interact with strengthwithin a factor of two of that of solid targets and so inthis regime NV based hyerpolarisation appears to holdpromise. This could be applicable to micron-scale NVNMR modalities and hyperpolarisation of more fluid tar-gets could be achievable by exploiting the variation ofviscosity with temperature; polarising a slow-moving liq-uid at low temperature and then heating up, similar to afreeze-thaw cycle commonly used for solution-state DNPbut without the need for a convenient phase transition.Additionally, the apparent reduction in molecular dif-fusion near the diamond surface could be exploited toachieve greater polarisation transfer than would be ex-pected for a fluid with true bulk properties. Althoughthis effect requires more rigorous characterisation, it islikely that it is confined to within a few nm of the dia-mond surface and so molecular and/or spin diffusion willquickly take polarisation into the bulk fluid. III. DISCUSSION
Our results show that the coherence properties in cur-rent dense, shallow NV ensembles are sufficient to trans-fer a significant amount of polarisation to an externalnuclear spin bath, in both solids and sufficiently viscousliquids. The PulsePol protocol is successful in allowingthe use of ≈ NVs in parallel and the extension ofthe current experiment to an even larger active area isfeasible provided technical challenges of microwave de-livery and high-intensity laser illumination are met overthat area. A higher intensity source for the NV opticalpumping could allow a significant decrease in the laserpulse duration used, resulting in an improved polarisa-tion duty cycle that would provide an improvement inthe steady-state hydrogen polarisation over the currentexperiment.In the limiting case of achieving perfect NV initial-isation instantly, the cooling rate demonstrated withbiphenyl is sufficient to generate an average polarisa-tion of P = 2 . × − within the 1- µ m-thick layerclosest to the diamond (taking the uniform NV density σ NV = 1400 µ m − and T ,n = 1 s). This representsan over three orders of magnitude enhancement over theBoltzmann polarisation under our laboratory conditions,owing mainly to the low magnetic field used ( ∼
450 G)and operation at room temperature. The absolute po-larisation is small, however, and would not scale withmagnetic field or temperature where a brute-force Boltz-mann polarisation enhancement could be obtained. Fur-thermore, practical realisation of this technique for bulkNMR enhancement would require structuring a diamondpolarisation cell such that the volume above the diamondslab is of a micron scale or smaller, which represents asignificant engineering challenge [20]. However, there arealso significant material improvements that can be madeto enhance the polarisation obtained.The NV yield in both diamond samples used in thisstudy (1.4% for D1 and 0.9% for D2) is low compared tothat of typical deeper ensembles [46] and it has been sug-gested that techniques such as Fermi engineering couldenhance this yield towards 100% [47]. In the latter case,an improvement of nearly two orders of magnitude maybe achieveable in the area-normalised polarisation gen-erated, whereas even in the former case a factor of 2-5improvement is possible. The difference between yields inshallow and deeper ensembles can be understood in termsof band bending due to imperfections in the oxygen-terminated diamond surface. Improving this is an activearea of research, for example there are current efforts tounderstand and control the diamond surface through op-timised cleaning and annealing strategies [48].Reducing near-surface band bending will also resultin a shallower mean NV depth, resulting in strongercoupling with the external spin bath and larger coolingrates (scaling with d − / NV in the coherent case and d − NV in the strong-dephasing limit). The dependence shownin Sec. II B of NV T on hydrogen target also showsthat, even with the high nitrogen densities of the sam-ples used, surface spins contribute significantly to NVdecoherence. The combined action of reducing the meanensemble depth to that of the expected ion implantationrange of a 2.5 keV implant ≈ T to a nitrogen-limited value would, according to our theo-retical model outlined in Sec. II A, result in an additionalcooling rate enhancement of upwards of four times.Control over the diamond surface also has a final ben-efit: unpaired surface electron spins also contribute tothe dephasing of the hydrogen spins closest to the dia-mond [23]. We included this factor in the the analysisof Sec. II A, taking a typical surface electron density of σ e = 0 . − [26, 27] which reproduced our experimen-tal results well. Numerical integration of the quantity A ( R ) / Γ tot2 ( R ), the cooling rate in the strong-dephasinglimit, shows that this electron density results in a 44%drop in the effective coupling between an NV 6 nm fromthe surface and the hydrogen bath (for biphenyl).Considering all of the above factors, we estimate thata total improvement of up to two orders of magnitudeis achievable with realistic diamond material advance-ments. This would be sufficient, following successful di-amond nanostructuring and integration with an NMRprobe, to achieve significant enhancements over thermalpolarisation [20].The results of Sec. II C confirm that NV hyperpolar- isation of low-viscosity liquid targets is beyond currentcapabilities but the cooling rates obtained for more vis-cous targets were within a factor 2-3 of the solids. Thetransfer appears to be aided by an effective reduction inmolecular diffusion near the diamond surface, possiblydue to surface dragging effects or local drying broughtabout by laser heating. This surprising result may bebeneficial for polarisation to fluids with moderate vis-cosity ( D n ≈ − m s − ), whereby polarisation canbe transferred to regions of locally low diffusion and al-lowed to diffuse into the bulk fluid. Diffusion constantsof this order of magnitude are typical in liquid crystaland lipid bilayer targets [49, 50], which could be appeal-ing targets for NV-based polarisation. In particular, ifpolarisation transfer to these targets remains within anorder of magnitude of solid targets as in our experiment,the improvements to the diamond materials discussedabove could provide a realistic avenue towards hyperpo-larised NV-based micron-scale NMR [20]. Further workis required to fully characterise the near-surface fluid dy-namics, however. We emphasise that we do not have adirect measurement of the diffusion constants of the tar-gets used in our experiments (local or bulk) and so theinterpretation of our current results can only be qualita-tive. IV. CONCLUSION
We have presented the first reported experimentalstudy of external hyperpolarisation using an NV ensem-ble. We demonstrated evidence of polarisation transferin the closest to ideal case, to hydrogen nuclei within asolid target, finding agreement between experiment andan analytical model combining coherent and incoherenttransfer mechanisms. We found that the polarisation rateobtainable with current materials and with realistic ex-perimental conditions is sufficient to achieve a modest(three orders of magnitude over room temperature, lowfield Boltzmann conditions) enhancement over thermalpolarisation levels although spin diffusion prohibits di-rect detection within the NV sensing volume. Still, thisresult is compatible with the vision of achieving mean-ingful NMR enhancement with a shallow NV ensemblefollowing realistic diamond material improvements.Polarisation of nuclear targets within the liquid stateproved to be more challenging due to the theoreticallypredicted reduction in effective dipolar coupling strengthinherent to this technique in the presence of molecu-lar diffusion. However, although polarisation of highlydiffusive liquids (e.g. water) is unrealistic, our resultsshow polarisation transfer efficiency to more viscous flu-ids within an order of magnitude of that to solid targets.This is a promising result that could mean NV-based liq-uid state hyperpolarisation is viable following successfulincorporation of a diamond hyperpolariser with a liquidNMR probe. Other methods of polarisation transfer suchas lab frame cross relaxation are expected to perform bet-0ter than PulsePol in the fluid target regime [23], althoughthis protocol faces other challenges such as poor initiali-sation fidelity F at the resonance condition [51].Considering the above points, the single largest driverof improved future prospects for NV-based NMR en-hancement will be centred around improving diamondmaterial properties, particularly regarding the diamondsurface. Our characterisation of the diamond samplesused in this study suggests that near perfect control ofdiamond surface chemistry could result in multiple or-ders of magnitude improvement in polarisation transferefficiency using the PulsePol sequence, as well as the pos-sibility of using other protocols. ACKNOWLEDGEMENTS
We acknowledge support from the Australian Re-search Council (ARC) through grants DE170100129,CE170100012, and DP190101506. A.J.H. and G.A.L.W.are supported by an Australian Government ResearchTraining Program Scholarship. T.T. acknowledges thesupport of JSPS KAKENHI (No. 20H02187 and20H05661), JST CREST (JPMJCR1773) and MEXT Q-LEAP (JPMXS0118068379).
Appendix A: Experimental details
All experiments were carried out on a purpose-builtwidefield NV microscope, elements of which are depictedschematically in Fig. 1 of the main text. A 532 nmlaser with an incident intensity of ≈
300 mW was usedto excite and initialise the spin states of the NV ensem-bles. Red photoluminescence (PL) is emitted in a spinstate-dependent manner by the NVs as they relax backto the ground state and imaged onto a scientific comple-mentary metal oxide semiconductor (sCMOS) camera.This setup allows for imaging of the NVs’ behaviour un-der a variety of experimental protocols over a maximumof 200 × µ m field of view with a diffraction-limitedspatial resolution of ≈
400 nm.Quantum sensing and polarisation-inducing protocolstypically require the delivery of radio frequency (RF) ra-diation to the NV ensemble in order to manipulate itsspin state. This is achieved in our setup via a goldring-shaped resonator deposited on a glass coverslip ontowhich the diamond sample is mounted. The RF radiationis delivered using a Rhode & Schwartz SMBV100A signalgenerator IQ modulated by a Keysight P9336A arbitrarywaveform generator (AWG) with 1 ns time resolution.A PulseBlaster ESR-pro card controls the timing of RFpulse sequences, laser pulses, and camera triggers with atime resolution of 2 ns.The diamond samples used in this study are electronicgrade chemical vapour deposition (CVD) substrates pur-chased from Delaware Diamond Knives. A 1 µ m thicklayer of isotopically enriched (99.95%) C diamond was overgrown via microwave plasma-assisted CVD [52] toboth limit spin noise and eliminate spurious harmonicsignals due to C spins in NV NMR experiments [53].The shallow NV ensembles used for sensing and polarisa-tion were then created via a low energy N ion implanta-tion procedure (2.5 keV, dose 1-2 × cm − , InnovIon)and annealed using a ramp sequence culminating at 1100 ◦ C to maximise NV yield and ensemble coherence proper-ties [31]. Oxygen surface termination was achieved usinga boiling mixtures of sulfuric and nitric acid. The resultis a high density NV ensemble with mean distance fromthe diamond surface of d NV ≈ Appendix B: Sample and target characterisation
Two diamond samples were used for this study, one fea-turing a 2.5 keV N implant with a dose of 1 × cm − (sample D1) and the other a N implant of the same en-ergy but higher dose of 2 × cm − (sample D2). TheNV − density of these samples was estimated by compar-ing their fluorescence as measured on a confocal micro-scope to that given by a single NV (in a separate sam-ple) and assuming the measured PL is purely from thenegative charge state. The estimated overall N to NV − conversion ratios in these samples were 1.4% (D1) and0.9% (D2), lower than typical conversion rates in deeperensembles which can exceed 5% [46].Following the method of [55], we measure the depthdistribution of the NV ensembles in our samples. Wefit the pairwise differences of 5-6 XY8- k spectra with k ranging from 32 to 256 to the signal given by a model NVdistribution. The NV distribution was modelled as theproduct of a Gaussian fit to the expected N depth distri-bution as simulated using the stopping range in matter(SRIM) software package (mean 4.6 nm, width 3.0 nm)and a Sigmoid function (1 + exp( − p ( x − p ))) − repre-senting an effective cut-off in NV − charge stability due toband bending. The slope p and position p of the cut-offwere allowed to vary in the fitting routine, as was a finalparameter p which multiplies the distribution to ensurenormalisation. The distributions obtained are likely notuniquely defined by only a small number of XY8 spectraand we only use approximate mean depths in our analy-sis in the main text. Using the simpler method [54] andobtaining a single mean depth is consistent with our ap-proach provided k >
64 and so would be sufficient for thiswork. However, it is useful to know that our NV distri-bution is well described by a known implanted N distri-bution and band bending, and motivates further work inimproving near-surface NV yield through diamond sur-face engineering. The reduced overall NV yield is largelyexplained by this cut-off, suggesting that the local NVyield could be constant for depths greater than ≈ k=48k=64k=96 k=128k=192k=256 τ (ns) τ (ns) N VP L ( a . u . ) Depth distribution fit N V − den s i t y ( a . u . ) Constant NV yield(SRIM distribution)D1 fit distributionD2 fit distribution (a) (b)
FIG. 6. a) Comparison of fit NV − depth distributions for samples D1 (blue) and D2 (cyan) to simulated N implant distribution(grey, same for both samples up to a factor of two). b) Set of XY8- k spectra used to fit the depth distribution for sample D1,where k is the total number of π pulses used in the sequence. The signal reconstructed from the fit distribution (solid bluelines) gives good but not perfect agreement with the experimental data, indicating that a larger data set would be required toperfectly reconstruct the NV depth distribution. Fitting directly to individual spectra using a single discrete depth as in [54](dashed pink curves) results in a better fit to the data but a variable NV depth depending on k . Using a constant discrete depth(dashed light blue curves), chosen to match the mean of the fit distribution ( ≈ . k . This indicates that while knowledge of the full distribution is required to successfully reproducethe signal for all sequences, using the mean depth captures the main behaviour, justifying the analytical approach used in themain text. to the surface acting as an efficient vacancy trap dur-ing annealing, so the task of optimising near-surface NVproduction is not trivial.Example distributions are shown in Fig. 6 alongsidethe implanted nitrogen distribution predicted by a SRIMsimulation. The fit distributions are consistent with therebeing a constant NV − yield (likely similar to that ofdeeper ensembles) for depths deeper than some sharpcut-off that is dependent on the surface properties of in-dividual samples. For shallower depths than this cut-off,the NV charge state is expected to dominate. Here wesee that sample D2 has a deeper cut-off than D1, match-ing the difference in conversion ratios estimated from thesamples’ PL in comparison to that given by a stable singleNV − centre. The difference could be due to the higherimplantation dose used on D2 creating greater damage tothe diamond surface and explains why less polarisationtransfer was measured with this sample (even accountingfor the greater N density).Most liquid hydrogen targets were simply depositedonto the surface of the diamond where they were ob-served to be stable for the duration of the experiments.A polydimethylsiloxane (PDMS) well and shorter totalmeasurement times were used for the water experiment toprevent evaporation. PMMA was deposited on the dia-mond and then allowed to cure at room temperature priorto measurement. Biphenyl crystals were deposited by dis-solving biphenyl powder (Sigma-Aldrich, 99.5% purity)in isopropanol and allowing this solution to dry on thediamond surface. To prevent degradation of the crystals,they were encased within water and UV-curing epoxy.The resulting crystals, visible in bright-field images suchas Fig. 1(b), were observed to be stable for the durationof the experiments. Between measurements of differenttargets, diamonds were cleaned first using an appropri- τ ( μ s) P L ( a . u . ) (a)(b) P L ( no r m . ) μs) FIG. 7. a) Off-resonance PulsePol decays with glycerol (red),viscous oil (blue), and PMMA (green) on the diamond surfacecompared to in air (grey). Solid lines are fits to the equationexp (cid:0) − ( t/T ) β (cid:1) with β ≈ .
47 in each case. Data normalisedto the maxiumum NV spin contrast. b) Hahn echo decaysfor the same targets, showing a similar T trend. τ defined asthe total length of the sequence. Solid lines are fits to singleexponential decays. ate solvent (dichloromethane, acetone, or ethanol) andthen in a boiling mixture of sulfuric and nitric acid toensure a clean, oxygen-terminated surface. In each casethe hydrogen signal was observed to return to the barediamond baseline.The correlation time τ c of the target spin bath can be2 P L ( a . u . ) τ (ns)
10 μm P L ( a . u . ) μs) P o l a r i s a t i on s i gna l ( a . u . ) PulsePolNOVEL N V depo l a r i s a t i on r a t e ( s - ) t ( μs) N o m i na l R ab i f r eq . ( M H z ) τ ( n s ) (c)(a) (e)(d) (f) (g)(h) 𝜋2 𝑥𝜋2 𝑥 (spin lock) y t (b) FIG. 8. a) NOVEL pulse sequence schematic. b) NV PL image of 50 × µ m FOV with areas for comparison highlightedby blue and red squares. c) Spectra obtained using NOVEL with spin locking time t = 20 µ s showing hydrogen resonances(biphenyl). Red and blue traces are data obtained over the regions highlighted by red and blue squares in (b) respectively. d) Colourmap of full 50 × µ m FOV showing position of hydrogen resonance at each pixel, given by fitting to a Lorentzian dipshape. e) Same as c) but for a τ sweep using the PulsePol sequence as defined in the main text ( N = 30). f ) Colourmap ofPulsePol hydrogen resonance position, fit as in d). g) Polarisation signal normalised to background NV decoherence obtainedusing PulsePol (grey) and NOVEL (light blue). NOVEL data taken over a ≈ × µ m region while PulsePol data is averagedover the full FOV. h) Cooling rates obtained (using the same definition as in the main text) using PulsePol (grey) and NOVEL(light blue). measured using XY8 correlation spectroscopy [39]. Forthe hydrogen spins in the solid samples, τ c directly givesthe nuclear dephasing time T ∗ ,n as molecular motion canbe neglected. For the fluid targets the opposite is true: τ c is governed primarily by spatial diffusion. These mea-sured parameters are used in the theoretical calculationsin the main text.Fig. 7 shows the variation of NV T with hydrogen tar-get obtained using both off-resonance PulsePol sequences(a) and the Hahn echo sequence (b). The T scaling issimilar in both cases, showing that the variation is dueto a changing noise spectrum rather than polarisationbehaviour. Appendix C: Protocol comparison
As discussed in the main text, the PulsePol protocolwas selected for this work due to its suitability in ad-dressing an NV ensemble over a wide field of view. To il-lustrate this, we compared the behaviour of PulsePol andthe well known NOVEL sequence [56], depicted in Fig.8(a), over an identical region (Fig. 8(b)) with biphenylas the hydrogen target. Panels (c) and (e) show the ap-pearance of the hydrogen resonance using the NOVELand PulsePol sequences respectively, with red and bluetraces showing data averaged over the pixels containedwithin the corresponding regions marked on the NV PLimage (b). The NOVEL spectra are obtained by using aspin locking time of 20 µ s and sweeping the microwavepower, which corresponds to a Rabi frequency in the ro-tating frame. The hydrogen resonance appears when, lo-cally, the Rabi frequency matches the hydrogen Larmor frequency and indicates the transfer of spin polarisationfrom NV to the hydrogen bath. A microwave power gra-dient across our FOV results in the resonance appearingfor different nominal driving powers between the two re-gions. Fitting the position of the resonance for everypixel in the image, shown in panel (d), confirms thatthere is a sharp gradient in resonance position across thewhole FOV, meaning that is is impossible to transfer po-larisation using more than 1% of this region at any onetime under our experimental conditions.On the contrary, the spectra in Fig. 8(e) overlap, andthe colourplot Fig. 8(f) confirms that the PulsePol reso-nance position does not vary by more than its linewidthacross the entire FOV, owing to the sequence’s robustnessto microwave power detuning. The PulsePol resonancesare also much deeper, corresponding to more efficient po-larisation transfer, despite the theoretical effective cou-pling being reduced by 28% compared to NOVEL. Thisis due to the fact that PulsePol achieves T > µ swhereas resonant T ρ ≈ µ s with B ∼
450 G. It is alsopossible that even the power gradient over a single µ mscale is enough to reduce the efficiency of transfer usingNOVEL.Fig. 8(g) and (h) show the difference between off-and on-resonance NV decay, normalised to the back-ground decoherence and converted to a cooling rate re-spectively, for the two sequences (PulsePol shown in greyand NOVEL in light blue). As in the main text, thePulsePol signal is averaged over the entire FOV whilethe NOVEL signal is averaged over only the blue re-gion. The influence of the longer PulsePol T is clear,with much more efficient polarisation transfer obtainedper NV with PulsePol than with NOVEL. The maxi-3 τ c ( μ s ) n (x10 -12 m s -1 ) 242220 N V T ( μ s ) (a)(b) n (m s -1 )10 -15 -14 -13 -12 -11 -10 -9 u m a x / ( A T t o t )( a . u . ) FIG. 9. a) Normalised cooling rate plotted against diffu-sion constant D n . Solid lines show a theoretical predictionfor NV-H distances of 7 nm (blue) and 14 nm (purple). b) Variation of correlation time τ c measured by XY8-64 cor-relation spectroscopy (red points, left axis), and NV PulsePol T (blue points, right axis) for glycerol/water mixtures with χ g = 1 , . , . , .
5. Error bars show the standard fittingerror. Diffusion constant D n given by equation in Ref. [45]. mum cooling rate per NV obtained using NOVEL is 1604spins/sec, 79% less than that obtained using PulsePol.Again assuming a proportionality between these valuesand the theoretical strong-dephasing cooling rate and re-calling that A (PulsePol) = 0 . A (NOVEL) suggests T ρ < T P P /
10, in agreement with the measured values.Considering that NOVEL is only active over ≈
1% ofthe FOV, the steady-state hydrogen polarisation possi-ble to be enacted using this sequence in our experimentis likely to be approximately three orders of magnitudelower than that obtained using PulsePol.
Appendix D: Diffusion data
In Sec. II C we presented data showing the reductionin polarisation transfer efficiency associated with increas-ing levels of molecular diffusion. Due to the uncertaintyand potential inconsistency in reporting diffusion con-stants D n for different targets, we presented that data only in terms of the kinematic viscosity (readily avail-able in the literature for glycerol mixtures and providedby the manufacturer for viscous oil). For completeness weplot the same data as in the main text against estimatedvalues of D n in Fig. 9(a). For the glycerol mixtures, wetake values from the empirically derived formula in Ref.[45], while in the absence of manufacturer specificationof molecular mass or hydrodynamic radius for the vis-cous oil, we use a value D n = 3 × − m s − estimatedin previous work for a similar viscous oil [39]. In theblue and purple solid lines we plot the curve τ D τ D + τ L forNV-H distances 7 nm and 14 nm respectively, represent-ing the approximate bounds of the NV sensing volume.This equation gives the expected reduction in effectivecoupling to the hydrogen spin bath as a result of usingthe PulsePol sequence [23], which should be the only re-maining diffusion-dependent factor following the normal-isation described in the main text. The maximum valuewas set arbitrarily, to match the solid target providingthe least signal for illustration.We can see some qualitative agreement between exper-iment and theory, with the viscous oil diffusing slowlyenough to not be greatly affected, while a relativelyrapid drop-off in effective coupling is observed for χ g ≤ .
75. However, overall the points belonging to the glyc-erol/water mixture series are not well described by thetheory. As mentioned in the main text, two possible ad-justments to these data points could recover the expectedtrend: either a systematic decrease in D n of around oneorder of magnitude due to interactions between the dia-mond surface and the fluid, or less dramatic increase indiffusivity near the surface with decreasing χ g . The lattercase could arise due to the local properties of the mixtureschanging near surface, for instance due to laser heatingcausing water to evaporate leaving χ g > . τ c varies inversely with D n as expected, but not as sharply as predicted. Assuming T ∗ (cid:29) T diff2 ≈ τ c , we expect D − n scaling, implying that D varies by less than 20% between χ g = 1 and χ g = 0 . χ g . 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