Quantum probe hyperpolarisation of molecular nuclear spins
David A. Broadway, Jean-Philippe Tetienne, Alastair Stacey, James D. A. Wood, David A. Simpson, Liam T. Hall, Lloyd C. L. Hollenberg
QQuantum probe hyperpolarisation of molecular nuclear spins
David A. Broadway,
1, 2, ∗ Jean-Philippe Tetienne,
1, 2
Alastair Stacey,
1, 3
James D. A.Wood,
1, 2, 4
David A. Simpson, Liam T. Hall, † and Lloyd C. L. Hollenberg
1, 2, ‡ Centre for Quantum Computation and Communication Technology,School of Physics, University of Melbourne, Parkville, VIC 3010, Australia School of Physics, University of Melbourne, Parkville, VIC 3010, Australia Melbourne Centre for Nanofabrication, Clayton, VIC 3168, Australia Department of Physics, University of Basel, Klingelbergstrasse 82 , 4056, Basel, Switzerland
The hyperpolarisation of nuclear spins within target molecules is a critical and complex challengein magnetic resonance imaging (MRI) [1] and nuclear magnetic resonance (NMR) spectroscopy [2].Hyperpolarisation offers enormous gains in signal and spatial resolution which may ultimately leadto the development of molecular MRI and NMR [3]. At present, techniques used to polarise nuclearspins generally require low temperatures and/or high magnetic fields, radiofrequency control fields,or the introduction of catalysts or free-radical mediators [4–7]. The emergence of room tempera-ture solid-state spin qubits has opened exciting new pathways to circumvent these requirements toachieve direct nuclear spin hyperpolarisation using quantum control [6, 8]. Employing a novel cross-relaxation induced polarisation (CRIP) protocol, we demonstrate the first external nuclear spinhyperpolarisation achieved by a quantum probe, in this case of H molecular spins in poly(methylmethacrylate). In doing so, we show that a single qubit is capable of increasing the thermal polar-isation of ∼ nuclear spins by six orders of magnitude, equivalent to an applied magnetic fieldof 10 T. The technique can also be tuned to multiple spin species, which we demonstrate usingboth C and H nuclear spin ensembles. Our results are analysed and interpreted via a detailedtheoretical treatment, which is also used to describe how the system can be scaled up to a universalquantum hyperpolarisation platform for the production of macroscopic quantities of contrast agentsat high polarisation levels for clinical applications. These results represent a new paradigm fornuclear spin hyperpolarisation for molecular imaging and spectroscopy, and beyond into areas suchas materials science and quantum information processing.
With the prospect of molecular MRI [3] revolutionis-ing many areas of research and clinical applications, thegeneration of hyperpolarised molecular targets attractsintense interest. Well known techniques include high-field/low temperature brute-force methods [4], dynamicnuclear polarisation [6], optical pumping [5], and parahy-drogen induced polarisation [7]. On the other hand,the rapid advances in semiconductor spin qubit technol-ogy for quantum computing [9, 10] and quantum sensing[11, 12] has opened up the exciting possibility of hyperpo-larising nuclear spins at a fundamental level via quantummechanical protocols [6, 8, 13–20]. Despite early progress[21, 22], the application of quantum probe technology tothis problem still faces a number of significant challenges.To be of practical use, a quantum probe must be capableof polarising a relatively large number of remote nuclearspins external to the probe substrate, ideally under am-bient conditions. We address these challenges using aquantum spin probe in diamond as an entropy pump,and demonstrate polarisation of external molecular spinensembles over relatively large volumes at room temper-ature, with the prospect of scaling up to a universal hy-perpolarisation platform suitable for clinical applications.In contrast to existing methods, our quantum polarisa-tion approach is tunable to a range of nuclear species,operates at room temperature, and is inherently free ofradiofrequency (RF) fields and extraneous chemistry.For this study, we employ a nitrogen-vacancy (NV) quantum spin probe in a diamond substrate (Fig. 1 a )[11]. The protocol employs an external magnetic field, B , to tune the ground-state spin transition frequencyof the NV ( ω NV ) into resonance with target nuclearspins ( ω n ) (Fig. 1 b ). For a given target species, thespin resonance condition is fulfilled at a magnetic field B ∗ ( γ n ) ≈ D/ ( γ NV − γ n ) [23], where γ n , γ NV are thetarget and NV gyromagnetic ratios, and D is the NVzero-field splitting (Fig. 1 c ). Entropy pumping is facili-tated by repeated application of the cross relaxation in-duced polarisation (CRIP) sequence (Fig. 1 d ), whereinthe NV spin is optically initialised into | (cid:105) state and theNV-target hyperfine interaction is allowed to occur fora given period of time, τ (of order microseconds). Thetransfer of magnetisation caused by this interaction thuspolarises the target spins into their |↓(cid:105) state (Fig. 1 c ).For the sake of comparison, depolarisation may be facil-itated by interleaving the initialisation of the NV spininto the opposite state |− (cid:105) by the application of an RF π -pulse (Fig. 1 e ).To quantitatively understand the effect of the CRIPprotocol on the target spin ensemble, we developed amicroscopic theory that explicitly includes the dipole in-teractions of ensemble spins and their interaction with asingle NV quantum probe (see Supplementary Informa-tion for details). We define the polarisation of a spin atposition R (relative to the NV) and time t to be P ( R , t ); a r X i v : . [ qu a n t - ph ] A ug P L DiamondPMMA
L a s e r PMMA b ea
Init.Flip-flopInit.Flip-flop c PL Dichroicmirror fd UnpolarisedPolarised Laser CRIPRF Polarisation DepolarisationCRIP -1 CRIPPolarisedUnpolarisedObjective Polarisation diffusionEntropyremovalNV EntropyLaser P L Time g H F C P H He FIG. 1.
Quantum probe hyperpolarisation of nuclear spin ensembles. a,
Schematic of the system showing a near-surface nitrogen-vacancy (NV) spin probe in diamond and a hydrogen nuclear spin target ensemble in molecular Poly(methylmethacrylate) (PMMA) on the surface. The NV probe is initialised by a green laser (532 nm), and read out via its photolu-minescence (PL) signal. The shaded blue surfaces denote different regimes of polarisation capabilities arising from the spatialdependence of the nuclear spin coupling to the NV qubit. b, Schematic of cross relaxation induced polarisation (CRIP) imple-mented on a spin system illustrating the build up of polarisation from repeated application of the CRIP sequence. Diffusioneffects act in competition with the CRIP entropy pumping mechanism, but also allow for polarisation at distances beyond thatreachable via the hyperfine interaction. c, Energy-level diagram of the NV showing the relative positions of various targetnuclear spin resonance conditions. d,e,
The control sequences laser pulses in green, RF pulses in red) used for polarising atarget spin ensemble using CRIP ( d ) and for controlled depolarisation using the combined CRIP − × CRIP protocol ( e ). f, Schematic showing the cross-relaxation spectrum obtained by measuring the PL during the CRIP (blue) or depolarisation(orange) sequence with a constant interaction time τ , while scanning the NV frequency ω NV . g, Similarly, the cross-relaxationcurve is obtained by scanning τ with ω NV set at the resonance. with the evolution of P ( R , t ) described by ∂∂t P ( R , t ) = (cid:0) β ∇ − u ( R ) − Γ SL (cid:1) P ( R , t ) + u ( R ) , (1)subject to an initial unpolarised state P ( R , t ) = 0; where u ( R ) = A ( R ) / is the effective cooling coefficient re-sulting from the hyperfine coupling A ( R ) with the NVspin, Γ is the dephasing rate of the NV spin β is theeffective polarisation diffusion coefficient related to theintra-target interactions, and Γ SL is the spin-lattice re-laxation rate of the target spin ensemble. This formula-tion allows us to predict and describe the spatial extentof polarisation for a given target sample of arbitrary ge-ometry.To probe the polarisation effect experimentally, wemonitor the spin-dependent photoluminescence (PL)from the NV [24–26] during the laser pulses, which de-cays as a function of the CRIP sequence time as e − Γ tot τ .Here Γ tot is the NV longitudinal relaxation rate, whichcan be expressed as the sum Γ tot = Γ bg + Γ CR , whereΓ bg is the background rate caused by lattice phonons orsurface effects, and Γ CR is due to cross-relaxation. Thelatter follows a Lorentzian dependence on the detuning between the probe and target transition frequencies[24],Γ CR = A P Γ + 2 ( ω NV − ω n ) , (2)where A P is the total hyperfine field variance seen by theNV due to the target ensemble, which is related to thepolarisation distribution via A P = n t (cid:90) [1 − P ( R , t )] A ( R ) d R , (3)where n t is the density of the target spin ensemble.The key indicator of significant polarisation is thereforea reduction in Γ CR , which manifests as the disappear-ance of the target ensemble’s spectral feature from thecross-relaxation spectrum (Fig. 1 f ), and can be quanti-fied by measuring the cross-relaxation curve at resonance(Fig. 1 g ).Experimentally, we first demonstrate our technique onthe inherent 1.1% C spin ensemble surrounding a NVprobe in the diamond substrate by tuning to the Cresonant condition at B ∗ ( C) = 1024 . a ) shows the complete removal of P L ( a . u . ) Interaction time, τ (ms) a bc d P L ( a . u . ) NV frequency, ω NV (MHz) Polarisation
Pol.
Radial distance, R (nm)0 50 10010 T o t a l t i m e , T = N τ ( s )
00 20 P o l . µs Unpolarised BackgroundPolarised
FIG. 2.
Cross-relaxation induced polarisation of Cspins in diamond. a,
Cross-relaxation spectra of a sin-gle NV spin near the C resonance ( ω NV = 1 . τ = 4 µ s using the CRIP se-quence (blue) and the depolarisation sequence (orange, onlythe readout following the NV initialisation in | (cid:105) is shown).Sequences were repeated N = 10 times at each point. b, Cross-relaxation curves obtained by increasing τ at the Cresonance with the CRIP sequence (blue) and depolarisa-tion sequence (orange), and off-resonance to obtain the back-ground relaxation curve (green). Zoom-in at short times forthe polarised (blue) and unpolarised case (orange, top andbottom curves correspond to the NV initialised in | (cid:105) and | − (cid:105) , respectively). c, Calculated radial polarisation profilesrelative to the NV spin (averaged over all angles), calculatedfrom Eq. (1) for a random 1.1% C spin ensemble for vary-ing total polarisation times, T = Nτ . Inset: profile alongdashed line, corresponding to T = 2 h. d, Three-dimensionalrepresentation of the polarisation distribution at T = 2 h. the C resonance peak for interaction times of τ = 4 µ s,indicating efficient polarisation of the nearest spins, ascompared with the target prepared using the depolarisingsequence. This is confirmed in the cross-relaxation curvesas a function τ (Fig. 2b, inset), where the polarised caseshows no evolution of the NV spin state, while the un-polarised case shows coherent flip-flops between the NVand the C spins.To investigate the extent of the polarisation effect,we increase the interaction time τ so as to be sensi-tive to more remote C spins, up to the limit set bythe NV centre’s intrinsic spin-phonon relaxation rate,Γ bg ≈
200 ms − . The resulting cross-relaxation curvesobtained at the C resonance using the CRIP and de-polarisation sequences are shown in Fig. 2 b , from which we extract the total relaxation rate, Γ tot . By subtract-ing Γ bg obtained from the off-resonance relaxation curve(Fig. 2 b , green data), we deduce the C-induced re-laxation rate Γ CR = Γ tot − Γ bg , which decreases fromΓ unpolCR ≈
250 ms − with the depolarisation sequence, tobelow the noise floor of the measurement after 5 hours ofCRIP, Γ polCR (cid:46)
19 s − . We use Eq. (1) (with β = 0 . s − corresponding to the given C density) to calcu-late the time-dependence of the radial polarisation pro-file for total polarisation times of 1-10 s, as depicted inFig 2 c . By relating the spatial polarisation distribution, P ( R , t ), to the cross-relaxation rate, Γ CR , via Eq. (2),we find the theoretical results are consistent with the ex-periment for polarisation times in excess of two hours(Fig. 2 c , dashed line). Examination of the spatial polar-isation distribution (Fig. 2 c , inset, and Fig. 2 d ) impliesa polarisation level of more than 99% within 21 nm ofthe NV, equating to a 6 × -fold increase on thermalpolarisation for 3 × spins.With the basic protocol established, we now moveto the polarisation of molecular H nuclear spins exter-nal to the diamond crystal. A solution of poly(methylmethacrylate), PMMA, was applied directly to a di-amond substrate [12] with single NV spin probes lo-cated 8-12 nm below the surface. CRIP was appliedwith the external magnetic field tuned to resonance at B ∗ ( H) = 1026 . β = 781 nm s − ,Γ SL = 1s − ) relative to the intrinsic C case, the Hsystem effectively reaches steady-state within a few sec-onds. Application of the CRIP sequence to NV1 (datafor other NVs are shown in the Supplementary Informa-tion) for τ = 20 µ s (Fig. 3 a ) shows the removal of the hy-drogen spectral feature (blue), as compared with the de-polarising sequence (orange). From the cross-relaxationcurves after 1 hour of CRIP (Fig 3 b ), we extract H-induced rates for the unpolarised (Γ unpolCR ) and polarised(Γ polCR ) PMMA H spin ensembles to be 2.71 ms − and0.96 ms − , respectively. The ratio Γ unpolCR / Γ polCR = 2 . . c , indicating that thesystem reaches 50% average polarisation over a volumeof ∼ (26 nm) . Thus, we conclude that the single spinquantum probe has increased the average polarisation ofroughly a million hydrogen spins by some six orders ofmagnitude over the room temperature Boltzmann ther-mal background.There is scope for improvement on these proof-of-concept results: for example, engineering NV depthsto 5 nm would increase the rate of target spin polar-isation by an order of magnitude, and improvementsin the inherent NV dephasing rate Γ (e.g. via im- c ( a . u . ) L P ) . ua . ( P L NV1NV1 ba Unpolarised BackgroundPolarised Z (nm) X (nm)
30 15Polarisation,
15 30 NV -10
NV frequency, ω NV (MHz) Interaction time, τ (ms) FIG. 3.
Polarisation of external molecular H spins.a,
Cross-relaxation spectra near the H resonance ( ω NV =4 . τ = 20 µ s and N = 10 with theCRIP sequence (blue) and the depolarisation sequence (or-ange). b, Cross-relaxation curves obtained by increasing τ at the H resonance with the CRIP sequence (blue) and de-polarisation sequence (orange), and off-resonance to obtainthe background relaxation rate (green). c, Three-dimensionalrepresentation of the H spin polarisation distribution in thePMMA, calculated from Eq. (1) in the steady state. proved surface properties) will allow for more precisetuning to different nuclear spin species. As the pro-tocol is all optical, scaling up for high-volume produc-tion could be achieved by stacking multiple NV arrays(Fig. 4 a ) and/or increasing the effective interaction areavia surface patterning [27]. The results presented hereindicate that the CRIP protocol could produce macro-scopic quantities of MRI contrast agents with high polar-isation levels. For example, we consider C isotopicallyenriched HEP (cid:0) hydroxyethyl propionate, C H O (cid:1) , awell-known MRI contrast agent [28]. Using a singlehyperpolarisation cell comprised of two NV arrays indiamond membranes separated by 1 µ m (see zoomedschematic in Fig. 4 a ; we assume an NV density of 4 × cm − over a 4 mm × µ L/s at a polarisation level of 80%.The polarisation levels for different contrast agents in 1Mprecursor solutions are plotted against polarisation time
Unpolarised liquid Polarised liquidLaser Dilution liquidNV ensemble ab B V o l u m e R a t e ( µ L / s ) Polarisation -3 -2 -1 P o l a r i s a t i on c HEP H O N - TMPA
Single polarisation cell Sample delivery
Total time, T (ms) FIG. 4.
Scale-up for a universal MRI contrast agenthyperpolarisation platform. a,
Schematic of a quantumpolarisation stack comprising multiple diamond membranes,each containing NV array layers on both sides, in a homoge-neous magnetic field tuned to the nuclear gyromagnetic ratioof the target agent spin species. The unpolarised agent inconcentrated solution (orange) flows into the stack channels,where the liquid is polarised through the application of CRIP(via a pulsed laser). The out-flowing polarised liquid (blue)is then diluted for use. Zoomed schematic shows a single po-larisation cell comprising a channel formed by dual diamondmembranes each with a near-surface NV layer. b, Averagepolarisation level from a single polarisation cell, for varioustargets (HEP, H O, and N-TMPA), calculated for varyingpolarisation times assuming perfect mixing of a 1 M targetagent solution with a cell height of 1 µ m. c, Outflow rate(after dilution to 1mM for application delivery) from 10 po-larisation cells at different levels of polarisation. (assuming perfect mixing occurs over these timescales)in Fig. 4 b . In Fig. 4 c , we plot the final delivery rate afterdilution to 1 mM for a stack of 10 cells, showing thatdelivery rates of order 100 µ L/s for clinical applications[30] are achievable.In summary, we have experimentally demonstrated hy-perpolarisation of molecular nuclear spins under ambientconditions by employing a quantum spin probe entropypump. The technique works at low field, room temper-ature, requires no RF fields, and operates directly onthe target molecules without the need for catalysts orfree radicals. With high polarisation rates and tunabil-ity, there are excellent prospects for scale-up of the sys-tem to produce macroscopic quantities of a range of con-trast agents at polarisation levels required for molecularMRI/NMR. The technique can be extended to other nu-clear spin species and may also offer new pathways inquantum information for initialisation of quantum sim-ulators, or increasing the fidelity of operations throughspin-bath neutralisation.
Author Contributions:
The CRIP protocol wasconceived by LTH. Experiments were performed by DABand J-PT, with input from AS, DAS, JDAW, LTH,and LCLH. LTH developed the theory, with input fromLCLH. DAB, J-PT, AS, and DAS prepared the samples.LCLH, DAB and LTH wrote the manuscript with inputfrom all authors. LCLH supervised the project.
Acknowledgements:
This work was supported inpart by the Australian Research Council (ARC) un-der the Centre of Excellence scheme (project No.CE110001027). This work was performed in part at theMelbourne Centre for Nanofabrication (MCN) in the Vic-torian Node of the Australian National Fabrication Fa-cility (ANFF). L.C.L.H. acknowledges the support of anARC Laureate Fellowship (project No. FL130100119).J.-P.T acknowledges support from the ARC throughthe Discovery Early Career Researcher Award scheme(DE170100129) and the University of Melbourne throughan Establishment Grant and an Early Career ResearcherGrant. D.A.B is supported by an Australian GovernmentResearch Training Program Scholarship.
Competing Interests:
The authors declare that theyhave no competing financial interests.
Correspondence:
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