Technical Field

[1] This disclosure relates to systems and methods for manufacturing hyperpolarised agents. For example, this disclosure relates to manufacturing agents that can be used as contrast agents in MRI imaging.

Background

[2] Magnetic resonance imaging (MRI) has improved medical diagnostics significantly as it is able to create a 3-dimensional representation of the human body. Current MRI generally creates a static image of water and fat in the body. However, contrast agents can also be used in order to image the passage of the contrast agent through the blood system, or the flow of air through the lungs, or in metabolic imaging. In order to create an agent that contrasts against the body tissue, the magnetic properties of the agent are changed, which results in a significantly increased response to the MRI stimulus and therefore a significantly increased contrast to the body tissue. Changing the magnetic properties in this context is referred to as hyperpolarisation.

[3] However, it is difficult to manufacture such contrast agents and current methods require extremely low temperatures and/or strong magnetic fields and/or additive components requiring removing prior to use.

[4] Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present disclosure as it existed before the priority date of each claim of this application.

[5] Throughout this specification the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps. Summary

[6] This disclosure provides a method for hyperpolarizing an agent that addresses the problems of the prior art, such as the need for extremely low temperatures and strong magnetic fields. The disclosed method uses an effect called cross-relaxation, where the spin of a probe is transferred to a particle of the agent, such as a nucleus of a molecule. For example, the lowest two probe spin states are tuned in a magnetic field to be in resonance with the agent's particular nuclear spin states. The probe is put into a specific spin state where it exchanges spin with the agent's nuclear spin states that are opposite to the desired hyperpolarised spin state. The probe spin then is re-initialised, leaving a higher number of agent nuclear spins in the desired spin energy state. The process is repeated until sufficient agent hyperpolarisation is acquired.

[7] The result is an incremental polarisation of the agent's nuclear spins. Repeating these steps leads to a large number of polarized agents particles. The strength of the magnetic field is set such that it tunes the spin energy levels of the probe to be in resonance with the energy levels of the agent's particular nuclear spins being targeted.

[8] A method for manufacturing a hyperpolarised agent comprises:

locating the agent in close proximity to a quantum probe that is in a first energy state; applying a magnetic field to the quantum probe and the agent;

applying quantum control radiation to the probe to bring the quantum probe to a second energy state to allow cross-relaxation between the quantum probe and the agent while the magnetic field is applied,

wherein the magnetic field is of a magnetic field strength that adjusts the energy states of the quantum probe to bring a probe spin transistion of the quantum probe into resonance with an agent spin transition of the agent to allow transfer of energy and thereby activate the cross- relaxation between the quantum probe and the agent to polarise the agent.

[9] It is an advantage that the magnetic field strength that brings the spin transitions of the quantum probe the agent into resonance is significantly weaker than the magnetic field strengths that are required for some other methods of polarisation. A further advantage is that the polarisation can occur at room temperature due to the efficient initialisation of the quantum probe through optical pumping, which removes the need for external cooling. As a result, the method can be used without expensive and complex equipment so that the hyperpolarised agent can be produced more efficiently.

[10] The method may further comprise removing the quantum control radiation while the magnetic field is applied.

[11] The magnetic field may be aligned with a spin axis of the quantum probe.

[12] Applying the magnetic field may comprise using a permanent magnet to apply the magnetic field.

[13] Using the permanent magnet maycomprise tuning the magnetic field by moving the permanent magnet or controlling the temperature of the permanent magnet or both.

[14] Transfer of energy may comprise magnetic interaction between the quantum probe and the agent.

[15] The quantum probe may comprise an electron spin of a nitrogen-vacancy centre in a diamond.

[16] The magnetic field may have a field strength between 1020 G and 1028 G.

[17] The magnetic field may have a field strength of one of:

1020.65 G or 1026.15 G for polarising 1H;

1024.06 G or 1024.66 G for polarising ² H;

1023.85 G or 1024.84 G for polarising ¹³ C;

1023.5 G or 1025.12 G for polarising ³¹ P;

1023.8 G or 1024.89 G for polarising ¹²⁹ Xe; and

1021.3 G or 1026.05 G for polarising ¹⁹ F.

[18] Applying the quantum control radiation may comprise applying light to the quantum probe.

[19] The quantum control radiation may be applied for a time between 100 ns and 1 ms. [20] The quantum control radiation may be applied for a time between 1 and 10 microseconds.

[21] The quantum control radiation may be removed to activate diffusion of polarisation via magnetic dipole interactions within the agent.

[22] The quantum control radiation may be removed for 1 us to 1 s.

[23] The quantum control radiation may be removed for 1 to 10 microseconds.

[24] The method may further comprise repeating the method to increase an amount of the agent that is polarised.

[25] The method may be repeated for a sufficient number of cycles to achive a polarisation level of 10-80%.

[26] The method may be repeated for more than one hour.

[27] The method may further comprise reading out a current energy state of the quantum probe during the application of quantum control radiation to allow real-time monitoring of an amount of polarisation transfer.

[28] The reading out of the current energy state of the quantum probe may be achieved by measuring a luminescence intensity.

[29] A system for manufacturing a hyperpolarised agent comprises:

a carrier to carry the agent;

a quantum probe in close proximity with the carrier and in a first energy state;

a magnetic field source to apply a magnetic field to the quantum probe and the agent carrier;

a controller to

activate a quantum control radiation source to apply quantum control radiation to the quantum probe to bring the quantum probe to a second energy state to allow cross- relaxation between the quantum probe and the agent while the magnetic field is applied; wherein the magnetic field is of a magnetic field strength that adjusts the energy states of the quantum probe to bringe a probe spin transition of the quantum probe into resonance with an agent spin transition of the agent to allow transfer of energy and thereby activate the cross- relaxation between the quantum probe and the agent to polarise the agent.

[30] The quantum probe may be located less than 20 nm from the agent.

[31] The quantum probe may be below a surface of a substrate.

[32] The agent may be a liquid, or in a liquid, of specified viscosity, and the carrier is configured to provide a flow of the agent past the quantum probe.

[33] The system may comprise multiple quantum probes and the quantum control radiation and the magnetic field may be applied to the multiple quantum probes

simultaneously.

[34] The carrier may comprise multiple channels to provide multiple streams of liquid agent and the system comprises multiple quantum probes arranged in close proximity to the surfaces of each of the channels.

[35] The magnetic field and the quantum control radiation may be applied to the multiple channels simultaneously.

[36] Optional features described of any aspect of method, computer readable medium or computer system, where appropriate, similarly apply to the other aspects also described here.

Brief Description of Drawings

[37] An example will be described with reference to the following drawings: [38] Fig. la illustrates a system for manufacturing a hyperpolarised agent.

[39] Fig. lb illustrates a method for manufacturing a hyperpolarised agent.

[40] Figs. 2a, 2b, 2c and 2d illustrate the principle of cross -relaxation. [41] Fig. 3 illustrates an energy-level diagram of the NV showing the relative positions of various target nuclear spin resonance conditions.

[42] Fig. 4 is a schematic of cross relaxation induced polarisation (CRIP) implemented on a spin system.

[43] Fig. 5a illustrates a control sequence for polarisation using laser pulses. Fig. 5b illustrates a control sequence for de-polarisation using laser pulses and RF pulses.

[44] Fig. 6a illustrates the cross -relaxation spectrum obtained by measuring the photoluminescence (PL) during the CRIP 601, or depolarisation 602 sequence, with a constant interaction time T , while scanning the NV frequency ω _Νν . Fig. 6b illustrates a cross-relaxation curve obtained by scanning T with _m set at the resonance.

[45] Fig. 7 illustrates measured cross-relaxation spectra of 13 C nuclear spins from CRIP applied to a single NV spin probe.

[46] Fig. 8 illustrates calculated radial polarisation profiles of 13 C nuclear spins relative to the NV probe spin.

[47] Fig. 9 illustrates a three-dimensional representation of the polarisation distribution for 1 ⁱ 3 ³ C spins in the case shown in Fig 8..

[48] Fig. 10 illustrates for polarisation of external molecular ¹ H spins cross-relaxation spectra near the ¹ H resonance ( ω _Νν = 4.4 MHz), for a single NV spin located 10 nm below a

PMMA layer, obtained using τ = 20 μ s and N = 10 ⁵ repeats with a CRIP sequence and a depolarisation sequence. The figure further illustrates cross-relaxation curves obtained by increasing T at the ¹ H resonance with the CRIP sequence (middle) and depolarisation sequence (bottom), and off -resonance to obtain the background relaxation rate (top).

[49] Fig. 11 illustrates a three-dimensional representation of the ¹ H spin polarisation distribution in the PMMA in the steady state. [50] Fig. 12 illustrates a scale-up for a universal MRI contrast agent hyperpolarisation platform.

[51] Fig. 13 illustrates a zoomed in representation of the polarisation stack in Fig. 12.

[52] Fig. 14 illustrates average polarisation levels and volume rates for example target agents.

[53] Fig. 15 is a simplified depiction of the energy levels of the NV spin at the ground state level anti-crossing GSLAC as a function of the applied magnetic field, and the polarisation transfer mechanism when on resonance with a target nuclear spin.

[54] Fig. 16 illustrates the transition frequencies as a function of the applied magnetic field, showing the NV-nuclear spin resonance conditions for multiple different nuclear spin species. The black lines represent the two allowed NV transitions which act as the probe frequency.

[55] Figs 17a and 17b illustrate spatial coupling distributions before and after the GSLAC comparison. Contours of constant coupling for after (Fig. 17a) and before (Fig. 17b) the GSLAC with (l 11) and (lOO) surfaces shown shaded.

[56] Fig. 18 illustrates polarisation profiles at the diamond surface for four possible scenarios, considering the example of an NV located 10 nm below the surface and polarising a bath of PMMA spins.

[57] Fig. 19 illustrates the effect of the protocol on the naturally occurring (1.1% abundant) ¹³ C nuclear spin bath in the diamond crystal using 1000 randomly initialised ¹³ C spins. Solid lines represent the polarisation of 10 spins randomly chosen from the bath, the dashed line represents the average |T> state probability (i.e. polarisation) of all 1000 ¹³ C spins with interaction time τ = 3.8 s.

[58] Fig. 20 illustrates radial polarisation profiles for ¹³ C resonances before (top) and after (bottom) the GSLAC constructed using their respective experimentally measured longitudinal relaxation rates after approximately 5 hours of polarisation. [59] Fig. 21 illustrates ¹ H polarisation distributions in the X— Z and X— Y planes of the PMMA layer for total polarisation times of t = 1 ms, 1 s, and 1 hr (steady state, SS). The PMMA-diamond interface defines Z = 0 .

[60] Fig. 22 relates to cross -relaxation between a single NV and the ¹³ C bath and shows T _x -relaxometry spectrum performed around the GSLAC (middle feature) with two signals (outer features) corresponding to the ¹³ C resonances, with a wait time τ = 5μ s. The top and bottom lines ( 1 0 > and I -1 > ) are obtained with a CRIP and CRIP ^_1 interleaved pulse sequence. The pulse sequence acts to prevent polarising the bath and allows the NV- ¹³ C interaction to be measured. The solid line is a guide to the eye.

[61] Fig. 23 illustrates the difference between the I -1 > and 1 0 > state ( Δ PL = PL (I -1 >)- PL (I 0 >)) against the transition frequency measured in ODMR for before the GSLAC (top) and after (bottom).

[62] Fig. 24 illustrates short time spin dynamics using the same interleaved pulse sequence and varying the interaction time, T . The measurement is taken on resonance with the ¹³ C bath (after GSLAC), revealing flip-flop interaction between the NV and the ¹³ C bath with a total hyperfine coupling of 250 ± 40 kHz.

[63] Fig. 25 relates to polarising the ¹³ C bath and shows the ¹³ C spectrum (three peaks) obtained using the depolarisation sequence and the polarised spectrum (one peak) using CRIP. This is the same NV as the one in Fig. 6b.

[64] Fig. 26 illustrates ¹³ C around the GSLAC with polarisation (top) and without polarisation (bottom two lines) on a different NV. With the interleaved sequence, both NV initialisation states are shown, 1 0 > (middle) and I -1 > (bottom).

[65] Fig. 27 illustrates time dynamics of the NV-bath interaction at the after-GSLAC ¹³ C resonance.

[66] Figs. 28a, 28b, 28c and 28d related to polarisation dynamics. Fig. 28a shows a pulse sequence used to investigate the polarisation dynamics. Fig. 28b shows a full sequence of 30 CRIP ^_1 pulses followed by 30 CRIP as shown in Fig. 28a, for different interaction times T . Fig. 28c illustrates a characteristic time for polarisation as a function of interaction time. Fig. 28d shows T _x -relaxometry spectrum across the GSLAC, as a function of CRIP pulse number, obtained using the sequence shown in a with a fixed total number of CRIP and CRIP ^_1 pulses ( N' = N = 30 ). The interaction time was 3 μ s. Negative frequency denotes past the GSLAC.

[67] Figs. 29a and 29b relate to polarisation extent measurements. Fig. 29a shows full TJ measurements taken for the after GSLAC case in three conditions: measured on resonance with ¹³ C (top), closer to the GSLAC i.e. < 0.9 MHz (bottom) and further away from the GSLAC i.e. > 1.3 MHz (middle). Fig. 29b shows the decay rate the of NV around the ¹³ C resonance, before the GSLAC (top, top, bottom) giving T _Tes « 62 Hz and after (bottom, bottom, top), where no change is seen within noise, giving T _ies « 19 Hz.

[68] Figs. 30a-30f illustrate the effect of ¹³ C polarisation on the free induction decay. Fig. 30a illustrates a pulse sequence for CRIP polarisation at the resonant frequency followed by an FID measurement at a different frequency, using a magnetic field offset pulse. Fig. 30b illustrates a schematic of the experimental set up with the coil for the field offset. Fig. 30c illustrates an example ODMR of the NV during the CRIP phase (left) and during FID measurements (right). Fig. 30d illustrates an FID signal as a function of NV frequency as measured during the CRIP phase (top axis) and during the FID phase (bottom axis). The FID wait time is τ = 4 μ s. A detuning of 0.2 MHz was applied when driving the NV in the FID measurement. Fig. 30e illustrates an FID curves obtained from a similar sweep as in Fig. 30d. The two curves show the case where the CRIP phase is on resonance (earlier curve, polarisation) and off resonance (later curve, no polarisation). Fig. 30f illustrates a long FID measurement taken at a fixed frequency with the CRIP phase on resonance (earlier curve, polarisation) and off resonance (later curve, no polarisation). The applied driving detuning was different in the two case in order to obtain the same oscillation frequency.

[69] Fig. 31 illustrates the effect of ¹³ C polarisation on the resonance linewidth. The graph shows the ¹³ C spectrum under the sequence shown in Fig. 2.5a, with N = 10 and N' = 0, 2, 4, 6 , from top to bottom. The interaction time is τ = 5 μ s. A clear trend is found from fitting the signal with a Lorentzian (solid line): there is an increase in the FWHM of the feature as the bath becomes less polarised. [70] Figs. 32a and 32b relate to additional ¹ H polarisation measurements. Fig. 32a shows a spectrum of ¹ H unpolarised (bottom) and polarised (top) for NV2. Fig. 32b shows full- length TJ measurements for NV3 on resonance unpolarised (bottom), polarised (midde) and a background off resonance measurement (top).

Description of Embodiments

[71] General

[72] Hyperpolarisation is polarisation of the nuclear spin of a material far beyond thermal equilibrium conditions. This can be applied to liquids, gasses and solids. The

hyperpolarisation of nuclear spins within target molecules is an important and complex challenge in magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy. Hyperpolarisation offers gains in signal and spatial resolution which may ultimately lead to the development of molecular MRI and NMR.

[73] This disclosure utilises room temperature solid-state spin qubits to circumvent these requirements to achieve direct nuclear spin hyperpolarisation using quantum control.

Employing a cross-relaxation induced polarisation (CRIP) protocol, the disclosed method provides external nuclear spin hyperpolarisation achieved by a quantum probe, for example of ¹ H molecular spins in poly(methyl methacrylate). This way a single qubit is capable of increasing the thermal polarisation of ~ 10 ⁶ nuclear spins by six orders of magnitude, equivalent to an applied magnetic field of 10 ⁵ T. The technique can also be tuned to multiple spin species, such as ¹³ C and ¹ H nuclear spin ensembles. The disclosed system can be scaled up to a universal quantum hyperpolarisation platform for the production of macroscopic quantities of contrast agents at high polarisation levels for clinical applications.

[74] In general, the quantum probe should be capable of polarising a relatively large number of remote nuclear spins external to the probe substrate, ideally under ambient conditions. In this disclosure, these challenges are addressed using a quantum spin probe in diamond as a spin entropy pump, which enables polarisation of external molecular spin ensembles over relatively large volumes at room temperature. This allows scaling up to a universal hyperpolarisation platform suitable for clinical applications. The proposed quantum polarisation approach can be tuned to a range of nuclear species, can operate at room temperature, and can be inherently free of radiofrequency (RF) fields and the need for extraneous chemistry prior to polarisation and/or use.

[75] Single NV System

[76] Fig. la illustrates a system 100 for manufacturing a hyperpolarised agent. The system comprises a near- surface nitrogen- vacancy (NV) spin probe 101 in diamond 102 and a nuclear spin target ensemble 103 in molecular Poly(methyl methacrylate) (PMMA) 104 on the surface of diamond 102. The NV probe 101 is initialised by a green laser (532 nm) 105, and read out via its photo luminescence (PL) signal 106 by a photo detector 107. A magnetic field 108 is applied to the probe 101 and the agent 103. In one example, the magnetic field 108 is applied by a permanent magnet. The figure also shows different spatial regimes of polarisation capabilities 107 indicated by dashed lines arising from the spatial dependence of the nuclear spin coupling to the NV qubit 101.

[77] Fig. lb illustrates a method for manufacturing a hyperpolarised agent, the method comprises locating 151 agent 103 in close proximity to quantum probe 101 that is in a first energy state. It is noted that the first energy state may be a mixture of quantum states.

Quantum probe means that probe 101 has different quantum states, like a qubit. Quantum states may be nuclear spin states. Close proximity in this context means a proximity that is sufficiently close for hyperfine interaction to occur, such as closer than 20 nm or even closer than 10 nm, such as 5 nm. The method 150 then proceeds by applying 152 magnetic field 108 to probe 103 and agent 103. In one example, the magnetic field 108 is applied over the entire time method 150 is performed. The method 150 then comprises applying 153 quantum control radiation, such as laser light, to the probe to bring the probe in resonance with a second energy state. This may be a quantum energy state. It is noted that in some examples provided herein the second energy state is higher than the first energy state but in other cases, the second energy state can be lower than the first energy state. In this sense, the terms 'first' and 'second' are used to denote a sequence rather than a relative value of energies. The next step of method 150 is to remove 154 the quantum control radiation to allow cross -relaxation between the probe and the agent while the magnetic field is applied.

[78] Generally, cross-relaxation occurs between two particles, when a first particle initially in an excited state exchanges energy with a second particle that is initially in the ground state, resulting in both particles simultaneously changing to the ground state and excited state, respectively.

[79] The magnetic field is of a magnetic field strength that aligns the energy states of the probe with the energy states of the agent to allow transfer of energy and thereby activate the cross-relaxation between the probe and the agent to polarise the agent. In other words, the magnetic field leads to the energy gap in the probe 101 to be substantially equal to the energy gap in the agent 103.

[80] Cross -relaxation and energy levels

[81] System 100 employs the principle of cross-relaxation, which is illustrated in Figs. 2a to 2d. In particular, Fig. 2a illustrates the probe energy states 201 of the probe 101 and the target energy states 202 of the target 103. Probe energy states 201 comprise a low energy state 211, and high energy state 212. In this case, these two energy states result from Zeeman splitting caused by the external magnetic field 108. Similarly, target energy states 202 comprise low energy state 221, and high energy state 222. The target energy states 202 are largely independent of magnetic field 108 because the target energy states 202 are also subject to Zeeman splitting in the magnetic field.

[82] In Fig. 2a, the energy states are not adjusted . In particular, the probe spin transition (i.e. gap) between the low 211 and the high 212 states of the probe 201 is different to the agent spin transition (i.e. gap) between the low 221 and high 222 states of the agent 202. For this difference, there is little resonance and transfer of energy would rarely occur. Therefore, cross-relaxation could not be used effectively. By applying magnetic field 108 in step 152 the energy states are adjusted as shown in Fig. 2b. In particular, the gap between the low 212 and high 212 states of the probe 201 is now equal to the gap between the low 221 and high 222 states of the agent 202, which brings the probe spin transition into resonance with the agent spin transition. Therfore, transfer of energy is possible and cross-relaxation can be used effectively.

[83] As seen in Fig. 2b, both probe 101 and target 103 are in the low energy state 211 as indicated by circles 231 and 232. In this example, the energy states relate to different spin of the probe 101 and target 103, respectively. It is noted, however, that probe 101 may also be in the high energy state 212 and the method below would work, which is useful because the probe can be manupilated into various spins states.

[84] Fig. 2c illustrates how the application of quantum control radiation 204, such as laser light, brings the probe 101 to the high energy state 212. It is noted that this is a simplification and the applied light 240 may raise the probe state 231 significantly higher but the probe state 231 then drops back to high energy state 212. This occurs regardless of the state of the probe 101 before this initialisation. That is regardless of the state in Fig. 2b the probe 101 is initialised to high energy state 212. Fig. 2d illustrates that when the laser light 240 is removed, cross-relaxation between the probe 101 and the target 103 leads to the probe state 231 'drop' to lower energy state 211. At the same time, target state 232 is 'lifted' to the high energy state 222 of target 103. In this sense, energy is transferred from the probe 101 to the target 103 leaving the target 103 polarised. In other words, the external magnetic field, B , is applied to adjust (or tune) the ground-state spin transition frequency of the NV { co _m ) into resonance with target nuclear spins ( ω _α )by adjusting the Zeeman effect to split the energy levels by the right amount. Interestingly, if the method is repeated, the probe 101 does not interact with the polarised agent 103 because their magnetic fields are aligned. This means there is a one-way energy transfer and the energy transferred to the agent cannot return back onto the probe. When the method is now repeated, more and more energy can be transferred to other nuclei of the target thereby implementing a process similar to a pump with a nonreturn valve. Hence, this disclosure refers to the system as an entropy pump.

[85] Fig. 3 illustrates an energy-level diagram of the NV showing the relative positions of various target nuclear spin resonance conditions.. For a given target species, the spin resonance condition is fulfilled at a magnetic field Β„(γ _α ) « 2D I (γ _Νν -γ _η )

[BROADWAY16], where γ _α , / _NV are the target and NV gyromagnetic ratios, and D is the NV zero-field splitting.

[86] CRIP

[87] Fig. 4 illustrates a schematic 400 of cross relaxation induced polarisation (CRIP) implemented on a spin system illustrating the build up of polarisation from repeated application of the CRIP sequence. Diffusion effects act in competition with the CRIP entropy pumping mechanism, but also allow for polarisation at distances beyond that reachable via the probe-target magnetic interaction interaction.

[88] Fig. 5a illustrates a control sequence using laser pulses 501 for polarising a target spin ensemble using CRIP. Fig. 5b illustrates a control sequence using laser pulses 502 and RF pulses 503 for controlled depolarisation using the combined CRIP ^~ ' x CRIP protocol. Entropy pumping is facilitated by repeated application of the cross relaxation induced polarisation (CRIP) sequence, wherein the NV spin is optically initialised into | O) state and the NV-target hyperfine interaction is allowed to occur for a given period of time, T (of order microseconds). The transfer of magnetisation caused by this interaction thus polarises the target spins into their |>l^ state (Fig. 4). For the sake of comparison, depolarisation may be facilitated by interleaving the initialisation of the NV spin into the opposite state | -l by the application of an RF 71 -pulse (Fig. 5b).

[89] The following disclosure provides a quantitative assessment of the effect of the CRIP protocol on the target spin ensemble based on an approach that explicitly includes the dipole interactions of ensemble spins and their interaction with a single NV quantum probe. The polarisation of a spin at position R (relative to the NV) and time t can be defined as P(R,r)

; with the evolution of P(R, t) described by

^■ f- P(R, = (/?V ² - «(R) - r _sL ) P(R, + «(R), ( 1 ) subject to an initial unpolarised state P R,t) = 0 ; where w(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 intra-target interactions, and T _SL is the spin-lattice 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.

[90] To probe the polarisation effect experimentally, photo detector 107 monitors the spin-dependent photoluminescence (PL) from the NV [HALL 16], [WOOD16I], [WOOD16II]

-Γ τ during the laser pulses, which decays as a function of the CRIP sequence time as e ^tot . Here T _tot is the NV longitudinal relaxation rate, which can be expressed as the sum Γ _(ο( = r _bg + T _CR , where T _bg is the background rate caused by lattice phonons or surface effects, and T _CR is due to cross -relaxation. The latter follows a Lorentzian dependence on the detuning between the probe and target transition frequencies [24],

where is the total effective hyperfine field seen by the NV due to the target ensemble, which is related to the polarisation distribution via

A* = ^{[l- P(R,f)] A ² (R)d ³ R, (3) where n _t is the density of the target spin ensemble.

[91] Fig. 6a illustrates the cross -relaxation spectrum of the target. One indicator of significant polarisation is a reduction in T _CR , which manifests as the disappearance of the target ensemble's spectral feature from the cross -relaxation spectrum as can be seen in the difference between the polarised spectrum 601 and the unpolarised spectrum 602 at reference numeral 603. The polarisation can be quantified by measuring the cross-relaxation curve at resonance, which is shown in Fig. 6b.

[92] Experiments

[93] Experimentally, we first demonstrate our technique on the 1.1% ¹³ C spin ensemble surrounding a NV probe in the diamond substrate by tuning to the ¹³ C resonant condition at S,( ¹³ C) = 1024.9 G.

[94] Fig. 7 illustrates cross-relaxation spectra of a single NV spin 701 near the ¹³ C resonance (ω _Νν = 1.1 MHz), obtained with an interaction time τ = 4^s using the CRIP sequence 702 and the depolarisation sequence 703 (only the readout following the NV initialisation in |0) is shown). Sequences were repeated N = 10 ⁵ times at each point. Fig. 7 also illustrates the cross-relaxation curves 704 obtained by increasing τ at the ¹³ C resonance with the CRIP sequence 705 and depolarisation sequence 706, and off-resonance to obtain the background relaxation curve 707. Zoom- in at short times for the polarised 708 and unpolarised case if the NV initialised in |0) 709 and |— 1) 710. [95] Comparison of the cross-relaxation spectra for CRIP and depolarisation sequences at 701 shows the complete removal of the ¹³ C resonance peak 711 for interaction times of τ = 4μ8, indicating efficient polarisation of the nearest spins, as compared with the target prepared using the depolarising sequence. This is confirmed in the cross -relaxation curves as a function τ 704 (inset), where the polarised case shows no evolution of the NV spin state, while the unpolarised case shows coherent flip-flops between the NV and the ¹³ C spins.

[96] Fig. 8 illustrates calculated radial polarisation profiles relative to the NV spin (averaged over all angles), calculated from Eq. (1) for a random 1.1% ¹³ C spin ensemble for varying total polarisation times, T = Ντ. Inset: profile along dashed line, corresponding to T = 2 h. Fig. 9 illustrates a three-dimensional representation of the polarisation distribution at T = 2 h.

[97] To investigate the extent of the polarisation effect, we increase the interaction time T so as to be sensitive to more remote ¹³ C spins, up to the limit set by the NV centre's intrinsic spin-phonon relaxation rate, Y _bg = 200 ms ^-1 . The resulting cross -relaxation curves obtained at the ¹³ C resonance using the CRIP and depolarisation sequences are shown at 704 in Fig. 7, from which we extract the total relaxation rate, T _tot . By subtracting Y _bg obtained from the off-resonance relaxation curve 707, the ¹³ C-induced relaxation rate r _CR = T _tot — T _bg is deduced, which decreases from T^ ^po1 = 250 ms ^"1 with the depolarisation sequence, to below the noise floor of the measurement after 5 hours of CRIP, < 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 8. By relating the spatial polarisation distribution, P(R,t) , to the cross- relaxation rate, r _CR , via Eq. (2), we find the theoretical results are consistent with the experiment for polarisation times in excess of two hours (Fig. 8, dashed line). Examination of the spatial polarisation distribution (Fig. 8, inset, and Fig. 9) implies a polarisation level of more than 99% within 21 nm of the NV, equating to a 6 x l0 ⁶ -fold increase on thermal polarisation for 3 x l0 ⁵ spins.

[98] The basic protocol described above can be used for 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 substrate [MAMIN13] with single NV spin probes located 8-12 nm below the surface. CRIP was applied with the external magnetic field tuned to resonance at fi^H) = 1026.2 G. With a much higher diffusion constant and spin- lattice relaxation rate (β = 781 nm ² s ^"1 , T _SL = 1 s ^"1 ) relative to the intrinsic ¹³ C case, the ¹ H system effectively reaches steady-state within a few seconds. Application of the CRIP sequence to NV1 (data for other NVs are shown below) for τ = 10 ^s (numeral 1000 in Fig. 10) shows a hydrogen spectral feature at 1001 for the depolarising sequence 1002, which is removed by the polarising sequence 1003. From the cross -relaxation curves after 1 hour of CRIP (numeral 1050 in Fig 10), ¹ H-induced rates can be extracted for the unpolarised (r" _R ^npoi ) and polarised PMMA ¹ H spin ensembles to be 2.71 ms ^-1 and 0.96 ms ^-1 , respectively. The ratio ^CR _ol = 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. 11, indicating that the system reaches 50% average polarisation over a volume of ~ (26 nm) ³ . This shows 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.

[99] Production of macroscopic quantities

[100] There is scope for improvement on these results: for example, engineering NV depths to 5 nm may 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) may allow for more precise tuning to different nuclear spin species.

[101] Fig. 12 illustrates a scale-up for a universal MRI contrast agent hyperpolarisation platform 1200 comprising a quantum polarisation stack 1201. Fig. 13 is a more detailed schematic of the quantum polarisation stack 1201 comprising multiple diamond membranes 1202 (in Fig. 13 reference numerals are provided only for one membrane for clarity). Each membrane 1202 contains NV array layers 1203 and 1204 on both sides, in a homogeneous magnetic field 1205 generated by coils 1206, for example. The magnetic field 1205 tunes the NVs to the nuclear gyromagnetic ratio of the target agent spin species. The unpolarised agent in concentrated solution 1210 flows into the stack channels 1201, where the liquid is polarised through the application of CRIP (via a pulsed laser). The out-flowing polarised liquid 1211 is then diluted in mixer 1212 by dilution liquid 1212 for use.

[102] As the protocol is all optical in this example, scaling up for high-volume production can be achieved by stacking multiple NV arrays as shown in Fig. 12 and/or increasing the effective interaction area via surface patterning [KEHAYIAS 17].

[103] Results

[104] The results presented here indicate that the CRIP protocol can 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 ) , an MRI contrast agent.

Using a single hyperpolarisation cell comprised of two NV arrays in diamond membranes separated by 1 μιη (see zoomed schematic in Fig. 13; we assume an NV density of 4 x l0 ⁿ cm ^" over a 4 mm x 4 mm diamond surface [SCHMIDT17]), the rate of polarisation transfer to a concentrated 1M precursor HEP solution is 4 μΕ/s at a polarisation level of 80%.

[105] The polarisation levels for different contrast agents in 1M precursor solutions are plotted against polarisation time (assuming perfect mixing occurs over these timescales) in Fig. 14 at 1401. In Fig. 14 at 1411, the final delivery rate is plotted after dilution to 1 mM for a stack of 10 cells, showing that delivery rates of order 100 pIJs for clinical applications

[GOLMAN06] are achievable.

[106] Fig. 14 illustrates an average polarisation level 1401 from a single polarisation cell, for various targets (HEP 1402, H ₂ O 1403, and ¹⁵ N-TMPA 1404), calculated for varying polarisation times assuming perfect mixing of a 1 M target agent solution with a cell height of 1 μιη and outflow rate 1411 (after dilution to ImM for application delivery) from 10 polarisation cells at different levels of polarisation (HEP 1412, H ₂ O 1413, and ¹⁵ N-TMPA 1414).

[107] In summary, this disclosure provides methods and systems for hyperpolarisation of molecular nuclear spins under ambient conditions by employing a quantum spin probe entropy pump. The technique works at low field, room temperature, requires no RF 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 scale-up 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 offer new pathways in quantum information for initialisation of quantum simulators, or increasing the fidelity of operations through spin-bath neutralisation.

[108] Theoretical Background

[109] The following description provides further theoretical background and experimental data. For the sake of clarity, it is noted that equation numbers start from (1).

[110] Hamiltonian of the system

[111] The Hamiltonian describing the coupling of an NV- ¹³ C- ¹ H system is given by

Ή ^{= ~} JV + ^C13 ^~I~ '¾V-C13 ^~I~ '¾V-H ^C13-H ' ( ^ )

where 7i _NV , 7^, ₁₃ , and describe the self-Hamiltonians of the NV, ¹³ C, and external ¹ H spin systems, respectively; and the remaining three terms describe the interactions between these systems. In general, the system described by Eq. 1 may have no closed form solution. In what follows however, a theoretical framework is provided that accurately describes the polarisation process for the special cases presented in the main text.

[112] To simplify this system, it is possible to ignore the 7t^ ₁₃ _ _H term on the basis that the nuclear-nuclear interactions between the two systems are intrinsically weak, and made more so by the fact that they are significantly detuned from mutual resonance by about 3.3 MHz at an operating points around 1024 G. Further simplifications are made according to which system is being targeted: polarisation of the ¹³ C bath was carried out for deep NVs (h = ΙΟμιη) with no surface PMMA, henceH _{NV H} = 0; alternatively if a near-surface NV spin is tuned to resonance with the ¹ H system, it will be detuned from ¹³ C by 3.3 MHz, which is significantly larger than their measured ~ 500 kHz linewidth, hence/f _NV _ _cl3 = 0. Thus the theoretical approach to modelling these two systems in response to CRIP is the same for both cases, and will be developed below independent of the choice of the intended system to be polarised. [113] The overarching principle of this disclosure is to bring the chosen environment into resonance with the NV centre via precise control of an external magnetic field aligned with the NV axis. As the NV may be optically initialised in its I 0) state, any proximate unpolarised environmental spins (of which there will initially be many) will absorb the polarisation of the NV spin via their mutual hyperfine interaction. This polarisation will then diffuse to distant environmental spins via their magnetic dipole interactions. By repeating this process many times over, the system may produce polarised regions surrounding the NV of up to a few tens of nanometres in size.

[114] Given the generality of this approach with respect to the target species of nuclear spin, the below description refers to a general environmental target spin system, E. Assuming alignment of the external field with the NV axis, the Hamiltonian becomes

H = InDS + y _m B ₀ S _z +∑[S - A Ϊ. - ] + ¾ · B _jk ^■ ¾ , (2) where S _{x z} are the Pauli spin matrices of the spin-1 system of the NV, D = 2.87 GHz is the corresponding zero-field splitting, B ₀ is the external field strength, y _m and y _a are the gyromagnetic ratios of the NV and target spins, are the Pauli spin matrices of nuclear spin j , A . is the hyperfine tensor describing the spin- spin interaction between the NV and spin- j , 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. 2, y _m is defined positive, while y _a can be positive or negative depending on the species considered.

[115] Cross -relaxation resonances

[116] Transforming to the interaction picture and applying the rotating wave

approximation to the NV-target resonances, the consideration may be restricted to the NV subspace spanned by (|0) ,| -l)} , since the |θ) -» |+l) transition is detuned from the nuclear spin transitions by approximately 5.7 GHz. A |θ) -» |-l) NV transition frequency can be defined as &> _NV ≡ 2πΌ - y _NY B ₀ , and the target transition frequency as ω _α ≡y _a B ₀ . The cross- relaxation resonances occur when I CD _NV 1=1 ω _η I . Since _m changes sign at the NV ground state level crossing at B ₀ = 2πΌ I y _NV « 1024G , there are two resonance points before and after the crossing, at magnetic fields B _< (χ _η ) ^ 2DI (γ _ν + γ _η ) and B _> (y _a ) - 2D I (γ _ν - γ _α ) , respectively. It can be assumed that γ _n > 0 . A negative sign would simply swap the two resonances and their associated NV-target interaction strengths, relative to the crossing.

[117] Near the NV level crossing, the hyperfine interaction of the NV electron spin with its own intrinsic nuclear spin (associated with the nitrogen atom) causes the NV levels to mix and anti-cross, adding small corrections to the above resonance conditions. A detailed description of this NV ground state level anti-crossing (GSLAC) may be found in Ref.

[BROADWAY 16]. The relevant energy levels of the NV electron spin and target nuclear spin are depicted in Fig. 15. As the polarisation transfer is mediated by the NV-target hyperfine interaction, the resulting target spin state ( | or | ) depends on which nuclear spin transition the NV spin is tuned to. Before the GSLAC (e.g. at fi _< ( ¹³ C) = 1023.9 G), CRIP will polarise nuclear spins into the lT> state (Fig. 15 at 1501). On the other hand, when applied at the resonance condition after the GSLAC (e.g. S _> ( ¹³ C) = 1024.9 G, or β _> ( ¹ Η) =

1026.2 G) the target is polarised into the \i> state (Fig. 15 at 1502). The NV-nuclear resonance conditions for various species of nuclear spins is shown are Fig. 16. This shows that some target nuclear spin species, including ¹ H for example, do not have a resonance condition before the GSLAC, as the requisite NV spin transition is forbidden. After the GSLAC, however, there is no significant state mixing, which allows all spin species to be addressed via the CRIP protocol. In the following disclosure, only cases are considered where state mixing is negligible, so that the NV nuclear spin need not be not included in the model.

[118] Definitions

[119] Under this simplification the hyperfine component of the Hamiltonian becomes

S - A J. - X = A x ⁽ x ^J) S x x + A x ⁽ y ^J) ( \ x X y ^(J) + S y X x ^(J) ) J + A y ⁽ y ^J) S y X y ^(J) + A z ⁽ z ^J) S z Z z ^(J) ,' (3) which may be written more compactly for near-resonant cases before and after the GSLAC as

1

. 7.

2V2 ι-ι>μ>, <οΐ<τ|, ι-ι>μ>, <oi<†i; 72. 7 respectively, where 1 0>,l— 1) refer to the NV spins states, and A ^> = A^> - A^> ₊ 2iA^>. (5)

[120] As these two transitions are spectrally distinct, from this point forward, this disclosure will simply refer to the transverse hyperfine coupling between the NV spin and spin j as A _j , where it is understood that its particular functional definition (^Α^ οΐΑζ ^ depends on the choice of resonant field strength, 5 _< or B _> .

[121] For a radial separation distance R _j and polar angle , the effective transverse coupling rates between the NV spin and environmental spin j are given by

for magnetic fields of B , and B _> , respectively, corresponding to resonant transitions either side of the NV GSLAC.

[122] For 5 ₀ ~ 1000G magnetic field strengths studied in this work, the Zeeman energies of the nuclear spins far exceed their mutual nuclear dipole couplings, hence any spin flip-flop dynamics they exhibit are magnetisation conserving, and it is possible to apply the secular approximation to the Hamiltonian describing their mutual dipole-dipole interaction

¾ · ^B ,* · ¾ =∑ ^B * (^ ^k + y ^{) }} - 21^^ ) , (7)

k>j

where l - 3cos ² (¾ )] ' (8) and r _jk and Θ _jk are the separation distance and polar angle between spins j and k .

[123] Discussion of competing time and length scales [124] ¹³ C Environment [125] For the purposes of discussion of the relative strengths of the two transitions, it is useful to average over the angular components of Eq. 6, giving for before or after the GSLAC, respectively

where

(10)

An

[126] Determination of the total hyperfine field strength then proceeds via summation over R _j , where we now index R _j according to the expected distance from the NV to its nearest ¹³ C spin; the distribution of which is given by Ref. [HALL16]

where n = 1.95nm ³ is the density of ¹³ C nuclei in diamond. Using this result in Eq. 9, yields

A _< « 6.24an = 1.43 x l0 ⁶ rads ^_1 = 228kHz (11) * 15.280» = 3.51 x l0 ⁶ rads ^~1 = 559kHz. (12)

[127] ¹ H Environment

[128] For the ¹ H bath in PMMA, the NV-environment separation distance (approximately 10 nm) is much larger than the separation distances between adjacent ¹ H spins. As such, the total hyperfine field strength may be evaluated via a standard integral over the effectively continuous, semi-infinite PMMA slab.

[129] Due to the avoided crossing in NV spin level structure before the GSLAC (see Fig.

1) , the only resonance point between the NV spin and ¹ H spins occurs after the GSLAC at B _> = 1026.2 G. In addition, the angular dependence of the interaction (see Eq. 6) should be considered when choosing the NV orientation relative to the surface. For instance, an NV normal to the surface of a l 1 cut crystal, which is optimal as far as photon collection is concerned, would place the nearest ¹ H spins in the node of the hyperfine coupling (see Fig.

2) . In one example, an NV is used in a standard (l00) cut diamond crystal, which gives a relatively good coupling. As such, the original coordinate system, R = (x, y, z) can be transformed to the new coordinate system, R' = (X, Y, Z) , defined by

x = X cos(or)— Z sin(or)

y = Y

z = X sin(or) + Zcos(or), (13) where = arccos ^l / j « 54.7 ^° . The hyperfine integral then proceeds as

^ = ^A W ^dxdYdz

₌ 1 ,

24 h ³

where n = 56nrrf ³ is the density of ¹ H spins in PMMA, and h is the depth of the NV below the diamond-PMMA interface (measured to be approximately 10 nm herein).

[130] Description of CRIP Protocol

[131] The following description shows how to solve for the evolution of a number of special cases of Eq. 2 in order to motivate and develop a general continuum description for an environment containing an arbitrary number of spins.

[132] Single hyperfine coupled spin

[133] Assuming a starting density matrix of

y (0) = (| 0)(0|) _Nv ® ( _/? |†) (†| ₊ (l - _/? ) ^) ^ |) _n , (15) where p denotes the probability of the target spin being in its state, the probability of finding the target spin in its †^ state at some later time, t , is given by

where δ = c¾ _v - ω _η is the detuning between the transition frequencies of the NV and the target spin. By tuning the magnetic field such that δ = 0 , and choosing the evolution time to facilitate the maximum possible magnetisation exchange, t = ≡ τ , the probability of

A finding the spin in its up state becomes ρ(τ) = 0 , indicating that the polarisation of the NV has been transferred to the target spin. In the following, we will take δ = 0 for simplicity. The effect of quasistatic magnetic noise, which amounts to a fluctuating detuning, will be be incorporated in the continuum description by introducing the NV dephasing rate, Γ ₂ .

[134] Two independent hyperfine coupled spins

[135] In the case of two target spins coupled to the NV, complete polarisation cannot be achieved within a single interaction. Assuming an initial state of

(0) = (|o>(o|) _w ®( |†)(†| + (i- )|l)(l|) _ti ® ( _J p ₂ |†)(†| + (i- _J p ₂ )|l)(l|) _t2 , (iv) the time-dependent 0) state population of the NV is

[136] Therefore, the maximum possible contrast corresponds to the minimum of p _m , given by

2 + P ₂ ²

A ² + 4 ²

when δ = 0 and

t = T fe r ^<20)

[137] Substituting T into the expressions for p and p ₂ , the change in populations is

^--*^- ^< *- ^»> (i¾7 ⁽²¹⁾

[138] The terms proportional to p _x - p ₂ are mixing terms that facilitate faster polarisation of the farthest spin due to the back action of the NV spin in response to the closest spin. [139] Two dipole coupled spins

[140] It is possible to add an additional magnetic dipole-dipole interaction between the two spins. In general, this system does not exhibit a closed-form solution, however, the timescale of the dipole coupling between the two environmental spins, τ _Β = 1/B ₁₂ , is much longer than that of the hyperfine dynamics,^ = 1/A. Hence, the dipole-dipole dynamics are expanded for times t < 1 / B _n to give

A + (A ² + A ² ) A +

A ² A ² A ² B ²

[141] For cases where both spins exist outside the strongly hyperfine coupled core surrounding the NV, the two spins will thermalise on the timescale of their dipole coupling, τ _Β . Hence, for outside the core on timescales of T holds

A ⁺ A A +A)

[142] General case and continuum description

[143] For the case of N _s spins, each having hyperfine coupling A _j to the NV, mutual dipole couplings B _jk , and initial state, (0) = (|0)<0|) _NV (x)(p |†)(†| ₊ (l - p )|^)^|) _tj , (24) the population of the NV 0) state is at a minimum when t = τ = , and is given by

A

where A ² is the total hyperfine coupling field. [144] The change in robability of spin j is given by j = -Pj (26)

where B _jk is the magnetic dipole coupling between spins j and k , and C ≡ A ² A ² I A ² is the effective hyperfine-mediated diffusion strength. For approximately N _s = 10 ⁴ spins, the evolution of discrete spins in this system may be solved numerically, an example of which is given in Fig. 19.

[145] Spins residing in the hyperfine core are characterised by having a stronger coupling to the NV than to all other spins in the environment, i.e. A ² >∑ _k B ² _k . Typically, the interest is in relatively long total times t » τ with t = Ντ (hours vs μ8, respectively) for which the polarisation region has far exceeded the hyperfine core, as a result of dipole -mediated flip- flops between the polarised core and the unpolarised outer region. As such, the focus may not be on the relatively fast dynamics associated intra-core diffusion, and instead on the rate at which the NV polarises spin in the core ( A _k ), and the rate at which this effect is

communicated to the rest of the bath B _jk . Therefore, C _jk = 0 can be used.

[146] In modelling these systems, it is desirable to consider regions of at least 200 nm in size, which means of order N _s ~10 ¹⁰ spins and ~10 ²⁰ couplings for the case of PMMA, thereby making modelling of discrete spin states computationally unfeasible. Eq. 26 can be mapped to a temporally and spatially continuous description via the following:

[147] a) Time-dependent probability field— As the regions of polarisation considered herein may be larger than the hyperfine core of the environment, which itself is comprised of the order of 10 ⁴ spins, instead of considering the time-dependent populations of discrete spins, this disclosure instead considers the time-dependent probability field of the

environmental spins having an average density, n ,

_Pj →p(R,t). (27)

In essence, p (R,r) is the average probability of spins in an infinitesimal volume at position R from the NV being in state |†^ at time t . [148] b) Probability field dynamics— In the discrete description, the probability of finding spin j in its |†^ state is monitored at discrete multiples of the optimal dark time, T . Ignoring probability diffusion, this would behave as a geometric series. As the focus is on times t ^> τ , changes in p . over time can be mapped to

&P _j \→ T - p (R, t) (28)

[149] c) Hyperfine coupling field— As with the population field, the discrete hyperfine couplings can also be mapped to a continuous field whose strength is determined by its position relative to the NV, R .

A _j →A(R) . (29)

[150] d) Total hyperfine coupling strength— The summation over all hyperfine couplings is mapped to an integral,

[151] e) Probability diffusion— Let p . i— > p (R, t) and p _k i— » p(R + r, t) , and discretise the Laplacian o erator to get

[152] f) Additional sources of relaxation— To account for additional sources of environmental spin-lattice relaxation, where applicable, an additional probability sink can be added in which any probability outside equilibrium decays at a rate T _SL =— , whose rate is given by

[153] The differential equation describing the evolution of this system is thus given by ■ p(R, t) = -«(R)p(R, t) + {N ² p(R, t) - r _sL { p (R, t) - , (33)

v 2

where «(R) = ^ (34) is the effecti e source, or cooling, coefficient at position R relative to the NV, and

is the effective probability diffusion coefficient related to the intra-bath interactions B _jk .

[154] Finally, it is noted that 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. , Γ ₂ » A ₀ t e population of the |0) state of the NV spin will exhibit an exponential time dependence given by (see Ref. [HALL 16 for details)

[155] As such for this regime the following replacement can be made:

[156] Experimentally, Γ ₂ can be obtained via the TJ -relaxometry spectrum (with the interleaved sequence), since Γ ₂ defines the width of the cross-relaxation resonances

[HALL16]. It is noted that Γ ₂ is expected to decrease upon polarisation of the ¹³ C bath. However, the effect is relatively small (see above), and as such in the calculations shown above Γ ₂ is kept constant and equal to the off-resonance 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.

[157] The table below summarises the parameters associated with the three example systems provided herein: the diamond ¹³ C bath before the GSLAC and after the GSLAC (Figs. 7, 8 and 9), and the PMMA ¹ H bath after the GSLAC (main text Figs. 10 and 11).

[158] Determination of Polarisation Extent

[159] Upon solution of Eq. 33 for the probability field /?(R,f) at some time, t , the total hyperfine coupling may be found from

Al( ) = n _t f p(R, t)A ² (R, t)d ³ R (38)

[160] For the initial case of /?(R,0) = - , this expression reduces to the definition employed above for ,

2 ₀ = f J ,4 ² (R, t)d ³ R (39)

[161] Thus, the total reduction in the hyperfine field at time t due to polarisation is determined from η≡^, (40) and the total number of spins polarised at time t is

N _pol (t)≡n _t j[2p(R,t)-l]d ³ R. (41)

[162] The reconstructed radial profiles for the ¹³ C polarisation above are shown in Fig. 20 for both before and after the GSLAC. In a similar fashion the PMMA polarisation can be reconstructed. 2D slices of the polarisation extent in the PMMA for different polarisation times are shown in Fig. 21.

[163] Scale-up strategy

[164] After analysing the CRIP protocol above for the case of a single NV spin, this technique may be scaled up for the purpose of polarising macroscopic quantities of arbitrary nuclear spin labels for clinical applications such as MRI imaging.

[165] Polarisation rates [166] From the analysis above, the maximum rate (spins/s) at which polarisation is delivered to the target spin ensemble from a single NV is equal to the effective hyperfine field,

Rsin le ⁼ ^

where n is the numerical density of the target spins, is the distance of the NV from the a,

diamond/target interface; and a =—^ / _{Νν τ} Μ _Ν , where g _T is the g-factor of the target species,

An

and μ _Ν is the nuclear magneton. For a planar NV density within the diamond substrate of (J , the total polarisation delivery rate is

R = ax Ar _ea xR _sm , _e . (43)

[167] Time-dependent polarisation

[168] Assuming that the spatial diffusion of target spins is sufficiently fast to ensure perfect mixing (i.e. uniform polarisation throughout the cell on timescales of the order of 1/A), the polarisation of the target spins is governed by

where P is the average polarisation of the target spins, and T _SL is their spin-lattice relaxation time. Solution of this equation yields where N≡n x Area x h _ceU is the total number of target spins in the cell, and h _{c ell} is the height of the cell.

[169] Optimal geometry

[170] Eq. 45 shows that the steady-state polarisation and characteristic polarisation time are given by N71,

τ _Ρ = — (47)

N + RT _SL

respectively. It is clear that these expressions define a critical effective number of spins, N _crit ≡ RT _SL , that may be polarised before that polarisation is lost to spin-lattice relaxation effects. As such, any delivery system of spin-polarised contrast agents necessitates that N _crit ^> N . As both of these quantities are proportional to the area of the NV array, we may rewrite this constraint in terms of the coupling parameters h _NV and cell height h _cell to give ^u «^n„ (48)

where

_¾ 65nms ¹ x g _T r _si /A , (49) where N _m is the number of target spins in the target molecule, and we have assumed a target concentration of 1 M (mol/L). This allows us to define an effective length scale by which to characterise the suitability of candidate systems to this scheme.

[171] Volume delivery rate

[172] From E . 45, the time required to achieve a desired polarisation, P , is

and the volume delivery rate of polarised contrast agent is

dh

£) ₌ ____IL _x Area, (51) where d is the dilution factor, typically of order 10 ³ to reach mM concentrations. In the limit of RT _SL N , this becomes

dR

Q =

?z , log ⁽ 1

1 - P

= 1.03434Ls ^'1 x (52)

i log ¹

I i- p [173] It is noted that T _SL does not enter into Eq. 52, as it is assumed RT _SL N , and hence Keii ^ ^crit · Values of these quantities are given in Table 2 for various candidate contrast agents.

Table 2: Values used for the scaling up.

[174] Additional experimental information

[175] Apparatus

[176] In one example, apparatus 100 in Fig. la consists of a custom-built confocal microscope and a permanent magnet mounted on a scanning stage, the same setup used, and described, in ref. [WOOD16I] . In summary, the excitation source is a solid-state laser emitting at a wavelength λ = 532 nm (Laser Quantum Gem 532). The objective lens

(Olympus UPlanSApo 100 x , NA = 1.4 Oil) is mounted on an XYZ scanning stage (PI P- 611.3 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 band-pass filter, and coupled into a multimode fibre connected to a single photon counting module (Excelitas SPCM-AQRH-14-FC). For TJ measurements, the laser beam is modulated by an acousto- optic modulator (AA Opto-Electronic MQ180-A0,25-VIS) in a double pass configuration, and the PL signal is analysed by a time digitizer (FastComTec P7889). For optically detected magnetic resonance (ODMR) measurements, a 20- μ m 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 (Mini-Circuits ZASWA-2-50DR+). Laser and microwave modulations are controlled by a programmable pulse generator (SpinCore PulseBlasterESR-PRO 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 M-511) 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 [TETIENNE12].

[177] Diamond samples

[178] The sample (#132) used for the ¹³ C measurements may be a ^l 11^ -oriented single crystal, electronic grade, chemical vapor deposition (CVD), 100 μιη thick diamond purchased from Delaware Diamond Knives. The measurements reported in Figs. 6a and 6b are based on native (as grown) NV centres located far (several μιη) from the surface.

[179] The sample (#122) used for the ¹ H measurements may be a (lOO) -oriented single crystal CVD overgrown on a HPHT substrate from Element Six. The overgrowth is roughly 50 μ m and electronic grade. The sample has been implanted with ¹⁵ N and ¹⁴ N at 3 keV at a density of 5 x 10 ⁸ cm ^"2 each. The sample was annealed at 950 ° C for 2 hours and was exposed to a soft O ₂ plasma for 1 minute [FAVAR015]. The PMMA was baked onto the surface of the diamond by a heat gun at 85 " for 40 minutes. The diamond has a range of near surface NV depths (approximately 3-13 nm) determined by NV-NMR spectroscopy using the dynamical decoupling method [PHAM16].

[180] General acquisition procedure

[181] The spectra shown in Figs. 6a and 7 were obtained as follows. The magnetic field was first aligned along the NV axis by maximising the PL intensity [EPSTEIN05,

TETIENNE12, WOOD16II ]. When doing this near the GSLAC, the alignment may be 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 _Νν via a Lorentzian fit, before the CRIP sequence is applied. The latter consists of a series of 3^s laser pulses, sufficient to completely initialise the NV spin state, separated by a wait time τ. The signal plotted in Figs. 6a and 7 (at 701) 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 non-polarised case, the scan may be repeated but by interleaving CRIP and CRIP ^"1 pulse sequences, which acts to prevent polarisation build up in either direction. The CRIP ^"1 adds a radiofrequency (RF) pulse to flip the NV spin from |0) to |— 1). This π pulse was applied 1 μ$, 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.

[182] For the full-length 7j measurements presented in main text Figs. 6b and 7 (at 704), 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. It can thus be ensured that the NV remains on resonance with the target transition, within the NV linewidth (see details below).

[183] ¹³ C detection and polarisation

[184] Before proceeding with the polarisation the ¹³ C spin bath, the 7j -relaxometry spectrum of the ¹³ C bath was first obtained using the interleaved sequence, while scanning the magnetic field across the GSLAC. The full spectrum is shown in Fig. 22 for the NV used in relation to Figs. 6a and 6b. The spectrum resolves three peaks, the two outer peaks correspond to the signal from the ¹³ C (before and after the GSLAC), the inner peak is an intrinsic feature of the GSLAC [B ROADWAY 16]. The GSLAC feature of the |0) state (top, readout from the CRIP sequence) is narrower than that of the |— 1) state (bottom, readout from the CRIP ^"1 sequence) due to experimental errors in implementing a π-flip in this region. This is caused by the rotating wave approximation breaking in this regime. This is because the driving field term in the Hamiltonian becomes similar in size to the quantisation axis itself. This needs to be considered for pulse experiments near the GSLAC as it can lead to artefacts in the measurements.

To elucidate the origin of the signal the PL difference (APL) between the |0) and |— 1) states versus the transition frequency (o) _NV ) is shown in Fig. 23. The expected transition frequency, in the weakly coupled regime, is ω _α = γ Β _ζ « 1.09 MHz. There is a slight shift in the frequency measured which is possibly due to a hyperfine coupling between the NV and the nearest ¹³ C spins that remain slightly polarised. Measuring the short time dynamics of the NV spin on resonance shows a coherent evolution caused by the hyperfine coupling to the surrounding ¹³ C spins. The frequency of the oscillation corresponds to the sum of the total hyperfine coupling of the bath to the NV (A _Q = ∑ _K see above) but will be dominated by the nearest ¹³ C . The damping is given by fluctuations in the spin configuration of the remaining bath spins, which causes the detuning, δ, to randomly vary. This is shown in Fig. 24 and has an approximate coupling strength of 250 ±40 kHz.

[185] The NV-bath coupling strength depends on the particular configuration of the bath around a given NV. It can therefore be expected that there is a variability in the spectrum and degree of polarisation depending on the specific location of the ¹³ C spins in relation to the central NV spin. The ¹³ C polarisation has been tested over a variety of diamonds including deep NVs near surface NVs in bulk diamond, and NVs in micro -pillars. All of the different samples and NVs have shown the capability to polarise the ¹³ C spin bath provided that the transition is observable around the GSLAC. The full CRIP and interleaved spectra (including the GSLAC feature) for the NV used in Figs. 6a and 6b are shown in Fig. 25. Also shown in Fig. 26 are the spectra from another NV. The time dynamics for this NV on resonance with the ¹³ C bath is shown in Fig. 27, revealing a similar hyperfine coupling.

[186] ¹³ C polarisation dynamics

[187] The polarisation dynamics was investigated for the NV used in Fig. 6a/6b, when on resonance with the ¹³ C bath (after the GSLAC). To this end, a series of N = 30 pulses was performed with a π pulse (i.e. CRIP ^"1 ), which polarises the ¹³ C in the |T) state. This is followed by N pulses without the π pulse (i.e. CRIP) polarising the ¹³ C bath in the |l) state. The pulse sequence is shown in Fig. 28a. The PL readout for each laser pulse as a function pulse number for three interaction times τ = 3, 5, 10 μ$, is shown in Fig. 28b. The resulting polarisation curves were fitted with exponentials (PL = aexp^N / T _POL ^J + y ₀ ) in order to determine the characteristic polarisation time. The result of the fits is shown in Fig. 28c and shows a clear trend of decreasing the number of polarisation pulses required as the interaction time is increased. It is important to note that due to the relatively short interaction time used in these measurements, the contrast obtained is dominated by the few nearest spins and is therefore an indication of the polarisation of nearby ¹³ C spins only, which appear to be efficiently polarised by the CRIP protocol after a few tens of ^s. More remote ¹³ C spins can be probed using longer τ times, as done in Fig. 6b, but the significantly longer acquisition time for these measurements prevents a systematic study of the polarisation dynamics as done in Fig. 28a-d.

[188] Finally in order to test the robustness of the sequence to the resonance position a magnetic sweep can be performed across both resonances and the GSLAC, shown in Fig. 28d. Four features are present, two related to ¹³ C (outside peaks) and two related to the GSLAC (inside peaks). The width of the polarisation region is roughly 0.1 - 0.2 MHz. The width of this polarisation region is governed by the T ^* of the NV spin. A comparison of the number of pulses required to polarise the nearest ¹³ C spins on both sides of the GSLAC shows a distinct difference, which is explained by the difference in the angular dependence of the dipole- dipole coupling before and after the GSLAC.

[189] Spatial extent of ¹³ C polarisation

[190] To monitor drifts in the magnetic field (caused by thermal fluctuations), the full- length TJ measurements used to estimate the extent of polarisation (Fig. 6b) were

accumulated while monitoring the NV frequency via an ODMR spectrum taken every 30 minutes. In general, the NV frequency remained on resonance with the ¹³ C transition frequency (1.09 MHz) for several hours, before it drifted away by more than the NV intrinsic linewidth (« 200 kHz). For the data in Fig. 6b, the total acquisition time was 5 hours, during which the NV was on resonance within the NV linewidth, i.e. ω _Νν in the range 1.0- 1.2 MHz. This ensures nearly optimal interaction between NV and ¹³ C bath, which is important not only to polarise the ¹³ C bath but also to accurately probe the remaining NV- ¹³ C interaction which were used to estimate the polarisation extent.

[191] For the reference measurements off resonance, this procedure were repeated by maintaining the NV at lower frequency ( < 0.9 MHz), and then at higher frequency ( > 1.3 MHz), for more than 10 hours each. The final curves were then fitted with exponentials to determine the total relaxation rater _tot , which is expressed as T _tot = Y _bg + r _CR on resonance, and simply T _tot = Y _bg off resonance. The full-length Τ _γ curves are shown in Fig. 29a for the NV used in Fig. 6a near the after-GSLAC resonance, under the three conditions explained above. The extracted total decay times are shown in Fig. 29b for both before and after GSLAC cases. The data before the GSLAC (bottom) shows a slight change in the decay rate measured on resonance, i.e. T^R ¾ 62 Hz. After the GSLAC however, there is no discernible difference outside of error, r _CR < T _ERROR = 19 Hz, given by the uncertainty of the fit parameter.

[192] Effect of ¹³ C polarisation on NV spin coherence

[193] As the limiting factor of the dephasing time of the NV spin ( T ^* ) is noise from the ¹³ C bath (for the deep NVs considered here), it is expected that polarisation of the ¹³ C spins will result in an increase in the T ^* of the NV. To measure T ^* , one usually performs a free induction decay (FID, or Ramsey) experiment. However, such a measurement is difficult at the cross-relaxation resonance because it would interfere with the flip-flop dynamics of the NV- ¹³ C interaction. A solution is to polarise the bath at the resonant field then quickly shift the field to off the resonance and perform the T ^* measurement, following the sequence shown in Fig. 30a. To implement this, a coil was attached to the board holding the diamond

(schematic shown in Fig. 30b). A constant voltage induced current pulse was used to generate a DC field from the coil to act as a quick field switching mechanism, allowing the polarisation to occur at the resonance frequency and the measurement to be performed at another frequency, as illustrated by the ODMR spectra shown in Fig. 30c. The field offset thus applied was B _OFFSET « 0.7 G, turned on while a series of polarisation pulses was implemented.

The offset was then turned off and the FID measurement performed.

[194] Using the same NV as in Fig. 6a/6b, a single- T FID measurement can be made as a function of the magnetic field, across the ¹³ C resonance (after GSLAC). The resulting spectrum is shown in Fig. 30d, where CD _M (measured by an ODMR spectrum at each magnet position) was scanned from - 1.0 MHz to 1.5 MHz during the CRIP polarisation phase (with the field offset on), corresponding to 1 MHz to 3.5 MHz during the FID measurement (field offset off). For the polarisation phase, N = 10 CRIP pulses were used, and for the FID τ = 4 μ s was used , and a driving frequency detuned by 0.2 MHz from the NV frequency so as to induce an oscillation in the FID response. [195] The CRIP+FID sequence is repeated many times at each magnet position with the aim to polarise the ¹³ C bath. The data reveals a feature centred on the NV- ¹³ C resonance, i.e. when a> _NV = 1.1 MHz during the polarisation phase. To interpret this feature, full-length FID curves were measured while scanning the magnetic field. Fig. 30e shows the resulting curves with the CRIP at the resonance or off the resonance. The main difference between the two FID curves is in the frequency of the oscillation, which differ from each other by 58(27) kHz. This difference is attributed to a change in the DC magnetic field seen by the NV, induced by polarisation of the nearest ¹³ C spins. However, the envelope of the oscillation shows a similar decay time ( T ^* ) in both cases, which means the ¹³ C polarisation was not sufficient to significantly reduce the magnetic noise seen by the NV.

[196] To increase the extent of the ¹³ C polarisation, longer CRIP sequences were used. In addition, we adjusted the driving frequency detuning such that the FID oscillation showed the same frequency with and without polarisation, for ease of comparison. The results are shown in Fig. 30f, and reveal a ~ 50% increase of T ^* ₂ from 3.6(5) μ s to 5.5(5) μ s upon

polarisation, similar to previous results with Hartmann-Hahn based polarisation

[LONDON13, LIU14]. The improvement is limited by the stability of the resonance condition during CRIP, as the switching of the magnetic field to bring the NV into resonance is non ideal with our current setup (in particular, showing significant overshoot).

[197] Another way to probe a change in T ^* is by examining the width of the resonance feature in the 7j -relaxometry spectrum, since it is directly given by the dephasing rate 1 / T ^*

[HALL16]. To test this, the sequence of Fig. 5a/28a, was used with N = 10 and a varying number of CRIP ^_1 pulses, N' . The results are shown in Fig. 31. When N' = 0, there is no signal as the ¹³ C bath is polarised. As N' is increased, the width of the feature increase from 55(12) kHz for N' = 2 to 90(13) kHz for N' = 6. No difference in the width of the feature was observed for larger values of N' . The FWHM was extracted from a Lorentzian fit with a slight linear background to account for the tail of the GSLAC feature.

[198] ¹ H polarisation

[199] The polarisation of the ¹ H spin bath in PMMA was performed on multiple shallow NVs. Fig. 32a shows a spectrum showing the polarisation effect for a different NV (NV2) than that used in Fig. 7. Similarly, no ¹ H signal was observed for the polarised sequence (top) using an interaction time τ = 20μ s, whereas a signal is observed when the depolarisation sequence is used. We note that no measurable ¹ H signal was observed in the absence of PMMA (removed with dichloromethane) even with the depolarisation sequence, and that the polarisation effect was observed again after reapplying PMMA. This suggests that the ¹ H spins were detected and polarised are mainly from the PMMA, although it is difficult to exclude all contributions from contaminants trapped under the PMMA, e.g. water.

[200] Like for ¹³ C , the full T _x measurements at the ¹ H resonance were obtained by regularly monitoring the NV frequency to make sure it remains on resonance within the NV linewidth ( « 500 kHz here). Because the T _x time of shallow NVs is shorter than for bulk

NVs, the total acquisition time can be limited to about 30 minutes per T _x curve. To compare with the background T _x , the measurements were done on resonance ( ω _Νν « 4.4 MHz) and off resonance ( ω _Νν « 3.0 MHz). Fig. 32b shows full-length T _x curves from an additional NV (NV3) (bottom: unpolarised, middle: polarised, top: background). The data fit resulted in a ratio of relaxation rates of Γ^ ⁰¹ /Γ^ = 2.4(3) which is consistent with the measurement from NV1 discussed above, of 2.8(3). Error is given by the uncertainty in the decay rate fit parameter.

[201] It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the above-described embodiments, without departing from the broad general scope of the present disclosure. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

The following documents are incorporated herein by reference:

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[HALL16] Hall, L. T. et al. Detection of nanoscale electron spin resonance spectra demonstrated using nitrogen-vacancy centre probes in diamond. Nature Communications 7, 10211 (2016).

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[LONDON13] P. London, J. Scheuer, J.-M. Cai, I. Schwarz, A. Retzker, M. B. Plenio, M. Katagiri, T. Teraji, S. Koizumi, J. Isoya, R. Fischer, L. P. McGuinness, B. Naydenov, and F. Jelezko, Physical Review Letters 111, 067601 (2013).

[MAMIN13] Mamin, H. J. et al. Nanoscale Nuclear Magnetic Resonance with a Nitrogen- Vacancy Spin Sensor. Science 339, 557-560 (2013). [SCHMIDT17] Schmidt, A. B. et al. Liquid-state carbon-13 hyperpolarization generated in an MRI system for fast imaging. Nature Communications 8, 14535 (2017).

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