Optical Dynamic Nuclear Polarization of ¹³C Spins in Diamond at a Low Field with Multi-Tone Microwave Irradiation

Abstract

Majority of dynamic nuclear polarization (DNP) experiments have been requiring helium cryogenics and strong magnetic fields for a high degree of nuclear polarization. In this work, we instead demonstrate an optical hyperpolarization of naturally abundant ${}^{13}$C nuclei in a diamond crystal at a low magnetic field and the room temperature. It exploits continuous laser irradiation for polarizing electronic spins of nitrogen vacancy centers and microwave irradiation for transferring the electronic polarization to ${}^{13}$C nuclear spins. We have studied the dependence of ${}^{13}$C polarization on laser and microwave powers. For the first time, a triplet structure corresponding to the ${}^{14}$N hyperfine splitting has been observed in the ${}^{13}$C polarization spectrum. By simultaneously exciting three microwave frequencies at the peaks of the triplet, we have achieved ${}^{13}$C bulk polarization of 0.113 %, leading to an enhancement of 90,000 over the thermal polarization at 17.6 mT. We believe that the multi-tone irradiation can be extended to further enhance the ${}^{13}$C polarization at a low magnetic field.

1. Introduction

Dynamic nuclear polarization (DNP) is a technological breakthrough, which can significantly boost the signal-to-noise ratio in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) [1,2,3,4,5,6,7]. Enhanced signal enables extracting substantial amount of information at molecular resolution for a wide range of chemical, biological and physical processes [8,9,10,11,12,13,14,15,16]. Nevertheless, the high cost of conventional DNP instrumentation, based on helium cryogenics and strong magnetic fields, encourages the development of novel DNP techniques. Recently, optical dynamic nuclear polarization has been demonstrated, in which electronic polarization of negatively charged nitrogen-vacancy (NV) centers is transferred to bulk ${}^{13}$C nuclear spins in diamonds (Figure 1a) [17,18,19,20,21,22,23,24,25]. In addition to continuous and simultaneous irradiations of microwave and pump laser, a variety of techniques have been introduced, which include pulsed irradiation of microwave (MW) fields satisfying Hartman–Hahn condition [26], the cross polarization at the level anti-crossing in the ground state [17] and the excited state [18]. For nanodiamonds having significant line broadening due to their random orientation, frequency-swept microwave irradiation [21,22,23,24] has been applied. Hyperpolarization of ${}^{13}$C nuclear spins in diamond may open up new applications in quantum metrology, e.g., a high-field magnetometer [27,28] and a solid-state nuclear spin gyroscope [29]. Moreover, hyperpolarized nanodiamonds have a potential application in molecule-targeted in vivo imaging with the advantage of long spin life times [30,31,32,33,34].

NV-based optical DNP can be performed without a cryogenic apparatus and in the presence of only tens of millitesla. Although the instrumentation may contain elevated magnetic fields, they are essential for the readout of induced nuclear polarizations. The magnetic field in the range of tens of millitesla is easily accessible, but not favorable for an efficient hyperpolarization. Both weak thermal nuclear polarization and short T${}_1$ relaxation time [35] are disadvantageous. In addition, the positive and negative nuclear polarization spectra, being a part of solid-state DNP spectrum, are located in close proximity, separated by the order of nuclear resonance frequency [36]. Thus, the overlap of positive and negative nuclear polarizations often occurs and leads to a moderate net polarization. Nevertheless, the nuclear polarization spectrum, which reflects the weak ${}^{13}$C Zeeman splitting, has not been observed in optical DNP studies of diamonds. If ${}^{13}$C resonance frequency is less than ${}^{14}$N hyperfine splitting (2.16 MHz) of NV electronic spin (Figure 1b), the nuclear polarization spectrum would be duplicated three times at intervals of 2.16 MHz. Such triplet structure has not been reported either.

In the present study, we conduct NV-based optical DNP of bulk ${}^{13}$C nuclear spins in diamond at a low field and the room temperature. This hyperpolarization method requires continuous laser and MW irradiations with optimized powers. The applied field for optical DNP is 17.6 mT, which corresponds to ${}^{13}$C resonance frequency of approximately 0.2 MHz. After the hyperpolarization process, a diamond can be shuttled to a center of 6 T superconducting magnet for ${}^{13}$C polarization readout by NMR spectrometer. In the ${}^{13}$C nuclear polarization spectrum, we clearly observe the triplet structure revealing the ${}^{14}$N hyperfine splitting. As anticipated, nitrogen nuclear spin does not participate in the polarization transfer process except for determining the resonance frequency of NV spins through the hyperfine interaction. Such independence can be utilized. Inspired by frequency comb [22], we apply triple microwave frequencies simultaneously and obtain a ${}^{13}$C nuclear polarization of 0.113%, which is about 1.7 times as high as that with single MW frequency excitation.

2. Experimental Methods

HPHT-grown diamond crystal with natural abundance of ${}^{13}$C nuclear spins is used in all measurements presented in this paper. NV centers, with a concentration of 1.25 ppm, are created in the diamond via electron irradiation and thermal annealing process.

We have developed a system which includes a low-field region (17.6 mT) for hyperpolarizing ${}^{13}$C in diamonds by DNP, a high-field region (6 T) for all ${}^{13}$C NMR readouts, and a rapid shuttling device for moving the diamond from one region to another in 2 s. From ${}^{13}$C NMR signals at 6 T, enhancement factors and absolute polarization levels can be estimated. ${}^{13}$C NMR acquisition and the timing controls are conducted with a commercial NMR console. (More detailed explanation in the Appendix C).

3. Experimental Results

3.1. ${}^{13}$C Polarization Spectrum

The investigation of the ${}^{13}$C polarization spectrum reveals us the triple structure (Figure 2). Varying the frequency of MW irradiation for optical DNP allows us to record the ${}^{13}$C NMR signal as represented by the blue lines. The green lines illustrate optically-detected magnetic resonance (ODMR) lines of NV center, including the transitions of m${}_s$ = 0 → m${}_s$ = −1 (Figure 2a) and m${}_s$ = 0 → m${}_s$ = +1 (Figure 2b). All these measurements are performed through NV centers of 〈111〉 orientation, which is parallel with the direction of magnetic field. Each data point is averaged by 10 measurements. After each NMR scan, a series of 90 pulses are applied to deplete residual ${}^{13}$C polarization ensuring zero polarization for a next measurement. The triplet structures are clearly observed for both NV spin transitions. The ${}^{14}$N (I = 1) nuclear spin of the NV center splits the NV spin levels each into three hyperfine sublevels with an energy splitting of 2.16 MHz, and this explains the triplet shown in Figure 2. Although ODMR does not exhibit the ${}^{14}$N hyperfine splitting, it is clearly visible in the ${}^{13}$C polarization spectra. Notably, the signs of the ${}^{13}$C polarization are identical for both NV spin transitions.

The results in Figure 2 are obtained at a magnetic field of 17.6 mT with a diamond containing natural abundance of ${}^{13}$C nuclear spins. A similar measurement was performed in Ref. [19], where a magnetic field of 18 mT was applied. However, the ${}^{13}$C polarization spectrum showed no triplet structure. Since a diamond of 10% enriched ${}^{13}$C was used in Ref. [19], strong dipolar couplings between NV and proximate ${}^{13}$C spins may dominate over the ${}^{14}$N hyperfine interaction. In Ref. [25], a higher magnetic field of 473 mT was applied, corresponding to a ${}^{13}$C resonance frequency of 5 MHz. In this case, the overlap of three spectra with a separation of 2.16 MHz could wipe the triplet structure, resulting in a single curve.

3.2. Optimal Microwave Power and Laser Power

An optimization of the MW power is important for improving ${}^{13}$C polarization. Particularly at a low magnetic field, a strong MW excitation may not be a beneficial. As the separation between positive and negative peaks in the nuclear polarization spectrum is proportional to the nuclear Zeeman splitting [36], the strong MW that is on-resonant with one polarization can also induce the transition of the opposite polarization, which is off-resonant as illustrated in Figure 3a. Then, the opposite polarization will be imposed and eventually lead to a lower net nuclear polarization. Figure 3b shows the ${}^{13}$C nuclear polarization as a function of MW power. The polarization rises initially but decays afterwards as the MW power increases. From the curve in Figure 3, we can determine the optimal MW power, which is near 10 W. The solid line is the fitted curve with two exponents for a guide to eyes. A similar result was reported in Ref. [19], where it was explained by a transition from selective regime to $\mathsf{\Lambda }$ regime when MW becomes stronger.

An optimization of the laser power is also important for improving ${}^{13}$C polarization. Figure 4a shows that the maximum ${}^{13}$C polarization signal is obtained at a laser power density of 30 mW/mm${}^2$. After the maximum, the polarization gradually decreases as the laser power increases. Initially, we speculated that the ${}^{13}$C polarization decrease is due to the rise of diamond’s temperature. The temperature of the diamond crystal can be measured from the position of zero-field splitting. In the ODMR spectrum, the peak positions of the two transitions, m${}_s$ = 0 → m${}_s$ = −1 and m${}_s$ = 0 → m${}_s$ = +1, can be obtained. Then, their mean leads to the temperature with an aid of the conversion factor, $\frac{dD}{dT}\cong -74$ kHz/K [37]. As shown in Figure 4b, the temperature rise is linearly proportional to the laser power density. At the optimal near 30 mW/mm${}^2$, the diamond’s temperature is raised above 100 ${}^{\circ }$C. Because the thermal ${}^{13}$C polarization is inversely proportional to temperature, one may attribute the decrease in Figure 4a to the laser-induced heating shown in Figure 4b.

However, that the laser-induced heating alone is an insufficient to explain the ${}^{13}$C polarization decrease. It’s because the NV electronic spin polarization becomes higher with increasing the laser power (or power density). Figure 4c shows the fluorescence intensity from NV centers in the diamond. It increases proportionally to the laser power density. In contrast to Ref. [38], the reduction of the fluorescence when laser power is over a certain level is not observed. This indicates the laser-induced non-radiative process in optical cycle [38] is not activated. Thus, the average polarization of NV centers in the diamond increases linearly within the range of the laser power we apply. The enhancement factor should be proportional to the average NV spin polarization ($P_{\mathrm{NV}}$). ${}^{13}$C polarization ($P_{\mathrm{Hyper}}$) obtained by the optical DNP, then, is determined by the NV spin polarization ($P_{\mathrm{NV}}$) times the ${}^{13}$C thermal polarization ($P_{\mathrm{Thermal}}$) as $P_{\mathrm{Hyper}}\propto P_{\mathrm{NV}}·P_{\mathrm{Thermal}}$. Given a pump laser density ${\sigma }_{\mathrm{Laser}}$, $P_{\mathrm{NV}}$ and $P_{\mathrm{Thermal}}$ can be expressed as follows

$$\begin{array}{ccc}& & P_{\mathrm{NV}}=\beta {\sigma }_{\mathrm{Laser}},\hfill \\ & & P_{\mathrm{Thermal}}=\frac{c}{300+\alpha {\sigma }_{\mathrm{Laser}}},\hfill \end{array}$$

(1)

in which $\alpha$ and $\beta$ are the slopes of the curves in Figure 4b,c, respectively. (c is a constant from Curie’s law of nuclear para-magnetism.) The resulting curve of $P_{\mathrm{Hyper}}$ is shown in Figure 4d, which is certainly inconsistent with the result in Figure 4a. This discrepancy may indicate the existence of an additional ${}^{13}$C depolarization process in the diamond. Possibly, this depolarization process is thermally activated by the laser-induced heating. And we have measured the nuclear spin-lattice relaxation rate has almost no influence on the decrease of ${}^{13}$C polarization (More details in the Supplementary file).

3.3. ${}^{13}$C Hyperpolarization by Multi-Tone MW Frequencies

Since multiple peaks are observed in the ${}^{13}$C polarization spectrum (Figure 2), using several MW sources, we can further enhance the ${}^{13}$C polarization by simultaneous MW irradiations of the frequencies corresponding to those peaks. To estimate the ${}^{13}$C polarization obtained through the optical DNP, we compare the ${}^{13}$C NMR signal with that of thermal polarization at 6 T (300 K). A measurement of ${}^{13}$C thermal polarization, for the diamond, requires at least 4 days, for a better signal-to-noise ratio (SNR), with 400 averages and 20 min interval between each scan. ${}^{13}$C hyperpolarization, with triple MW irradiation, is performed by DNP through −1 state of NV${}^{-}$ in Figure 2a. The diamond is exposed to the pump laser beam with a power density of 25 mW/mm${}^2$ and the MW field with a power of 11 W, for 120 s.

Figure 5 shows results of the multiple MW irradiation. The number of MW frequencies are increased from one (f${}_1$) to three (f${}_1$, f${}_2$, f${}_3$). The three MW frequencies are indicated by the arrows in Figure 2a. The ${}^{13}$C polarization increases with the number of MW frequency, from 0.068 % with f${}_1$ only to 0.113 % with all three frequencies. However, the enhancement ratio of 1.7 is less than the ideal value of about 2.5 predicted by the summed intensities in the Figure 2a. This may be due to the effect of off-resonant excitation illustrated in Figure 3a. The polarization of 0.113 % corresponds to the enhancement of 90,000 over the in situ thermal polarization at 17.6 mT and the diamond’s temperature, as the calculation shown in the Appendix B.

4. Conclusions

We have demonstrated the optical DNP results obtained with a diamond crystal of natural abundance of ${}^{13}$C nuclei at room temperature and a low magnetic field of 17.6 mT. A triplet structure in ${}^{13}$C nuclear polarization spectrum has been observed, in which the splitting of 2.16 MHz attributes to ${}^{14}$N hyperfine interaction in NV centers. We have reached 0.113% of bulk ${}^{13}$C nuclear spin polarization. The optimal values of laser power density and MW power have been characterized. In addition, multi-tone MW excitation has been adopted. Simultaneous irradiation of three MW frequencies, matched to the peak frequencies in the ${}^{13}$C nuclear spectrum, results in an improvement of 1.7 times. The number of microwave frequencies in the multi-tone irradiation scheme could be extended to further enhance the ${}^{13}$C polarization at a low magnetic field.