Robust techniques for polarization and detection of nuclear spin ensembles

Highly sensitive nuclear spin detection is crucial in many scientific areas including nuclear magnetic resonance spectroscopy, magnetic resonance imaging (MRI), and quantum computing. The tiny thermal nuclear spin polarization represents a major obstacle towards this goal which may be overcome by dynamic nuclear spin polarization (DNP) methods. The latter often rely on the transfer of the thermally polarized electron spins to nearby nuclear spins, which is limited by the Boltzmann distribution of the former. Here we utilize microwave dressed states to transfer the high ($>92\%$) nonequilibrium electron spin polarization of a single nitrogen-vacancy center (NV) induced by short laser pulses to the surrounding ${}^{13}\mathrm{C}$ carbon nuclear spins. The NV is repeatedly repolarized optically, thus providing an effectively infinite polarization reservoir. A saturation of the polarization of the nearby nuclear spins is achieved, which is confirmed by the decay of the polarization transfer signal and shows an excellent agreement with theoretical simulations. Hereby we introduce the polarization readout by polarization inversion method as a quantitative magnetization measure of the nuclear spin bath, which allows us to observe by ensemble averaging macroscopically hidden polarization dynamics like Landau-Zener-Stückelberg oscillations. Moreover, we show that using the integrated solid effect both for single- and double-quantum transitions nuclear spin polarization can be achieved even when the static magnetic field is not aligned along the NV's crystal axis. This opens a path for the application of our DNP technique to spins in and outside of nanodiamonds, enabling their application as MRI tracers. Furthermore, the methods reported here can be applied to other solid state systems where a central electron spin is coupled to a nuclear spin bath, e.g., phosphor donors in silicon and color centers in silicon carbide.

Figure 1

Schematic representation of the experiments. The first pulse sequence is repeated $N$ times and is used to polarize the nuclear spin bath along the static magnetic field ($\left|\uparrow \uparrow \uparrow ...\right.〉$ state). By changing the MW manipulation, we can polarize the nuclear spin bath into the $\left|\downarrow \downarrow \downarrow ...\right.〉$ state by repeating the sequence $M$ times. The illustrations present the state of the spin bath around the NV center at different time instants. At the beginning the nuclear spins are polarized in the $\left|\downarrow \right.〉$ state. After repeating the polarization sequence $N$ times the nuclear spins are partially or fully inverted into the $\left|\uparrow \right.〉$ state depending on $N$. By polarization of the nuclear spin bath during the $M$ cycles the nuclear spin bath is both initialized and read out. Hence, $M$ has to be set large enough, so that the nuclear spin bath is completely polarized. At the start of the experiment at $N,R=1$ (*) the nuclear spin bath is unpolarized, but due to a larger number of repetitions of the measurements ($R=5\times {10}^4$) the first iteration can be neglected. For most of our experiments $N=50$ and $M=200$. See text for more details.

Figure 2

(a) Pulse sequences for the NOVEL experiment. (b) Fluorescence of the NV center measured with the $n\mathrm{th}$ laser pulse, where $n=0,1,...N$ for $N=2$, (yellow), $N=50$ (blue), and $N=200$ (red), where $M=200$ for all data sets; see also Fig. 1. (c) Fluorescence of the NV center measured with the $m\mathrm{th}$ laser pulse, where $m=0,1,...M$. (Inset) Measurement for $N=50$ and $M=200$. The red colored area enclosed by the two vertical lines is the PROPI signal, which gives the number of inverted nuclear spins and is a measure of the polarization. The dashed cyan curve is a simulation of the full experiment ($N=50;M=200$). (d) Comparison between simulated nuclear polarization, simulated NV readout, and initialization corrected PROPI data (see text). (e) Nuclear spin bath polarization as a function of the number of polarization cycles $N$, where $M=200$. The black line here is a fit, which serves as a guide to the eye.

Figure 3

(a) NOVEL experiment. Here the NV's fluorescence is observed as a function of the Rabi frequency of the spin locking pulse for a single polarization step where the nuclear spin bath is not polarized ($N=M=1$, blue curve). The red curve is a PROPI measurement which gives the average number of nuclear spin flips after polarizing the spin bath ($N=50$, $M=200$). An increase of the signal is observed when the condition (2) is fulfilled, which is a signature of polarization transfer. (b) NOVEL experiment where we measure how the signal depends on the length of the spin locking pulse for $N=M=1$ (blue curve) and $N=50$, $M=200$ (red curve). The oscillations in the single cycle measurement are due to coupling to the ${}^{14}\mathrm{N}$ nuclear spin of the NV.

Figure 4

DNP of the nuclear spin bath using ISE observed via PROPI. (a) Pulse sequence used in the experiments. (b) Dependence of the polarization on the sweep range of the MW. Transfer of polarization as a function of inverse sweep rate (c) and strength of the driving field (d). The red curves show the experimental data; the blue curves are simulations using three nuclear spins and without free parameters. The right axis presents the sum of the $I_z$ of all three spins.

Figure 5

(a) Energy levels of the NV's electron as a function of the strength of the applied static magnetic field $\vec{B}$ along the NV's crystal axis. The arrows indicate the two MW frequencies $f_3=f1+\mathrm{\Delta }$ and $f_4=f2-\mathrm{\Delta }$ which are used to drive the double-quantum transition $\left|-1\right.〉\leftrightarrow \left|+1\right.〉$. (b) Shift of the resonance line for the single- and double-quantum transitions as a function of the misalignment angle $\theta$ for $1770\mathrm{G}$ (solid) and for $1\mathrm{T}$ (dashed). (c) Experimental (blue markers) and theoretical [red curve, using the Hamiltonian (5)] DQT Rabi oscillations.

Figure 6

(a) Pulse sequence for the DQT-NOVEL experiment. Efficiency of the transfer of polarization for SQT (blue) and DQT (red) as a function of the Rabi frequency (b) and the length of the spin locking pulse (c). All experiments are measured using PROPI with optimal NOVEL conditions.

Figure 7

(a) Pulse sequence for the DQT-ISE experiment. (b) Polarization transfer as a function of the frequency range for SQT-ISE (blue) and DQT-ISE (red). Polarization transfer dependence on the sweeping rate (c) and MW amplitude factor $\alpha$ proportional to the Rabi frequency (d) for DQT (red markers). The blue curves are simulations. (e) Misalignment of the external magnetic field with respect to the NV axis of $5^{\circ }$; performance of DQT-ISE (red) and SQT-ISE (blue) depend on the range of the sweep (here $N=50$ and $M=300$). Readout is performed by PROPI with Hartmann-Hahn conditions matched.