Low-Field Nuclear Polarization Using Nitrogen Vacancy Centers in Diamonds

It was recently demonstrated that bulk nuclear polarization can be obtained using nitrogen vacancy (NV) color centers in diamonds, even at ambient conditions. This is based on the optical polarization of the NV electron spin, and using several polarization transfer methods. One such method is the nuclear orientation via electron spin locking (NOVEL) sequence, where a spin-locked sequence is applied on the NV spin, with a microwave power equal to the nuclear precession frequency. This was performed at relatively high fields, to allow for both polarization transfer and noise decoupling. As a result, this scheme requires accurate magnetic field alignment in order preserve the NV properties. Such a requirement may be undesired or impractical in many practical scenarios. Here we present a new sequence, termed the refocused NOVEL, which can be used for polarization transfer (and detection) even at low fields. Numerical simulations are performed, taking into account both the spin Hamiltonian and spin decoherence, and we show that, under realistic parameters, it can outperform the NOVEL sequence.

Figure 1

Schematic representation of the refocused-NOVEL sequence, as described in the main text.

Figure 2

(a) NV polarization, $⟨S_z⟩$, and (b) nuclear polarization, $⟨I_z⟩$, as a function of ${\omega }_f$ ($\pi /\tau$) and ${\mathrm{\Omega }}_{\mathrm{SL}}$. The simulation was performed using $N=60$, on a NV-${}^{13}\mathrm{C}$ model system with $A_{\parallel }=30\mathrm{kHz}$, $A_{\perp }$, ${\mathrm{\Delta }}_e=40\mathrm{kHz}$, and an external field of 80 G. The insets show the plot with ${\omega }_f$ in the range of 0.1–0.3 MHz. ${\omega }_n$ separation and $k$ conditions are marked schematically.

Figure 3

(a), (c) $⟨S_z⟩$ and (b), (d) $⟨I_z⟩$ as a function of $N$ and ${\mathrm{\Omega }}_{\mathrm{SL}}$, for the RNOVEL (a), (b) and NOVEL (c), (d) sequences $.\tau =2\mu \mathrm{s}$ was used, resulting in a total sequence duration of $T=2N\mu \mathrm{s}$. All other simulation parameters are as given in Fig. 2. The $k=1$, 2, 3 resonance conditions are marked in (a), and the $2{\omega }_n$ separation between the two polarization transfer conditions for each of these $k$ values is marked in (b).

Figure 4

(a), (c) $⟨S_z⟩$ and (b), (d) $⟨I_z⟩$ as a function of $N$ and ${\mathrm{\Omega }}_{\mathrm{SL}}$ under dephasing noise, for the RNOVEL (a),(b) and NOVEL (c),(d) sequences $.\tau =2\mu \mathrm{s}$ was used, resulting in a total sequence duration of $T=2N\mu \mathrm{s}$. The noise source was modeled using correlation times of ${\tau }_c=11$ and $150\mu \mathrm{s}$, and ${\mathrm{\Delta }}_{\text{noise}}$ of 0.5 MHz. The value of $b(t)$ was changed every $0.1\mu \mathrm{s}$, as described in the Supplemental Material [20], and the plotted $⟨S_z⟩$ and $⟨I_z⟩$ values were obtained by averaging over 100 realizations of the noise. All other simulation parameters are as given in Fig. 2.

Figure 5

Nuclear polarization during RNOVEL (a) and NOVEL (b) under dephasing noise, using repeated sequence application. This is plotted as a function of the total irradiation time, for sequences composed of $N=4$ (blue), 8 (red), 16 (yellow), 32 (purple), and 64 (green) $\pi$ pulses. ${\mathrm{\Omega }}_{\mathrm{SL}}/2\pi$ of 1.348 and 0.126 MHz were used in (a) and (b), respectively. All other parameters are the same as in Fig. 4.