Inductive measurement of optically hyperpolarized phosphorous donor nuclei in an isotopically-enriched silicon-28 crystal

We experimentally demonstrate the inductive readout of optically hyperpolarized phosphorus-31 donor nuclear spins in an isotopically enriched silicon-28 crystal. The concentration of phosphorus donors in the crystal was 1.5 x 10$^{15}$ cm$^{-3}$, three orders of magnitude lower than has previously been detected via direct inductive detection. The signal-to-noise ratio measured in a single free induction decay from a 1 cm$^3$ sample ($\approx 10^{15}$ spins) was 113. By transferring the sample to an X-band ESR spectrometer, we were able to obtain a lower bound for the nuclear spin polarization at 1.7 K of 64 %. The $^{31}$P-T$_{2}$ measured with a Hahn echo sequence was 420 ms at 1.7 K, which was extended to 1.2 s with a Carr Purcell cycle. The T$_1$ of the $^{31}$P nuclear spins at 1.7 K is extremely long and could not be determined, as no decay was observed even on a timescale of 4.5 hours. Optical excitation was performed with a 1047 nm laser, which provided above bandgap excitation of the silicon. The build-up of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the build-up at 1.7 K showed bi-exponential behavior with characteristic time constants of 578 s and 5670 s.