Coherent optical and spin spectroscopy of nanoscale ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{O}}_3$

We investigate the potential for optical quantum technologies of ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{O}}_3$ in the form of monodisperse spherical nanoparticles. We measured optical inhomogeneous lines of 27 GHz and optical homogeneous linewidths of 108 and 315 kHz in particles with 400- and 150-nm average diameters, respectively, for the ${}^{1}D_2\left(0\right)\leftrightarrow {}^{3}H_4\left(0\right)$ transition at 1.4 K. Furthermore, ground-state and ${}^{1}D_2$ excited-state hyperfine structures in ${\mathrm{Y}}_2{\mathrm{O}}_3$ are here determined by spectral hole burning and modeled by complete Hamiltonian calculations. Ground-state spin transitions have energies of 5.99 and 10.42 MHz, for which we demonstrate spin inhomogeneous linewidths of 42 and 45 kHz, respectively. Spin $T_2$ up to $880\mu \mathrm{s}$ was obtained for the $\pm 3/2\leftrightarrow \pm 5/2$ transition at 10.42 MHz, a value which exceeds that of bulk ${\mathrm{Pr}}^{3+}$-doped crystals reported so far. These promising results confirm nanoscale ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{O}}_3$ is a very appealing candidate to integrate quantum devices. In particular, we discuss the possibility of using this material for realizing spin-photon interfaces emitting indistinguishable single photons.

Figure 1

Pulse sequences. (a) Spectral hole burning sequence. (b) Two-pulse Raman spin-echo sequence. The spin-echo amplitude at $2\tau$ is probed by a single-frequency pulse referred to as a heterodyne pulse. (c) Two-pulse photon-echo sequence with heterodyne detection. We note that the role of the heterodyne pulse is not the same in (b) and (c). In (c), it is used as a local oscillator, while in (b) it also converts spin coherence into an optical one for detection. Thus, in the latter case, its frequency must match one of the two colors in the bifrequency pulses (either ${\nu }_{\mathrm{hf}1}$ or ${\nu }_{\mathrm{hf}2}$). Typical pulse lengths are hundreds of microseconds in (a), tens of microseconds in (b), and hundreds of nanoseconds in (c). Gray areas represent pulse intensities, and black lines show pulse frequencies.

Figure 2

Optical inhomogeneous lines and coherence lifetimes. (a) Optical inhomogeneous lines for the ${}^{3}H_4\left(0\right)\leftrightarrow {}^{1}D_2\left(0\right)$ transition for ceramic (blue line) and 400-/120-nm-diameter particles/crystallites (green line). Red lines correspond to Lorentzian fits. Zero-frequency detuning stands for 484.308 THz for the ceramic and 484.317 THz for nanoparticles. (b) Photon echo decays from ceramic (blue), 400-/120-nm-diameter particles/crystallites (green) and 150-/80-nm-diameter particles/crystallites (dark green). All decays show single-exponential character; therefore, optical $T_2$ values of $4.5\pm 0.5, 3.0\pm 0.3$, and $1.0\pm 0.1\mu \mathrm{s}$ were obtained by fitting the photon-echo amplitudes to $exp(-2\tau /T_2)$ (lines). The resulting homogeneous lines correspond to $72\pm 16, 108\pm 21$, and $315\pm 64\mathrm{kHz}$ for ceramic, 400-nm, and 150-nm particles, respectively.

Figure 3

Hyperfine level structure and spin population lifetime. (a) Single-shot spectral hole burning spectrum from ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{O}}_3$ ceramic (blue) compared to simulation (red). Main transitions are indicated by dashed lines. (b) Hole decay as a function of waiting time before readout $t_W$ as measured for ceramic (green dots) and 400-/120-nm particles (blue dots). Single-exponential fit to the ceramic data reveals a spin relaxation time of $5\pm 1\mathrm{s}$ (red line).

Figure 4

Measured hyperfine structure in ${}^{141}\mathrm{Pr}:{\mathrm{Y}}_2{\mathrm{O}}_3$ ($I=5/2$). The $\pm M_I$ quantum numbers are used only as labels and do not represent actual eigenstate projections.

Figure 5

Spin inhomogeneous linewidth obtained by two-pulse Raman spin echo at 1.4 K for ceramic (blue) and 400-/120-nm-diameter particles/crystallites (green). (a) $\pm 1/2\leftrightarrow \pm 3/2$ transition at 5.99 MHz. (b) $\pm 3/2\leftrightarrow \pm 5/2$ transition at 10.42 MHz. Lines correspond to curves fitted to the experimental data (dots).

Figure 6

Spin-echo decay curves at $T=1.4\mathrm{K}$. (a) Spin-echo decay for the 5.99-MHz transition from 400-/120-nm-diameter particles/crystallites (light green triangles) and 150-/80-nm diameter particles/crystallites (dark green dots). Lines correspond to fits to Eq. (9). (b) Spin-echo decay for the 10.42-MHz transition for 400-nm (light green triangles) and 150-nm nanoparticles (dark green dots). Lines correspond to single-exponential fits.

Figure 7

Low-temperature fluorescence spectroscopy of ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{O}}_3$ nanoparticles. (a) ${}^{1}D_2$ emissions in the 610–680-nm range. The peaks correspond to transitions towards different crystal field levels in the ${}^{3}H_4$ ground-state multiplet. The displayed spectrum is corrected from instrumental response. (b) ${}^{1}D_2$ fluorescence decay yielding an optical $T_1$ of $140\mu \mathrm{s}$.