Orbital and Spin Dynamics of Single Neutrally-Charged Nitrogen-Vacancy Centers in Diamond

The neutral charge state plays an important role in quantum information and sensing applications based on nitrogen-vacancy centers. However, the orbital and spin dynamics remain unexplored. Here, we use resonant excitation of single centers to directly reveal the fine structure, enabling selective addressing of spin-orbit states. Through pump-probe experiments, we find the orbital relaxation time (430 ns at 4.7 K) and measure its temperature dependence up to 11.8 K. Finally, we reveal the spin relaxation time (1.5 s) and realize projective high-fidelity single-shot readout of the spin state ($\ge 98\%$).

Figure 1

Direct observation of the fine structure of the ${\mathrm{NV}}^0$ center. (a) Electron microscope image of a solid immersion lens fabricated around the NV center. Optical (${\lambda }_{\text{yellow}}$, ${\lambda }_{\mathrm{red}}$) and mw control are indicated. (b) Experimental sequence for spectroscopy consisting of a preparation (1) and measurement (2) part. (c) Spectra obtained with linear ($H$, $V$) and circular ($L$, $R$) polarizations ($P_{\text{yellow}}=500\mathrm{pW}$), offset for clarity [19]. (d) Ground- and excited-state level structure. Spin-conserving optical transitions (solid arrows), excited-state decay (dashed arrows), and spin or orbital relaxations (dotted arrows) are indicated.

Figure 2

Time-resolved resonant pump measurements. (a) Experimental sequence consisting of preparation (1), measurement (2), and readout (3) parts. (b) Fluorescence of ${\mathrm{NV}}^0$ when driving the lower spin-orbit branch with $H$ polarization for $P_{\text{yellow}}=2,4,10,20\mathrm{nW}$ (bottom to top) averaged over at least $1\times {10}^6$ repetitions. Measurements have a timing resolution of 250 ps and are offset for clarity. Solid red lines are simulations of the full system dynamics with our theoretical model [19]. Inset: Decay of fluorescence counts after the AOM is closed. (c) Steady-state (ss) fluorescence counts as a function of $P_{\text{yellow}}$, for $H$ (squares) and $L$ polarization (circles). The data are fit with a saturation curve $f(P)=A[P/(P+P_{\mathrm{sat}})]$. (d) Optical Rabi frequency as a function of $\sqrt{P_{\text{yellow}}}$. Fits yield a slope of $5.3(1)/5.1(1)\mathrm{MHz}/\sqrt{\mathrm{nW}}$ for $L/H$ polarization.

Figure 3

Time-resolved pump-probe spectroscopy. The experimental sequence after state preparation is given in the inset in (b). (a) Example traces for a range of $t_{\text{delay}}$ (light to dark for increasing $t_{\text{delay}}$), at a temperature of 5.5(1) K, integrated over $5\times {10}^6$ acquisitions each, measured with $H$ polarization. The dashed line is a fit to the recovery behavior [19]. (b) Recovery rate $R_{\text{recovery}}$ as a function of the cryostat temperature. Circles (squares) describe data measured on the lower (upper) spin-orbit branch. Error bars for $R_{\text{recovery}}$ correspond to 1 s.d. fit errors. The solid lines are fits of form $f(T)=AT+B\exp [-\mathrm{\Delta }/k_{B}T]$, giving $A=0.53(3)\mathrm{MHz}/\mathrm{K}$ [$A=0.54(2)\mathrm{MHz}/\mathrm{K}$] and $B=1(1)\times {10}^7\mathrm{MHz}$ [$B=1(4)\times {10}^7\mathrm{MHz}$] for the lower (upper) branch.

Figure 4

Single-shot readout and spin pumping. (a) Histograms after preparation of the ${\mathrm{NV}}^0$ $|\downarrow ⟩$ state (dark colors) and mixed (light colors) spin states. (b) Relaxation (${\mathrm{T}}_1$) measurement for the $|\downarrow ⟩$ (circles) and $|\uparrow ⟩$ (squares) states, fitted with an exponential decay (recovery). The ${\mathrm{NV}}^{-}$ population (triangles) remains negligible in the dark. The data are averaged over $3\times {10}^3$ repetitions each. (c) Spin pumping: ${\mathrm{NV}}^0$ spin and total ${\mathrm{NV}}^{-}$ populations as a function of yellow illumination time. Solid lines are fits to solutions for the underlying three-level rate equations [19]. (d) Spin pumping with charge cycling: the same as (c) but with stroboscopic red illumination. The time axis is the yellow illumination time (half of the total sequence time).