Charge-state dynamics during excitation and depletion of the nitrogen-vacancy center in diamond

The charge-state dynamics of the nitrogen-vacancy (NV) center in diamond play a key role in a wide range of applications, yet remain imperfectly understood. Using single picosecond pulses and pulse pairs, we quantitatively investigate the charge dynamics associated with excitation and fluorescence depletion of a single NV center. Our pulsed excitation approach permits significant modeling simplifications and allows us to extract relative rates of excitation, stimulated emission, ionization, and recombination under 531 and 766 nm illumination. By varying the duration between paired pulses, we can also investigate ionization and recombination out of metastable states. Our results are directly applicable to experiments employing stimulated emission-depletion imaging and can be used to predict optimal operating regimes where excitation and stimulated emission are maximized relative to charge-state-switching processes.

Figure 1

Excitation and charge-state switching under green illumination. (a) Pulse sequence used for data shown in (b) and (c). CW green (532 nm) is used to initialize the charge-state distribution; low-power CW yellow (594 nm) is used to measure the NV charge state before and after pulsed illumination. Between the yellow pulses, a green pulse is applied. (b) Charge-dependent fluorescence during pulsed green excitation as a function of pulsed green average power. Fluorescence for ${\mathrm{NV}}^{-}$ initialization (red circles) is larger than for ${\mathrm{NV}}^0$ initialization (blue triangles) primarily due to spectral filtering. Black squares show total fluorescence without charge selection. (c) Single green pulse probability of ionization (blue triangles) and recombination (red circles). (d) Four-level rate equation model including transitions between the ground $g_{-}\left(g_0\right)$ and excited states $e_{-}\left(e_0\right)$ of ${\mathrm{NV}}^{-}$ and ${\mathrm{NV}}^0$, respectively. Here we show the transition rates under green illumination. Solid lines in (b) and (c) are found by using this four-level model to simultaneously fit data shown in Figs. 1 and 2.

Figure 2

Stimulated emission and charge-state switching under red illumination. (a) Top: Pulse sequence used for data shown in (a) (both with and without the red pulse) and (b) (with both red and green pulses). The delay between the pulses is 0.592 ns. Bottom: Example fluorescence depletion data with pulsed green only (green, top) and green-red pulse pair (red, bottom) illumination. Solid lines are exponential decay fits. Extrapolating these fits to the location of the red pulse (dashed vertical line) gives the values marked as A and B. (b) NV excited-state depletion probability (through stimulated emission or charge-state switching) calculated by $1-\frac{B}{A}$ as a function of red power. (c) Top: Pulse sequence used for data shown at bottom; the green-red pulse delay is 0.592 ns. Bottom: Red-induced increase in the probability of ionization (blue triangles) and recombination (red circles), measured by subtracting the charge-state switching probability of a single green pulse from that of a green-red pulse pair. (d) Four-level rate equation model comprising the ground and excited states of ${\mathrm{NV}}^{-}$ and ${\mathrm{NV}}^0$. We show the transition rates under red illumination. Solid lines in (b) and (c) are found by using the four-level model to simultaneously fit data shown in Figs. 1 and 2.

Figure 3

Green and red power dependence on charge-state switching rates. Red-induced increase in the probability of ionization (a) and recombination (b) are plotted as a function of red power for the five green powers shown in the legend. Solid lines are model predictions at the same powers, using rates determined from fits to Figs. 1 and 2. All powers are given at 1 MHz repetition rate.

Figure 4

Four-level model predictions. (a) Starting in the ${\mathrm{NV}}^{-}$ ground state, probability of green-induced excitation (green top) versus ionization (blue bottom). (b) Starting in the ${\mathrm{NV}}^{-}$ excited-state, probability of red-induced stimulated emission (red top) versus ionization (blue bottom). (c) Starting in the ${\mathrm{NV}}^{-}$ ground state, cycling probability of excitation followed by stimulated emission. Shaded regions in (a) and (b) represent one standard error.

Figure 5

Red-induced charge-state switching versus pulse separation. (a) Top: Pulse sequence used, with a variable delay $\tau$ between green and red pulses. A microwave $\pi$ pulse is optionally applied to initialize into the $m_s=\pm 1$ states. Bottom: Red-induced increase in the probability of recombination (red circles) and spin-dependent ionization for a $m_s=0$ (blue triangles) and $m_s=\pm 1$ (black squares) initial ${\mathrm{NV}}^{-}$ spin state. (b) Five-level rate equation model consisting of the ground and excited states of ${\mathrm{NV}}^{-}$ and ${\mathrm{NV}}^0$ as well as a level for the ${\mathrm{NV}}^{-}$ singlet state. The squiggly arrows indicate relaxation rates that are relevant during the separation time, including shelving ($\sigma$), deshelving ($D$), and spontaneous emission $\gamma$ ($\eta$) from ${\mathrm{NV}}^{-}$ (${\mathrm{NV}}^0$); straight and curved lines are red-induced transitions, with an additional ionization rate $I_s$ out of the ${\mathrm{NV}}^{-}$ singlet state. Note that the value of $\sigma$ is different for the two spin states.

Figure 6

Extracting ionization and recombination probabilities. (a) Photon count distribution from 1 h of 2 $\mu \mathrm{W}$ continuous yellow illumination in 50 ms bins. Fitting (green solid line) allows for extraction of the yellow charge-state switching rates. (b) Typical photon count distribution of a 4 ms, 2 $\mu \mathrm{W}$ yellow pulse after initializing the charge-state distribution with a pulse of CW green. Fits allow us to extract the yellow readout fidelities. (c) Probability tree representing processes with no applied experiment between two yellow pulses. Expressions next to arrows indicate the probability of a given process; e.g., $I^0$ is the probability to end up in state ${\mathrm{NV}}_f^0$ given an initial measurement of $m^0$. (d) Probability tree representing measurements from two yellow pulses with an applied experiment (green row), allowing for extraction of the probability to ionize ($P_I$) and recombine ($P_R$). For both (c) and (d), a similar tree can be constructed for an initial measurement $m^{-}$ by exchanging $0\leftrightarrow -$.

Figure 7

Steady-state measurements. (a) Steady-state ${\mathrm{NV}}^{-}$ charge-state population under pulsed green-only illumination, as a function of power. (b) Red-induced change in steady-state ${\mathrm{NV}}^{-}$ charge-state population during pulsed green-then-red illumination, as a function of green and red power. Repetition rates are 1 MHz.