Purcell-enhanced optical spin readout of nitrogen-vacancy centers in diamond

Nitrogen-vacancy (NV) color centers in diamond have emerged as promising quantum solid-state systems, with applications ranging from quantum information processing to magnetic sensing. One of the most useful properties of NVs is the ability to read their ground-state spin projection optically at room temperature. Using theoretical analysis of Purcell-enhanced NV optical coupling, we identify parameters for a significantly enhanced single-to-noise ratio (SNR) of the optical spin-state readout. We then demonstrate that a combined increase in spontaneous emission (through Purcell enhancement) and in optical excitation could significantly increase the readout SNR. Our combined analytical and numerical analysis, which is relevant for various optically active solid-state systems, differentiates between state-mixing processes and provides insights into the optimal light-matter coupling design.

Figure 1

NV coupled to an optical antenna, energy levels, and allowed transition. (a) A general schematic example of a plasmonic antenna designed to yield a Purcell enhancement of the radiative rate and to direct the emission. (b) Energy levels and allowed transitions for the NV center with nonradiative spin-mixing transitions in the excited state. The two singlet states between the ground and excited states are combined, since the dynamics between the two singlet states does not effect the following analysis. (c) Energy levels and allowed transitions in the NV center with radiatively activated spin-mixing transitions. Spin mixing of radiative origin [replacing $K_m$ in (b)] is described through $K_{m_e}$ and $K_{m_f}$ rates that scale with the Purcell Factor (PF).

Figure 2

(a) SNR as a function of the pulse duration $T$ for typical rates (see text). The optimal pulse duration is $T=0.9911\left[SL\right]$, at which the maximum value of $\mathit{\text{SNR}}=1.2516$ is reached. (b) SNR as a function of the excitation rate $K_e$ for typical rates and pulse duration $T=1\left[SL\right]$.

Figure 3

The effect of Purcell enhancement on the SNR. (a) SNR as a function of PF for typical rates and $T=1$. The SNR reaches a maximal value of $\mathit{\text{SNR}}=1.4867$ for $\mathit{\text{PF}}\approx 3$. The red dot shows the SNR for $\mathrm{PF}=1$. (b) SNR as a function of PF and $T$ for typical rates. The SNR reaches a maximum value of $\mathit{\text{SNR}}=1.5951$ for $\mathit{\text{PF}}=5.1903$ and $T=1.703\left[SL\right]$.

Figure 4

Saturated SNR as a function of PF, for both nonradiative and radiative spin-mixing transitions. (a) Nonradiative spin-mixing. The saturated optimal pulse duration is constant at $T=0.6752$. The red dot shows the saturated SNR with $\mathit{\text{PF}}=1$ and the red line is the analytic curve $1.579\sqrt{\mathit{\text{PF}}}$ based on Eq. (3). (The coefficient of $\sqrt{\mathit{\text{PF}}}$ is adjusted, since for $K_0\to 0$ it is 2.07.) Increasing the PF and $K_e$ and adjusting $T$ to its optimal value can increase the SNR significantly. (b) Radiative spin-mixing. The mixing rates were set to be $K_{m_f}=0.02K_f\approx 0.4615$ PF and $K_{m_e}=0.02K_e$. The red dot marks the saturated SNR with $\mathit{\text{PF}}=1$. Optimizing $K_f,K_e$, and $T$ results in a maximal SNR value at the optimal $\mathrm{PF}\approx 2$.