Scheme for Detection of Single-Molecule Radical Pair Reaction Using Spin in Diamond

The radical pair reaction underlies the magnetic field sensitivity of chemical reactions and is suggested to play an important role in both chemistry and biology. Current experimental evidence is based on ensemble measurements; however, the ability to probe the radical pair reaction at the single-molecule level would provide valuable information concerning its role in important biological processes. Here, we propose a scheme to detect the charge recombination rate in a radical pair reaction under ambient conditions by using single nitrogen-vacancy center spin in diamond. We demonstrate theoretically that it is possible to detect the effect of the geomagnetic field on the radical pair reaction and propose the present scheme as a possible hybrid model chemical compass.

Figure 1

Single-molecule radical pair reaction sensing using single spin in diamond. (a) Unit cell of diamond containing a nitrogen-vacancy (NV) center. The nitrogen-vacancy pair orientates along the $\widehat{z}$ axis that is the trigonal symmetry axis of the center, and three mirror planes are shown in green and red (the plane that contains the $\widehat{x}$ axis is in red). (b) The interaction between the NV center spin and the radical pair arises from the electric dipole of the radical pair in the charge separated state.

Figure 2

Quantum sensing of single-molecule radical pair reaction of Flavin radical (${\mathrm{FH}}^{•-}$) and tryptophan radical (${\mathrm{W}}^{•+}$). (a) The probability $P(t)$ that the NV center spin is in the state $|1⟩$ as a function of the evolution time $t$. The red dashed line is the analytic result and the green one is obtained from numerical simulation. (b) The sensitivity for the measurement of the charge recombination rate $k$ as a function of the interrogation time $T$. The best sensitivity ${\eta }_{\text{op}}=0.54\mathrm{kHz}{\mathrm{Hz}}^{-1/2}$ is achieved with $T=0.46\mu \mathrm{s}$. (c),(d) The probabilities that the radical pair remains in the charge separated state $|E⟩$ and the NV center is in the state $|1⟩$, respectively, as a function of the evolution time $t$. The Green lines are the results of $k_s=k_t=k_{\text{eff}}$, the purple dashed lines are that of $k_s$ and $k_t$ with different values. The parameters are $B_0=0.05\mathrm{mT}$, $\theta =\pi /2$, $\phi =2.0$, $k_s=0.02\mathrm{MHz}$, $k_t=0.2\mathrm{MHz}$, and $k=k_{\text{eff}}=0.1425\mathrm{MHz}$. For simplicity, we consider ${\mathrm{H}}^6$ with the dominant anisotropic hyperfine in the ${\mathrm{FH}}^{•-}$ radical [51]. The radical pair molecule is $d_2=2\mathrm{nm}$ apart. as located on the diamond crystal surface, with a horizontal distance about $d_3=4\mathrm{nm}$ from the NV center, and the depth of the NV center is $d_1=5\mathrm{nm}$; see Figs. 1 and 1.

Figure 3

Noise effect on the measurement sensitivity. (a) The probability that the NV center spin sensor is in the state $|1⟩$ evolves with time $t$ in a dephasing environment with a dephasing rate $\gamma =0.5\mathrm{MHz}$. The red dashed line is the analytical result as compared with the numerical simulation (green). (b) The influence of the dephasing rate $\gamma$ on the best achievable sensitivity ${\eta }_{\text{op}}$ and the optimal interrogation time $T_{\text{op}}$. The parameters are $B_0=0.05\mathrm{mT}$, $\theta =\pi /2$, $\phi =2.0$, and $k=k_{\text{eff}}=0.1425\mathrm{MHz}$. The location of the NV center and the radical pair molecule is the same as in Fig. 2.