Quantum Probe and Design for a Chemical Compass with Magnetic Nanostructures

Magnetic fields as weak as Earth’s may affect the outcome of certain photochemical reactions that go through a radical pair intermediate. When the reaction environment is anisotropic, this phenomenon can form the basis of a chemical compass and has been proposed as a mechanism for animal magnetoreception. Here, we demonstrate how to optimize the design of a chemical compass with a much better directional sensitivity simply by a gradient field, e.g., from a magnetic nanostructure. We propose an experimental test of these predictions, and suggest design principles for a hybrid metallic-organic chemical compass. In addition to the practical interest in designing a biomimetic weak magnetic field sensor, our result shows that gradient fields can serve as powerful tools to probe spin correlations in radical pair reactions.

Figure 1

Left: A radical pair, coupled with the surrounding nuclear spins (black arrows), in a weak magnetic field $\overrightarrow{B}$ to be measured (yellow [light gray] arrows) and a strong magnetic gradient ${\overrightarrow{L}}_A$ (blue [dark gray] arrows). Right: The directions of $\overrightarrow{B}$ and the gradient field at the location of the acceptor ${\overrightarrow{L}}_A$ depicted in the molecular coordinate frame.

Figure 2

Magnetic field sensitivity of a chemical compass enhanced by a gradient field. (a) Singlet yield ${\Phi }_S$ as a function of the angle $\theta$ of the weak magnetic field $\overrightarrow{B}$ ($B=0.46\mathrm{G}$) with different gradient field strengths on the acceptor, i.e., $L_A=0\mathrm{G}$ (red [○]), 20 G (blue [◇]), 40 G (green [▵]), 80 G (purple [*]), while $L_D=0$. The recombination rate $k=0.5\mu {\mathrm{s}}^{-1}$. (b) Visibility $V$ as a function of the radical pair lifetime $\tau =1/k$. The direction of the gradient field ${\overrightarrow{L}}_A$ is set as ${\theta }_A=0$. The same values of $L_A$ are used as in (a).

Figure 3

(a) Visibility of the average singlet yield $⟨{\Phi }_S(\theta )⟩$ as a function of the angle ${\theta }_A$ of the gradient field $L_A=80\mathrm{G}$. The blue dash-dotted line represents the visibility without the gradient field. (b) Ensemble average of the singlet yield ${\overline{\Phi }}_S(\theta )$ in Eq. (3) from a Monte Carlo simulation of $2\times {10}^4$ samples as a function of the angle $\theta$ of the weak field $\overrightarrow{B}$. The gradient field is $L_A=40\mathrm{G}$ with ${\theta }_A=0$ (purple [*]), while $L_D=0$. For comparison, we plot the singlet yield with no gradient field (red [○]), and the one with the gradient field $L_A=40\mathrm{G}$ (${\theta }_A=0$) without fluctuations (blue [▵]). The radical pair lifetime is $2\mu \mathrm{s}$ and $B=0.46\mathrm{G}$.

Figure 4

The singlet yield ${\Phi }_S$ as a function of the angles ($\theta$, $\varphi$) of the weak magnetic field $\overrightarrow{B}$ with $B=0.46\mathrm{G}$. The gradient field on the acceptor is $L_A=80\mathrm{G}$, on the donor it is $L_D=0$. The angle of the gradient field ${\theta }_A$ with respect to the $z$ axis is 0 (upper), $\frac{\pi }{4}$ (middle) and $\frac{\pi }{2}$ (lower). The radical pair lifetime is chosen as $2\mu \mathrm{s}$.