Quantum Control and Entanglement in a Chemical Compass

The radical-pair mechanism is one of the two main hypotheses to explain the navigability of animals in weak magnetic fields, enabling, e.g., birds to see Earth’s magnetic field. It also plays an essential role in spin chemistry. Here, we show how quantum control can be used to either enhance or reduce the performance of such a chemical compass, providing a new route to further study the radical-pair mechanism and its applications. We study the role of radical-pair entanglement in this mechanism, and demonstrate its intriguing connections with the magnetic-field sensitivity of the compass. Beyond their immediate application to the radical-pair mechanism, these results also demonstrate how state-of-the-art quantum technologies could potentially be used to probe and control biological functions.

Figure 1

Magnetic-field sensitivity $\Lambda$ of the radical-pair reaction [Py-$h_{10}^{·-}$ DMA-$h_{11}^{·+}$] as a function of the magnetic field $B$. (a) $N$: singlet initial state; $Z$: under $Z$ control; RB (RB-X): alternating magnetic field without (with) $X$ control. (b) $N$: singlet initial state; $T_0$: triplet initial state $|{\mathbb{T}}_0⟩$; Sep: optimal sensitivity for separable initial states; CS-P: applying a $\frac{\pi }{2}\mathrm{\text{−}}X$ pulse on the initial separable state ${\rho }_c=(|\uparrow \downarrow ⟩⟨\uparrow \downarrow |+|\downarrow \uparrow ⟩⟨\downarrow \uparrow |)/2$. The recombination rate constant is $k=5.8\times {10}^8{\mathrm{s}}^{-1}$ [13], and the control time is ${\tau }_c=0.5\mathrm{ns}$.

Figure 2

Connection between entanglement and magnetic-field sensitivity [$\mathrm{Py}\mathrm{\text{−}}{h}_{10}^{·-}\mathrm{DMA}\mathrm{\text{−}}{h}_{11}^{·+}$]. (a) Sensitivity of effective entanglement ${\Lambda }_E$ vs sensitivity of singlet yield $\Lambda$. The recombination rate is $k=5.8\times {10}^8{\mathrm{s}}^{-1}$ [13]. The blue arrows indicate variation of ${\Lambda }_E$ and $\Lambda$ when the magnetic field changes from $B=0.5\mathrm{mT}$ to $B=8\mathrm{mT}$. (b) Discontinuity of the lifetime of entanglement $T_E$ as a function of $B$.

Figure 3

Singlet yield ${\Phi }_s$ of the radical-pair reaction [${\mathrm{FADH}}^{•}\mathrm{\text{−}}{\mathrm{O}}_2^{•-}$] as a function of $\theta$, at $B=46\mu \mathrm{T}$. (a) $N$: without quantum control; $Q_c$: applying $\pi$ pulses along the direction of the magnetic field. (b) RB (RB-X): effect of an alternating magnetic field, without (with) additional quantum control pulses perpendicular to the direction of the magnetic field. For comparison, the RB curve has been shifted downwards by 0.1. The recombination rate is $k=5\times {10}^5{\mathrm{s}}^{-1}$ and the control times are ${\tau }_c={\tau }_a=10\mathrm{ns}$.

Figure 4

Singlet yield ${\Phi }_s$ of the radical-pair reaction [${\mathrm{FADH}}^{•}\mathrm{\text{−}}{\mathrm{O}}_2^{•-}$] as a function of the angle $\theta$, relative to the direction in which the $\pi$ pulses are applied. There is no external static magnetic field, i.e., $B=0$. The recombination rate is $k=5\times {10}^5{\mathrm{s}}^{-1}$, and the control time ${\tau }_c=100\mathrm{ns}$.