Chemical Compass Model for Avian Magnetoreception as a Quantum Coherent Device

It is known that more than 50 species use the Earth’s magnetic field for orientation and navigation. Intensive studies, particularly behavior experiments with birds, provide support for a chemical compass based on magnetically sensitive free radical reactions as a source of this sense. However, the fundamental question of how quantum coherence plays an essential role in such a chemical compass model of avian magnetoreception yet remains controversial. Here, we show that the essence of the chemical compass model can be understood in analogy to a quantum interferometer exploiting global quantum coherence rather than any subsystem coherence. Within the framework of quantum metrology, we quantify global quantum coherence and correlate it with the function of chemical magnetoreception. Our results allow us to understand and predict how various factors can affect the performance of a chemical compass from the unique perspective of quantum coherence assisted metrology. This represents a crucial step to affirm a direct connection between quantum coherence and the function of a chemical compass.

Figure 1

Quantum interferometer model of a chemical compass. (a) A quantum system is prepared (BS1) in a coherent superposition of two quantum states $|\alpha ⟩$ and $|\beta ⟩$, which gains different dynamical phases dependent on an unknown physical parameter, the information of which is revealed by the measurement after the interference (BS2). (b) A chemical compass is viewed as a quantum interferometer, the hyperfine coupling Hamiltonian ${\mathcal{H}}_0$ recasts the state ${\rho }_0$ of the combined system of a radical pair and nuclei into a superposition of its eigenstates. The magnetic field induces the change in coherence phases arising from the dynamic phases of individual eigenstate evolution. The spin-dependent chemical reaction channels lead to the interferometric observable which provides the information about the direction of the magnetic field.

Figure 2

Effective evolution of a radical pair (in which one radical contains three ${}^1\mathrm{H}$ nuclei and two ${}^{14}\mathrm{N}$ nuclei as ${\mathrm{FADH}}^{·}$). (a) The change of the absolute values of the (coherent) density elements $⟨ϵ(t)⟩$ averaging over time, with $ϵ(t)=[\sum _{m\ne n}(r_{mn}^t-r_{mn}{)}^2{]}^{1/2}$, see Eq. (8) and Eq. (9), for different magnetic field directions $(\theta ,\phi )$. (b) The singlet yield $Y_{\mathrm{s}}$ as a function of the magnetic field direction $(\theta ,\phi )$ including (lower) vs excluding (upper) the coherence phase changes ${\phi }_{mn}^{\widehat{B}}(t)$ resulting from the Earth’s magnetic field, see Eq. (9). The reaction rates are $k_S=k_T=0.5\mu {\mathrm{s}}^{-1}$, the Earth’s magnetic field is $b=50\mu \mathrm{T}$.

Figure 3

(a) The magnetic field sensitivity $D_{\mathrm{s}}({\mathcal{H}}_0,{\rho }_0)$ as defined in Eq. (11) (upper) and the average value $⟨D_{\mathrm{s}}⟩$ (lower) as a function of coherence $\mathcal{C}({\mathcal{H}}_0,{\rho }_0)$ given by Eq. (13) for $7\times {10}^4$ random hyperfine configurations with in total 5–6 nuclei initially in the depolarized state. The violet dots represent these configurations of reference-and-probe type molecules (one radical is free from hyperfine coupling). (b) The magnetic field sensitivity $D_{\mathrm{s}}({\mathcal{H}}_{\mathrm{f}},{\rho }_0)$ as a function of coherence $\mathcal{C}({\mathcal{H}}_{\mathrm{f}},{\rho }_0)$ for a radical pair (in which one radical contains three ${}^1\mathrm{H}$ nuclei and two ${}^{14}\mathrm{N}$ nuclei as ${\mathrm{FADH}}^{·}$) starting from $2\times {10}^4$ initial states, each has the singlet born radical pair and random nuclear spin polarizations. In both panels, the reaction rates are $k_S=k_T=0.5\mu {\mathrm{s}}^{-1}$, and the Earth’s magnetic field is $b=50\mu \mathrm{T}$.

Figure 4

The noise effect on the magnetic sensitivity of a radical pair (in which one radical contains three ${}^1\mathrm{H}$ nuclei and two ${}^{14}\mathrm{N}$ nuclei as ${\mathrm{FADH}}^{·}$) for the local dephasing (red, squares), the electron spin relaxation (blue, circles), and the singlet-triplet dephasing (violet, diamonds). (a) The magnetic sensitivity $D_{\mathrm{s}}({\mathcal{H}}_0,{\rho }_0)$ as a function of the decoherence rate $\xi$ (in the unit of $\mu {\mathrm{s}}^{-1}$). (b) The magnetic sensitivity $D_{\mathrm{s}}({\mathcal{H}}_0,{\rho }_0)$ as a function of the coherence $\mathcal{C}({\mathcal{H}}_0,{\rho }_0)$. In both panels, the reaction rates are $k_S=k_T=0.5\mu {\mathrm{s}}^{-1}$, and the Earth’s magnetic field is $b=50\mu \mathrm{T}$.