Quantum Coherence and Sensitivity of Avian Magnetoreception

Migratory birds and other species have the ability to navigate by sensing the geomagnetic field. Recent experiments indicate that the essential process in the navigation takes place in the bird’s eye and uses chemical reaction involving molecular ions with unpaired electron spins (radical pair). Sensing is achieved via geomagnetic-dependent dynamics of the spins of the unpaired electrons. Here we utilize the results of two behavioral experiments conducted on European robins to argue that the average lifetime of the radical pair is of the order of a microsecond and therefore agrees with experimental estimations of this parameter for cryptochrome—a pigment believed to form the radical pairs. We also find a reasonable parameter regime where the sensitivity of the avian compass is enhanced by environmental noise, showing that long coherence time is not required for navigation and may even spoil it.

Figure 1

Lifetime estimation of a radical pair. Each plot presents angular dependency of the singlet yield in the presence of a local geomagnetic field of $47\mu \mathrm{T}$ (•), in 30% weaker field (▪), and for the geomagnetic field augmented with the resonant rf field (▴). Calculations are performed for two strengths of the hyperfine coupling: slightly smaller than the geomagnetic strength ($\overline{a}=0.5\mu \mathrm{s}$, three lower plots), and slightly bigger than the geomagnetic strength ($\overline{a}=1.0\mu \mathrm{s}$, three upper plots). On plots from left to right we display the growing value of the recombination rate $k$ used in numerics. The radical pair lifetime is the inverse of $k$. Since birds are disoriented both in the weaker field and in the presence of the rf field we postulate that the criterion for estimating $k$ should be based on the comparison of the profile of triangles to the profile of squares. This leads to the average lifetime of the order of several microseconds (see main text for details) in agreement with experiments on pigment believed to be present in the bird’s retina.

Figure 2

Magnetic sensitivity of the avian compass in the presence of environmental noise. The upper plots present results of calculations for hyperfine coupling strength of $\overline{a}=1\mu \mathrm{s}$ and $k=2\times {10}^5$, the lower plots are for $\overline{a}=0.5\mu \mathrm{s}$ and $k=1.5\times {10}^5$. The left plots present angular dependence of the singlet yield for different environmental noise levels [$\Gamma =0$ (•), $\Gamma ={10}^4$ (▪), $\Gamma ={10}^5$ (▴), $\Gamma =4\times {10}^5$ (◆), $\Gamma =8\times {10}^5$ (▾), and $\Gamma ={10}^7$ (*)]. On the right plots we present the magnetic sensitivity defined in Eq. (7). They reveal the resonant character of the sensitivity for noise levels close to $\Gamma =4\times {10}^5$, which correspond to the optimal decoherence time of the order of a microsecond. Moreover, the upper right plot shows that the sensitivity is increased in the presence of environment.