Quantum dynamics of the avian compass

The ability of migratory birds to orient relative to the Earth's magnetic field is believed to involve a coherent superposition of two spin states of a radical electron pair. However, the mechanism by which this coherence can be maintained in the face of strong interactions with the cellular environment has remained unclear. This paper addresses the problem of decoherence between two electron spins due to hyperfine interaction with a bath of spin-1/2 nuclei. Dynamics of the radical pair density matrix are derived and shown to yield a simple mechanism for sensing magnetic field orientation. Rates of dephasing and decoherence are calculated ab initio and found to yield millisecond coherence times, consistent with behavioral experiments.

Figure 1

Decoherence of the Bloch vector ${\dot{\stackrel{⃗}{V}}}_B\left(\vec{x}\right)$ in the $xz$ plane for an efficient and an inefficient compass molecule. The $z$ component decays as $e^{-\overline{\Gamma }t}$, the $x$ as $e^{-{\lambda }_{+}t}$. (a) $\overline{\Gamma }/B\Delta \mu =8.5,\Delta \Gamma /B\Delta \mu =6\times {10}^{-4},\text{contrast}=0.99$. (b) $\overline{\Gamma }/B\Delta \mu =8.5,\Delta \Gamma /B\Delta \mu =5.8,\text{contrast}=0.01$. For both plots, a small value of $\overline{\Gamma }$ has been used to accentuate the decay of the $x$ component.

Figure 2

Contrast between North-South and East-West alignment using Eq. (8). Geomagnetic field strength in Hamburg, Germany is 47 $\mu \text{T}$. Consistent with [14], a rapid loss of contrast occurs as $B_{\text{osc}}$ increases from 1 to 10 nT.