Sensitive chemical compass assisted by quantum criticality

A radical-pair-based chemical reaction might be used by birds for navigation via the geomagnetic direction. The inherent physical mechanism is that the quantum coherent transition from a singlet state to triplet states of the radical pair could respond to a weak magnetic field and be sensitive to the direction of such a field; this then results in different photopigments to be sensed by the avian eyes. Here, we propose a quantum bionic setup, inspired by the avian compass, as an ultrasensitive probe of a weak magnetic field based on the quantum phase transition of the environments of the two electrons in the radical pair. We prove that the yield of the chemical products via recombination from the singlet state is determined by the Loschmidt echo of the environments with interacting nuclear spins. Thus quantum criticality of environments could enhance the sensitivity of detection of weak magnetic fields.

Figure 1

Model setup of sensitive magnetodetection based on a radical-pair chemical reaction assisted by quantum critical environments consisting of interacting spins. Two spins can be initially prepared in the singlet state and finally evolve into triplet states due to the couplings to their environments. The yield of the corresponding chemical product responds sensitively to the external magnetic field.

Figure 2

The product yield ${\Phi }_S$ vs the magnitude $B$ and direction $\theta$ of the magnetic field at a finite temperature $k_{B}T=0.2J$ with $N=1000$, $g_0=1$, $k_S=0.1J$, $J=100$ Hz, $g_N=1.905$, and $B_0=50\mu$T.

Figure 3

The product yield ${\Phi }_S$ and its derivative vs the geomagnetic field's direction $\theta$ (in degrees) for different $T$'s with $k_S=0.1J$, $N=1000$, $g_0=1$, $g_N{\mu }_{N}B/2=0.9J$, and $J=100$ Hz: blue dashed line for $k_{B}T=0.01J$, green solid line for $k_{B}T=0.3J$, and red dash-dotted line for $k_{B}T=0.9J$.

Figure 4

The product yield ${\Phi }_S$ and its derivative vs the geomagnetic-field direction $\theta$ (in degrees) for different $g_0$'s with $N=1001$, $g_N{\mu }_{N}B/2=J$, $T=0$, and $J=100$ Hz: green solid line for $g_0=0.1$, blue dashed line for $g_0=0.5$, red dot-dashed line for $g_0=1$, and black dotted line for $g_0=5$.