Electron Spin Relaxations in Biological [2Fe-2S] Cluster System

The phase coherence relaxation times as long as $T_2\sim 830-1030\pm 20$ ns were measured for the [2Fe-2S] cluster in the intrinsic protein environment. This relaxation corresponds to a relatively long lasting coherence of the low-spin $S=1\mathrm{/}2$ state. For this biological cluster, the phase coherence relaxation time was significantly affected by the nuclear hyperfine interactions of ${}^{14}$N with $I=1$. After labeling the cluster environments uniformly with the ${}^{15}$N isotope, $T_2$ exceeds $\sim 1.1-1.4\pm 0.1\mu$s at the canonical orientations. This is already an order of magnitude longer than the duration of a single-spin qubit manipulation $\sim 10-100$ ns. The transient nutation experiment corresponds to the coherent manipulation of the electron spin.