Figure 1

(a) Energy levels (left) and schematic model (right) for optical transitions between different electronic states ($|a⟩$ and $|b⟩$), with transition rates $r_{ba}$ and $r_{ab}$. The precession of the nuclear spin (${\overrightarrow{\omega }}_a$ or ${\overrightarrow{\omega }}_b$) (blue arrow) depends on the electronic state ($|a⟩$ or $|b⟩$) (orange arrow). (b) Random telegraph trajectory of the electron, and time-dependent precession of the nuclear spin. (c) Geometric representation of Larmor precession vectors. (d) The decoherence rate $\Gamma$ as a function of the differential precession frequency $\Delta \omega$, in units of $\gamma$.Reuse & Permissions

Figure 2

Comparison between experimental data (points) and simulation (lines). (a) Optically induced decoherence rate $\Gamma$ as a function of ground state Larmor precession frequency ${\omega }_g$ (data adopted from Ref. [1]). (b) Shift of average Larmor precession frequency $|⟨\overrightarrow{\omega }⟩|-{\omega }_g$ as a function of ${\omega }_g$. For both plots, the axes are also labeled in dimensionless units, normalized by the radiative decay rate $\gamma =86\mu {\mathrm{s}}^{-1}$. Experimental data points (blue triangles, red diamonds) include nuclear spins prepared along both directions ($\widehat{x}$, $\widehat{z}$) perpendicular to the Larmor precession vector ($\widehat{y}$). The full lines are from simulation of the generalized spin-fluctuator model, averaging over 50 different sets of randomly generated excited states, as described in the text. The simulation assumes $N=3$ for the fluctuator (i.e. one ground state and two excited states [19, 20]). The dashed lines are the statistical standard deviation of the different realizations. In panel (a), the curves from simulation are manually shifted upwards by ${\Gamma }_0=3.4\times {10}^{-3}\gamma$, as described in the text.Reuse & Permissions