Nuclear Spin Cooling Using Overhauser-Field Selective Coherent Population Trapping

We show that a quantum interference effect in optical absorption from two electronic spin states of a solid-state emitter can be used to prepare the surrounding environment of nuclear spins in well-defined states, thereby suppressing electronic spin dephasing. The coupled electron-nuclei system evolves into a coherent population trapping state by optical-excitation-induced nuclear-spin diffusion for a broad range of initial optical detunings. The spectroscopic signature of this evolution where the single-electron strongly modifies its environment is a drastic broadening of the dark resonance in optical absorption experiments. The large difference in electronic and nuclear time scales allows us to verify the preparation of nuclear spins in the desired state.

Figure 1

(a) The energy level diagram of a solid-state emitter exhibiting coherent population trapping (CPT). (b) Nuclear-spin diffusion rates depending on the nuclear-spin projection $\lambda$ assuming homogeneous coupling. Parameters are $N=4\times {10}^4$, $\Gamma =1\mathrm{GHz}$, $A_H={\omega }_z=100\mu \mathrm{eV}$, and $\Omega ={\Omega }_p={\Omega }_c=0.1\mathrm{GHz}$. The rates calculated using the quantum mechanical (for the subspace $J=\sqrt{N/2}$, dashed line) and the semiclassical (dotted line) descriptions show both qualitative and quantitative agreement. The solid (red) curve shows the nuclear-spin distribution for $\Omega =0.02\Gamma$ and $T_2^{-1}=100{\mathrm{s}}^{-1}$. (c) The dependence of the steady-state OF standard deviation ${\sigma }_{\mathrm{OF}}$ as a function of $\Omega$ in the limit of homogeneous coupling; the solid (dashed) line is obtained by taking $T_2^{-1}=100{\mathrm{s}}^{-1}$ ($T_2^{-1}=0{\mathrm{s}}^{-1}$). (d) The absorption line shape (arb. units) for $\Omega =0.2\Gamma$ (blue lines) and $\Omega =0.4\Gamma$ (green lines): in stark contrast to the standard CPT profile (dotted lines), the dark resonance is drastically broadened (solid lines). (e) ${\sigma }_{\mathrm{OF}}$ for ${\Omega }_p={\Omega }_c=0.2\Gamma$ (blue line) and ${\Omega }_p={\Omega }_c=0.4\Gamma$ (green line) is reduced to the level below that of a single nuclear-spin flip (red line). The black line shows ${\sigma }_{\mathrm{OF}}$ in the absence of lasers.