Optical free-induction decay of theF3+center in NaF

We have measured the optical dephasing time $T_2$ of the ${}_{}{}^1{}_{}{}^{}A_1^{}{}_{}{}^{}\leftrightarrow {}_{}{}^1{}_{}{}^{}E$ zero-phonon transition of the $F_3^{+}$ color center in NaF by optical free-induction decay. In this way we eliminate the effect of the 54-GHz inhomogeneous broadening, and find a homogeneous linewidth of 20 ± 5 MHz $T_2=16\mathrm{}\pm 4$ nsec). We have also measured a spontaneous emission lifetime of $T_1=10\mathrm{}\pm 2$ nsec. In the range 1.5-4 K, our results are consistent with the relation $T_2=2\mathrm{}{T}_1$, indicating that optical dephasing is limited by population-decay processes. This relation was even more clearly demonstrated by performing the same experiment on the $D$ lines of sodium vapor at 3 × ${10}^{-5\mathrm{}}$ Torr, where the effects of collisions are negligible. We find that the dephasing is again limited by radiative decay, and that $T_2(32\mathrm{}\pm 3 \mathrm{nsec})=2\mathrm{}{T}_1(16.3\mathrm{}\pm 0.4 \mathrm{nsec})$.