Measurement of the Positronium1S13−2S13Interval by Doppler-Free Two-Photon Spectroscopy

Abstract

We have measured the $1{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ interval in positronium (Ps) to be 1 233 607 185 ± 15 MHz, in agreement to within 1% of the ${\alpha }^3{R}_{\infty }$ QED prediction. The quoted 12-ppb uncertainty has equal contributions from the measurement of the Ps resonance relative to a ${\mathrm{Te}}_2$ absorption line and the calibration of the ${\mathrm{Te}}_2$ line relative to the deuterium $2S_{\frac{1}{2}}-4\mathrm{}{P}_{\frac{3}{2}}$ Balmer line.