Precision Microwave Spectroscopy of the Positronium $n=2$ Fine Structure

We report a new measurement of the positronium (Ps) $2{{}^{3}S}_1\to 2{{}^{3}P}_0$ interval. Slow Ps atoms, optically excited to the radiatively metastable $2{{}^{3}S}_1$ level, flew through a microwave radiation field tuned to drive the transition to the short-lived $2{{}^{3}P}_0$ level, which was detected via the time spectrum of subsequent ground state Ps annihilation radiation. After accounting for Zeeman shifts we obtain a transition frequency ${\nu }_0=18501.02\pm 0.61\mathrm{MHz}$, which is not in agreement with the theoretical value of ${\nu }_0=18498.25\pm 0.08\mathrm{MHz}$.

Figure 1

(a) Schematic of the positronium formation and excitation region and WR-51 waveguide and (b) the positions of the four LYSO detectors D1-4. The spatial profile of the UV excitation laser light is indicated by the (blue) rectangle in (a). $F$ and $B$ represent the electric field of the microwave radiation, and the externally applied magnetic field, respectively.

Figure 2

Example line shape and Lorentzian fit for the ${\nu }_0$ transition measured in a magnetic field of 32 G using detector D2. The vertical line at $\mathrm{\Delta }\nu =0$ corresponds to the calculated transition frequency, including the Zeeman shift. The inset shows the microwave (solid arrow) and optical (dashed arrows) transitions by which $2{{}^{3}S}_1$ atoms reach the $1{{}^{3}S}_1$ ground state.

Figure 3

Calculated Zeeman shifts of $n=2$ triplet Ps levels. The allowed ${\nu }_J$ transitions with $\mathrm{\Delta }{M}_J=0$ are indicated by the vertical arrows. The energies shown are relative to the $n=2$ Bohr [i.e., $\mathcal{O}(m{\alpha }^2)$] level. The $2{{}^{3}S}_1(0)\to 2{{}^{3}P}_1(0)$ transition is shown with a dashed line because the transition strength is zero. Here we designate levels with principal quantum number $n$ using the standard spectroscopic notation $n^{(2S+1)}{\ell }_J(M_J)$.

Figure 4

$2{{}^{3}S}_1\to 2{{}^{3}P}_0$ transition frequency shifts (a), linewidths (b), and Fano asymmetry parameters $q$ (c) measured in different magnetic fields. The dashed (gray) curve in (a) is the calculated Zeeman shift of the ${\nu }_0$ transition frequency (see Fig. 3), and the solid (red) curve is a quadratic fit to the data. These curves have the form $y=a{B}^2+c$. For the calculated curve the coefficient $a=6.7\times {10}^{-4}\mathrm{MHz}/{\mathrm{G}}^2$, and from the fit we obtain $a=(6.2\pm 1.2)\times {10}^{-4}\mathrm{MHz}/{\mathrm{G}}^2$. The data were averaged over all 4 detectors and multiple runs, with a total acquisition live time of 300 h.

Figure 5

Previous measurements of the Ps ${\nu }_0$ interval [35, 36] and the present result (UCL 2020). The vertical line indicates the theoretical value and uncertainty of the transition frequency [10]. The statistical and systematic errors of the measurements have been added in quadrature.