Precision continuous-wave laser measurement of the $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ interval in positronium

TL;DR

This work delivers a high-precision CW two-photon measurement of the positronium $1^3S_1 \to 2^3S_1$ interval, achieving $4.9$ ppb accuracy by combining enhanced CW excitation, triple-coincidence detection, and detailed lineshape modelling. A comprehensive MC simulation and a semi-analytical perturbative model are developed to account for second-order Doppler, AC Stark, finite lifetimes, and photoionization, enabling robust extraction of the transition frequency. The measured value $f = 1233607224.1(6.0)\ \mathrm{MHz}$ agrees with the latest QED calculations at $\mathcal{O}(\alpha^7\ln^2(1/\alpha))$, and when combined with previous measurements reduces the tension to about $1.4\sigma$. The introduced semi-analytical lineshape provides a transferable tool for unstable systems (e.g., muonium) and guides optimization of experimental parameters without heavy simulations, paving the way toward sub-ppb precision with future improvements such as frequency-comb metrology and Ramsey–Doppler techniques.

Abstract

We report a 4.9\,ppb measurement of the positronium $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ interval using continuous-wave two-photon laser spectroscopy. The transition is detected via photoionization by the same excitation laser. The resulting positrons are guided to a microchannel plate detector, surrounded by scintillators to detect the annihilation photons in coincidence, thereby reducing the background. A Monte Carlo lineshape simulation, accounting for effects such as the second-order Doppler shift and the AC Stark shift, is used to extract a transition frequency of $1233607224.1(6.0)\,\text{MHz}$, consistent with the previous 2.6\,ppb determination of this transition and with the most recent QED calculations at order $\mathcal{O}(α^7\ln^2(1/α))$, which predict $1233607222.12(58)\,\text{MHz}$. Combining the two measurements gives $1233607218.1(2.8)\,\text{MHz}$, reducing the tension with QED to about $1.4\,σ$. We also present a semi-analytical lineshape model of $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ of positronium, which shows excellent agreement with detailed simulations and is validated by the experimental data. This expands on previous work with stable atoms by incorporating effects such as limited lifetime of the atoms, photoionization and AC Stark shift. The lineshape modelling is also applicable to other unstable systems, such as muonium. This provides a powerful tool for optimizing the experimental parameters and gaining deeper insights without the need for computationally intensive simulations.

Figures (13)

• Figure 1: Sketch of the experimental scheme for positronium $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ spectroscopy. (a) A positron pulse impacts a porous target and forms positronium. The atoms are then emitted in vacuum and cross a CW laser at 486nm. The laser excites the atoms to the 2S state, which are ionised by another photon absorption. (b) The photoionized components of the atom ($e^+$, $e^-$) are separated by carefully selected voltages on the target, bottom MCP grid and electrostatic lenses. The photoionized positron is guided toward the detection region, spatially separated from the formation region to avoid annihilation background from the initial positron pulse. Lead shielding between the formation and detection regions further suppresses this background. The guided positron finally hits a microchannel-plate detector and annihilates, producing two back-to-back 511keV $\gamma$-rays that are detected in an array of ten calibrated BGO scintillators.
• Figure 2: MCP surrounded by BGO scintillators for the triple coincidence detection method (see text for more details).
• Figure 3: Sketch of the laser system. Extended cavity diode laser (ECDL), tapered amplifier (TA), second harmonic generation (SHG), lithium triborate (LBO), beam splitter (BS), electro-optic modulator (EOM), mode matching lenses (L1-L2), photodiode (PD), power monitor (PM), input coupler (IC), output coupler (OC), piezoelectric transducer stack (PZT), neutral density filter (ND filter.), ultra-low expansion cavity (ULE).
• Figure 4: Ps trajectory as it traverses the laser beam. The light field grows as Ps moves towards the beam, passing at its distance of closest approach of the beam axis, $\rho$.
• Figure 5: The data points display the simulated photoionization spectra of Ps given the experimental conditions (see Tab. \ref{['tab:exp_parameters']}) while the solid lines plot $\textbf{L}_{\textbf{ion}}$ for two indicated powers: 46 W and 460 W, the latter of these is the nominal power used to collect the experimental data. The inset displays the spectra near peak, highlighting the slight overestimate due to perturbation theory.