Refined determination of the muonium-deuterium 1$S$-2$S$ isotope shift through improved frequency calibration of iodine lines

We report a refined determination of muonium 1$S$-2$S$ transition frequency and its isotope shift with deuterium by recalibrating the iodine reference lines using an optical frequency comb. The reference lines for the muonium and deuterium 1$S$-2$S$ transitions are determined with a precision of $2.4\times {10}^{-10}$ and $1.7\times {10}^{-10}$, respectively. An updated muonium-deuterium 1$S$-2$S$ isotope-shift frequency is derived from these references to be 11 203 464.9(9.2)(4.0) MHz, in agreement with an updated bound-state quantum-electrodynamics prediction based on 2010 adjustments of Committee on Data for Science and Technology and 2.3 times better in the systematic uncertainty than V. Meyer et al. [Phys. Rev. Lett. 84, 1136 (2000)].

Figure 1

Schematic of this experiment. HWP: half-wave plate; PBS: polarizing beam splitter; F-P cavity: Fabry-Pérot cavity; AOM: acoustic-optical modulator; EOM: electro-optical modulator.

Figure 2

Hyperfine spectra for (a) Mu and (b) D (along with frequency markers) obtained at an oven temperature of 650 ${}^{\circ }$C following Ref. [16]. The insets are the stabilized phase-sensitive detection (PSD) outputs for a 10-s duration. The cold-finger temperatures of the cell are set at 43 ${}^{\circ }$C and 33 ${}^{\circ }$C for Mu and D, respectively. The experimental linewidth is 11.2 MHz for Mu and 23.0 MHz for D. The raw signal-to-noise ratio (SNR) is 41.2 for Mu and 98.3 for D. A time constant of 10 ms and 6 dB/octave slope are used in both spectra, which lead to an equivalent noise bandwidth (ENBW) of 25 Hz. Therefore, the calibrated 1-Hz noise bandwidth SNR are 206 $\sqrt{\text{Hz}}$ and 491 $\sqrt{\text{Hz}}$ for Mu and D, respectively.

Figure 3

Absolute frequency comb measurements for (a) Mu and (b) D. The red (gray) lines represent constants from the zero-slope linear fitting of each data set. The shaded areas indicate the standard error of the fits. The fitted values are $-0.6\left(0.1\right)$ MHz for Mu and 1.23(07) MHz for D. The insets are typical histograms of the beat frequencies in megahertz.