Absolute frequency and isotope shift of the magnesium $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ two-photon transition by direct frequency-comb spectroscopy

We use a picosecond frequency-doubled mode-locked titanium sapphire laser to generate a frequency comb at 431 nm in order to probe the $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ transition in atomic magnesium. Using a second, self-referenced femtosecond frequency comb, the absolute transition frequency and the ${}^{24}\mathrm{Mg}$ and ${}^{26}\mathrm{Mg}$ isotope shift is determined relative to a global-positioning-system-referenced hydrogen maser. Our result for the transition frequency of the main isotope ${}^{24}\mathrm{Mg}$ of $1391128606.14\left(12\right)$ MHz agrees with previous measurements and reduces its uncertainty by four orders of magnitude. For the isotope shift we find $\delta {\nu }^{26,24}=3915.13\left(39\right)$ MHz. Accurate values for transition frequencies in Mg are relevant in astrophysics and to test atomic structure calculations.

Figure 1

Direct frequency comb two-photon spectroscopy. Left: With one of the modes on resonance ($\mathrm{\Delta }\nu =0$), all other modes may combine pairwise to deliver the atomic transition energy $h{\nu }_{eg}$. Right: For constructive interference of all excitation paths, the modes of the frequency comb must be properly phased. For nonresonant intermediate states this is the case with time bandwidth limited pulses at the center of the pulse collision volume. For atoms at rest a possible frequency chirp only decreases the excitation rate by approximately the time bandwidth product [12]. The corresponding longitudinal increase of the pulse collision volume may compensate that drop in signal [13].

Figure 2

Magnesium levels relevant to this work. The $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ is excited by two 431-nm photons from a frequency comb and decays via the $\left(3s3p\right){}^1{P}_1$ level to the ground state by emitting an 881- and a 285-nm photon. The latter is used for detection. The natural linewidth of the $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ transition is 1.96 MHz [21]. The closely lying intermediate $\left(3s3p\right){}^3{P}_J$ triplet states ($J=0,1,2$) are weakly coupled to the laser (intercombination [18]) and in addition sufficiently far detuned ($>38$ THz, ps comb not drawn to scale) to avoid stepwise single-photon excitation.

Figure 3

The setup for the Mg spectroscopy consists of a mode-locked ps titanium sapphire laser (“ps comb”) with a repetition rate of $\sim 82$ MHz. This laser is resonantly enhanced for efficient frequency doubling and locked to an ULE cavity to narrow the linewidths of its modes. The frequency of one of its modes is measured by employing a second, self-referenced mode-locked fs titanium sapphire laser (“fs comb”) via a cw semiconductor laser (LD) that is used as a transfer oscillator. The mode number of the fs comb is determined with a $\lambda$ meter. The spectroscopy takes place in a vacuum chamber that is filled with gas from a Mg oven. The vacuum chamber is surrounded by a second enhancement cavity that is resonant for the spectroscopy laser. Fluorescence is detected with a photomultiplier tube (PMT) via the 285-nm decay (see Fig. 2) that is extracted through a CaF window. OI, optical isolator; OSA, optical spectrum analyzer; PD, photodiode; AOM, acousto-optic modulator; EOM, electro-optic modulator; PBS, polarization beam splitter; PZT, piezoelectric transducer; PCV, pulse collision volume.

Figure 4

Magnesium $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ excited with a ps frequency comb and detected via the $\left(3s3d\right){}^1{D}_2\to \left(3s3p\right){}^1{P}_1\to \left(3s^2\right){}^1{S}_0$ decay at 285 nm. The frequency comb is tuned by scanning a double-pass acousto-optic modulator (AOM) that is placed between the ps mode-locked laser and its reference cavity (see Fig. 3). The AOM frequency enters the optical atomic frequency with a factor of 8 as the ps comb is tuned by a double-pass AOM, is frequency doubled, and then excites a two-photon transition. The smaller peak at the left is identified with the ${}^{26}\mathrm{Mg}$ isotope (abundance 11%) while the right peak belongs to ${}^{24}\mathrm{Mg}$ (abundance 79%). The ${}^{25}\mathrm{Mg}$ (abundance 10%) line is split into five weaker hyperfine components that are not detected in this experiment. The solid red line is the fit result of a sum of two real-valued Lorentzian functions with a constant offset. From this fit we find a full width at half maximum of 3.47(6) MHz for ${}^{24}\mathrm{Mg}$ in reasonable agreement with the natural linewidth combined with the estimated time-of-flight broadening. Because the frequency comb is folded into the line structure, an integer multiple of ${\nu }_{\mathrm{rep}}=81.8338$ MHz needs to be added to the line splitting to obtain the isotope shift.

Figure 5

Magnesium $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ isotope shift between ${}^{26}\mathrm{Mg}$ and ${}^{24}\mathrm{Mg}$ measured with different repetition rates of the ps comb (${\nu }_{\mathrm{rep}}=81.8338$, 81.0232, and 82.6600 MHz). Each value is obtained from around ten line scans such as the one in Fig. 4. The statistical error bars are determined from the fit. The weighted mean (horizontal line) of this data set is $\delta {\nu }^{26,24}=3915.13\left(39\right)$ MHz with the total uncertainty given by the shaded region.

Figure 6

${}^{24}\mathrm{Mg} \left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ transition frequency. Each of the values is obtained from several line scans such as the one in Fig. 4 with a statistical error bar determined from the fits. These error bars indicate additional systematic effects that are taken into account to determine the overall uncertainty (shaded area) of the weighted mean ${\nu }_{eg}=1391128606.14\left(12\right)$ MHz (horizontal line).