Hyperfine constants and line separations for the ${}^{1}S_0-{}^{3}P_1$ intercombination line in neutral ytterbium with sub-Doppler resolution

Optical frequency measurements of the intercombination line $\left(6s^2\right){}^{1}S_0-\left(6s6p\right){}^{3}P_1$ in the isotopes of ytterbium are carried out with the use of sub-Doppler fluorescence spectroscopy on an atomic beam. A dispersive signal is generated to which a master laser is locked, while frequency counting of an auxiliary beat signal is performed via a frequency comb referenced to a hydrogen maser. The relative separations between the lines are used to evaluate the ${}^{3}P_1$-level magnetic dipole and electric quadrupole constants for the fermionic isotopes. The center of gravity for the ${}^{3}P_1$ levels in ${}^{171}\mathrm{Yb}$ and ${}^{173}\mathrm{Yb}$ are also evaluated, where we find significant disagreement with previously reported values. These hyperfine constants provide a valuable testbed for atomic many-body computations in ytterbium.

Figure 1

Sketch of the setup for saturated absorption spectroscopy of the $\left(6s^2\right){}^{1}S_0-\left(6s6p\right){}^{3}P_1$ transition on an atomic beam of Yb. The lock-in amplifier (LIA) outputs an error signal which is fed back to the 1112 nm laser for stabilization to the intercombination line. This light is also used to generate a heterodyne beat note with an element of a frequency comb, which is frequency counted. The magnetic ($B$) field is applied to cancel the Earth's vertical $B$-field component. AOM, acousto-optic modulator; CNTR, frequency counter; CE, cat's eye reflector; DAQ, data acquisition for spectra; $E$, electric-field polarization; f-comb, frequency comb (in the near-IR); $f_R$, repetition frequency; L, lens; LF, loop filter; LPF, long-wavelength pass filter (505 nm); M, mirror; MOD, modulation; PMT, photomultiplier tube; RFA, radio frequency amplifier; VCO, voltage controlled oscillator.

Figure 2

Sub-Doppler spectra of the intercombination line in ytterbium for all the abundant isotopes, displaying the relative strengths of the various lines. Each spectrum is labeled by the atomic number along with the upper $F$ state in parentheses for the odd isotopes. All traces are saturated absorption signals except for ${}^{171}\mathrm{Yb}$ ($F^{\prime }=1/2$), which is an inverted crossover resonance. a.u., arbitrary units.

Figure 3

Frequency separation and sequence of the ytterbium isotope levels, and hyperfine level structure of ${}^{171}\mathrm{Yb}$ and ${}^{173}\mathrm{Yb}$ drawn to scale (note the inversion with respect to $F$ for ${}^{173}\mathrm{Yb}$). The shift of the hyperfine levels in terms of the hyperfine constants is given in Table 5 of the Appendix.

Figure 4

(a) Frequency dependence on the lens' vertical position in the cat's eye for three bosonic ytterbium isotopes. Absolute optical frequencies have been subtracted and deliberate offsets have been applied to the ${}^{172}\mathrm{Yb}$ and ${}^{176}\mathrm{Yb}$ data to more clearly show the slopes. (b) Signal strength versus vertical (V) and horizontal (H) lens position.

Figure 5

(a) Absolute optical frequency dependence on the lens' vertical position in the cat's eye for several lines between hyperfine states. Only the upper $F$ state is stated on the plot. Optical frequencies have been subtracted and some offsets applied to discern the data points. (b) Optical frequency of the ${}^{172}\mathrm{Yb}$ intercombination line as a function of lens-mirror separation in the cat's eye. The single error bar is the approximate uncertainty (Allan deviation) for all the data points. (c) Frequency difference between the ${}^{171}\mathrm{Yb}$ ($F^{\prime }=3/2$) and ${}^{172}\mathrm{Yb}$ lines as a function of 556 nm beam intensity. The frequency separation has been offset by $2.80465\mathrm{GHz}$. (d) Optical frequency of the ${}^{172}\mathrm{Yb}$ line as a function of the vertical magnetic field. The frequencies in (b) and (d) are offset by 539 387 600 920 kHz.

Figure 6

(a) Center-line frequency vs the modulation amplitude applied to the 556 nm light. Different optical frequencies have been subtracted for each isotopic line. (b) Saturated absorption spectrum for ${}^{171}\mathrm{Yb}$ ($F^{\prime }=3/2$) and ${}^{173}\mathrm{Yb}$ ($F^{\prime }=3/2$). The residuals of the curve fit are shown above.

Figure 7

Experimental setup for generating the calibrated line spectra. A servo using a frequency-to-voltage converter (FVC) locks the 1112 nm laser to an element of the frequency comb. A function generator is used to sweep the green light's frequency by use of an acousto-optic modulator (AOM). BPF, band pass filter; CNTR, frequency counter; DAQ, data acquisition; $f_R$, repetition frequency; LF, loop filter; SAS, saturated absorption scheme.

Figure 8

Summary of the hyperfine constants and centers of gravity for the intercombination line in ytterbium. We make comparisons to some previous measurements; (i) [62], (ii) [47], and (iii) [34].