Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor

We report measurements of absolute transition frequencies and hyperfine coupling constants for the $8S_{1/2}$, $9S_{1/2}$, $7D_{3/2}$, and $7D_{5/2}$ states in ${}^{133}\mathrm{Cs}$ vapor. The stepwise excitation through either the $6P_{1/2}$ or $6P_{3/2}$ intermediate state is performed directly with broadband laser light from a stabilized femtosecond laser optical-frequency comb. The laser beam is split, counterpropagated, and focused into a room-temperature Cs vapor cell. The repetition rate of the frequency comb is scanned and we detect the fluorescence on the $7P_{1/2,3/2}\to 6S_{1/2}$ branches of the decay of the excited states. The excitations to the different states are isolated by the introduction of narrow-bandwidth interference filters in the laser beam paths. Using a nonlinear least-squares method we find measurements of transition frequencies and hyperfine coupling constants that are in agreement with other recent measurements for the $8S$ state and provide improvement by $2$ orders of magnitude over previously published results for the $9S$ and $7D$ states.

Figure 1

Energy levels of ${}^{133}\text{Cs}$ $(I=7/2)$ that are relevant to this work. The excitation pathways are shown in solid red along with the transition wavelengths. The decay channels used in the detection are shown in blue dashed lines. The total angular momentum of the hyperfine components is listed next to each state.

Figure 2

Block diagram of the experimental setup. The components are the following: BS 1 and BS 2, nonpolarizing beam splitters; F1, F2, and F3, interference filters; L, lens; PD, photodiode: PMT, photomultiplier tube; VC, Cs vapor cell.

Figure 3

Fluorescence from the $7P_J\to 6S_{1/2}$ decay as a function of laser repetition rate when no filters (F1 and F2 in Fig. 2) are used to restrict the laser’s spectral bandwidth.

Figure 4

The calculated spectrum (upper trace) and experimental signal (lower trace) of the $7P\to 6S$ fluorescence when the Cs atoms are excited to the $8S_{1/2}$ state through the $6P_{3/2}$ state. The groups of peaks in the calculated spectrum are labeled by $F$-$F^{″}$ to denote the hyperfine ground state and the hyperfine final state of the transition. The peaks in each group correspond to the different hyperfine components of the intermediate state. The peaks in the experimental spectrum that are labeled with letters were used in extracting the transition frequencies, as described in the text.

Figure 5

The $7P\to 6S$ fluorescence when the Cs atoms are excited to the $8S_{1/2}$ state through the $6P_{3/2}$ state. The peaks correspond to the d, e, and f peaks in Fig. 4. This data set was taken at a temperature of 319 K and was used in evaluating systematic effects related to temperature dependence.

Figure 6

The calculated spectrum (upper trace) and experimental signal (lower trace) of the $7P\to 6S$ fluorescence when the Cs atoms are excited to the $8S_{1/2}$ state through the $6P_{1/2}$ state. The peaks in the experimental spectrum that are labeled with letters were used in extracting the transition frequencies as described in the text.

Figure 7

The dependence of the center-of-gravity frequencies for the $6S_{1/2}\to 6P_{3/2}\to 8S_{1/2}$ state on the power (upper left), the magnetic field (upper right), and the Cs vapor pressure (bottom). The straight line for the power dependence is a weighted linear fit to the data. The vertical axis has been offset and centered so that the nominal operating point is at zero for the power-dependence plot. The magnetic field and pressure data are shown scattered about the weighted mean of the data. The horizontal axis for the power dependence is plotted as a function of the fraction of the maximum power. The horizontal axis for the magnetic field dependence is plotted as a function of the residual magnetic field, $\approx$50 $\mu T$.

Figure 8

The calculated spectrum (upper trace) and experimental signal (lower trace) of the $7P\to 6S$ fluorescence when the Cs atoms are excited to the $9S_{1/2}$ state through the $6P_{3/2}$ state. The peaks in the experimental spectrum labeled with letters were used in extracting the transition frequencies, as described in the text.

Figure 9

The dependence of the center-of-gravity frequencies for the $6S_{1/2}\to 6P_{3/2}\to 9S_{1/2}$ state on the power (upper left), the magnetic field (upper right), and the Cs vapor pressure (bottom). The straight line for the power dependence is a weighted linear fit to the data. The vertical axis has been offset and centered so that the nominal operating point is at zero for the power-dependence plot. The magnetic field and pressure data are shown scattered about the weighted mean of the data. The power is plotted as a function of the fraction of the maximum power. The magnetic field is plotted as a function of the residual magnetic field, $\approx$50 $\mu T$.

Figure 10

The calculated spectrum (upper trace) and experimental signal (lower trace) of the $7P\to 6S$ fluorescence when the Cs atoms are excited to the $7D_{3/2}$ state through the $6P_{1/2}$ state. The peaks in the experimental spectrum labeled with letters were used in extracting the transition frequencies as described in the text.

Figure 11

The dependence of the center-of-gravity frequencies for the $6S_{1/2}\to 6P_{1/2}\to 7D_{3/2}$ transition on the power (upper left), the magnetic field (upper right), and the Cs vapor pressure (bottom). The straight line for the power dependence is a weighted linear fit to the data. The vertical axis has been offset and centered so that the nominal operating point is at zero for the power-dependence plot. The magnetic field and pressure data are shown scattered about the weighted mean of the data. The power is plotted as a function of the fraction of the maximum power. The magnetic field is plotted as a function of the residual magnetic field, $\approx$50 $\mu T$.

Figure 12

The calculated spectrum (upper trace) of the $7P\to 6S$ fluorescence when the Cs atoms are excited to the $7_D$ state. The experimental signal (lower trace) shows the $7P\to 6S$ fluorescence when the Cs atoms are excited to both the $7D_{3/2,5/2}$ states through the $6P_{3/2}$ state. In the experimental spectrum data are shown for only those regions where there was a signal.

Figure 13

The experimental spectrum (upper trace), fit to the $6S_{1/2}\to 6P_{3/2}\to 7D_{5/2}$ transition (middle trace), and the spectrum of the calculated contribution from the $6S_{1/2}\to 6P_{3/2}\to 7D_{3/2}$ transition (lower trace). Note that the vertical scales are different for the two figures.

Figure 14

The dependence of the center-of-gravity frequencies for the $6S_{1/2}\to 6P_{3/2}\to D_{5/2}$ transition on the power (upper left), the magnetic field (upper right), and the Cs vapor pressure (bottom). The straight line in the power dependence plot is a linear weighted fit to the data. The vertical axis has been offset and centered so that the nominal operating point is at zero. The power is plotted as a function of the fraction of the maximum power. The magnetic field is plotted as a function of the residual magnetic field.