Precise measurement of hyperfine structure in the 3S1/2 state of 7Li

We report a precise measurement of hyperfine structure in the 3S1/2 state of the odd isotope of Li, namely 7Li. The state is excited from the ground 2S1/2 state (which has the same parity) using two single-photon transitions via the intermediate 2P3/2 state. The value of the hyperfine constant we measure is A = 93.095(52) MHz, which resolves two discrepant values reported in the literature measured using other techniques. Our value is also consistent with theoretical calculations.

(AOM). The frequency of the AOM is in the RF range, which is set by a frequency generator (HP8656B) with a timebase accuracy of 10 −6 . Both the unshifted and AOM-shifted 813 nm beams are used for the experiment. As seen in the figure, the two beams are separated and combined using PBSs. The polarization of the combined beam is adjusted using a λ/2 plate. The combined beam counter-propagates with the locked 671 nm beam for the two-step excitation to the 3S 1/2 state. The polarization of the combined 813 nm beam is adjusted to get significant heights for both unshifted and AOM-shifted beams.
All the required spectroscopy experiments are done by having an atomic beam inside an ultra-high vacuum (UHV) system, maintained at a pressure below 10 −7 torr using a 40 l/s ion pump. The Li source consists of an SS vial containing a small ingot of unenriched Li. The vial is resistively heated to a temperature of about 200 °C. When heated, the source produces an atomic beam containing both stable isotopes of Li, namely 6 Li and 7 Li. The atomic beam is mechanically collimated with a divergence angle of 0.1 mrad using apertures. The pressure rises by 2 orders-of-magnitude when the source is turned on. The two laser beams intersect the atomic beam at right     angles, which as mentioned before minimizes the first-order Doppler shift. The fluorescence signals are collected by photomultiplier tubes (PMTs).

Results and Discussion
Experimental results. A typical spectrum in 7 Li used for the experiment is shown in Fig. 3. The fluorescence signal obtained from decay of the 3S 1/2 state to the intermediate 2P 3/2 state is plotted as a function of 813 nm laser frequency. The AOM shift for the spectrum shown is 168 MHz. The first peak (P1) corresponds to the F = 2 level of the 3S 1/2 state; the second peak (P2) corresponds to the F = 1 level of the 3S 1/2 state; and the third peak (P3) is the second peak along with the AOM shift. The solid line is a multipeak fit to the 3 peaks with a Lorentzian lineshape for each peak. Even though, as mentioned in the introduction, the lineshape of each peak is a Voigt function, we have used a Lorentzian function because it fits the data quite well, as seen from the featureless residuals on top of each peak (there is some structure in the region between peaks P2 and P3, which arises because of electronics noise in our PMT). In addition, the error (which depends on the signal-to-noise ratio) is well-defined for a Lorentzian function.
The linewidth of each peak is 15-20 MHz, which is larger than the expected linewidth of the 3S 1/2 → 2P 3/2 transition-a combination of the 5.25 MHz natural linewidth of the 3S 1/2 state 8 convolved with the 6 MHz natural linewidth of the 2P 3/2 state. The increase in linewidth arises for the following reasons.
(i) Small misalignment angle from perpendicularity of the laser and atomic beams-we know that the angle is small because the increase in linewidth is quite small. (ii) Residual divergence of the atomic beam. (iii) Closely spaced (less than the natural linewidth) hyperfine levels of the 2P 3/2 state. The x axis in Fig. 3 is scaled with the known AOM shift between peaks P1 and P3. The axis is nonlinear because it varies as the sine of the grating angle, but is close to linear on this scale. This also shows why the exact lock point of the 671 nm laser is unimportant. A change in the lock point will cause the zero point in the figure to shift, but the separation between P1 and P3 will not change; thus the scaling of the laser scan axis will not be affected.
Since the hyperfine interval to be measured is near 190 MHz, the AOM shift is varied from 160 to 212 MHz, in steps of 2 MHz. At each value of AOM shift, a spectrum of the kind shown in Fig. 3 is recorded. A multipeak fit with Lorentzian lineshape for the 3 peaks yields each peak's location and error in the location. The hyperfine separation (HFS) is the difference in location between peaks P1 and P2, while the separation between peaks P2 and P3 is the AOM frequency. The quantity has a zero crossing when the AOM frequency is equal to the HFS. The above expression shows that the error in δ is equal to the sum of the errors in P1 and P3. The quantity δ as a function of AOM frequency is shown in Fig. 4. Each value also has an error bar as determined above. The solid line is a weighted polynomial fit, weighted by the error bar for each point. Since the laser scan axis is nonlinear, the order for the polynomial fit is chosen to be the minimum nonlinear one (namely second order) -first order (or linear) gives a ten times larger error. We have also verified that the zero crossing of the fit remains unchanged within its error when we use higher-order polynomials. The zero crossing of the fit along with its error yields the HFS as 186.19(10) MHz. Since the hyperfine interval is related to the hyperfine constant as 2A, the measured value of the constant is A = 93.095 ± 0.050 MHz, where the error is the statistical error in the curve fit.
Scanning the laser to get the entire spectrum has many advantages compared to the other technique that we have developed where the AOM frequency is locked to a hyperfine peak 9 . The main advantage is that the technique avoids servo-loop errors, as demonstrated by us in ref. 10 . Another advantage is that the measured interval is independent of scaling of the laser scan axis. Any such rescaling will change the y-axis of Fig. 4, but not the zero crossing. Comparison to previous values. Our present measurement is compared to the two conflicting earlier experimental values in Fig. 5. It is clear that our value is consistent with the value of Bushaw et al. 4 , but quite inconsistent with the value of Stevens et al. 3 . This shows that the work in ref. 3 may have been plagued by unaccounted systematic errors. The figure also shows that our value is consistent with theoretical calculations, done with Hylleraas variational method 5 and multiconfiguration Hartee-Fock method 6 . We also show that our value compares favorably with results of isotope-shift measurements in Li (both stable and short lived) done at GSI in Germany 11 . The authors extract the value of the relevant hyperfine constant using a combination of theory and experiment.

Conclusions
In summary, we have measured the hyperfine constant in the 3S 1/2 state of 7 Li. The state is populated using two single-photon transitions via the intermediate 2P 3/2 state. Both transitions are excited using diode lasers. This method is different from previous techniques used in refs 3,4 , which report discrepant values for the hyperfine constant. Our value of A = 93.095(52) MHz is consistent with the more recent measurement in ref. 4 , which uses two-photon spectroscopy for excitation from the ground state. Our value is also consistent with theoretical calculations.