A linearly polarized diode laser passes through a Rb cell inside oven to maintain the temperature (set to 100ºC). Helmholtz coils are used to generate magnetic field B to induce Larmor precession. The laser then passes through a Glan-Thompson (GT) prism, which separates the s- & p- polarization components. These components’ intensities are measured using a balanced photodiode detector, and their difference is amplified and input to a 250 MHz spectrum analyzer.

We measured 5 data points for B ~2-11 G (low field) and 5 data points for B ~30-40 G (high field).

Results

Low Field (g-factors & isotope abundance ratio)

By taking the Fourier transform of the spin noise we observe a Lorentzian for each isotope shown below (for a particular value of B):

The positions of the Lorentzian peaks give the g-factors g_F by fitting them into Equation (2), while the ratio of the areas under the Lorentzian peaks gives the square root of the isotope abundance ratio.

Our results for the g-factors are accurate up to 1%, yet the deviations from the true values are quite high.

Our results for the isotope abundance ratio were ~2x to 3x the theoretical value of 2.56, hence are unreliable.

High Field (hyperfine splittings)

At higher fields the Lorentzian peak for each isotope splits into multiple peaks. Shown here is the peak cluster for ⁸⁵Rb at B = 30.6 G, consisting of 6 main peaks & 4 smaller, buried peaks. For ⁸⁷Rb, there are 4 main peaks & 2 smaller peaks.

For each peak cluster, by fitting the positions of each main peak relative to the peak cluster center to the second term of Equation (3) (1-parameter quadratic fit), the values of the hyperfine splitting for each isotope can be obtained. Shown below are such plots for both isotopes along with the fits.

Using Equation (3), ΔE_hf from each fit was calculated. Taking the weighted mean for each isotope gave us the following results:

Discussion & Conclusion

We demonstrated that spin noise can be exploited to perform spectroscopy of atomic properties of Rb such as g-factors, isotope abundance ratio, and hyperfine splittings. This technique is preferred over the conventional ones since it is non-perturbative.

The g factors are accurate to ~1.2% for both isotopes. The large deviations are reflective of the fact that the error in the calibration of the field is comparable to the error in the peak position and is difficult to estimate due to hysteresis from the optical table we performed our experiment on.

The isotope abundance ratio disagrees with accepted values by a significant margin. We found that our noise peaks are too broad and resemble Gaussian peaks more than Lorentzian peaks. This may be due to field inhomogeneity, effects related to the windowing, or the laser width being too large.

The hyperfine splittings are accurate to ~2-3% and are of 1-2 standard deviations away from the true values for both isotopes.

Acknowledgements

Thanks to Prof. Paul Crowell, Prof. Greg Pawloski, Kurt Wick, Andrew Galkiewicz and Chad Geppert for their help and guidance.

References

• • S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. Smith, “Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance,” Nature (London) 431, 49–52 (2004).

  • Schulte et. al., "Analyzing atomic noise with a consumer sound card"," Am. J. Phys. 80 (3), 240-245 (2012).