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Atomic Hyperfine Splitting in Rubidium

Atomic Hyperfine Splitting in Rubidium . Qibin Ye with partner Mengdi Zheng Dec 16th 2009. Theory (1). Theory. From Lab Manual, Brown University. Allowed Transitions for 87Rb . Ideal Spectrum. Theory (2). Doppler Broadening

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Atomic Hyperfine Splitting in Rubidium

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  1. Atomic Hyperfine Splitting in Rubidium Qibin Ye with partner Mengdi Zheng Dec 16th 2009

  2. Theory (1)

  3. Theory From Lab Manual, Brown University

  4. Allowed Transitions for 87Rb

  5. Ideal Spectrum

  6. Theory (2) • Doppler Broadening full-width at half maximum (FWHM) • In the experiment, we can let T=300K. c/ v0=781.6nm, M=87u(in the second formula, M is in unit of u), △v is at the magnitude order of 0.51GHz

  7. Cartoon of actual spectrum

  8. Experiment

  9. From Lab Manual, Brown University

  10. Spectrum of Fine Structure

  11. 85Rb (72%) 87Rb (28%)

  12. Spectrum with Hyperfine Structure (1)

  13. Spectrum with Hyperfine structure (2)

  14. Spectrum without Hyperfine(up) and with Hyperfine (down) (3)

  15. Calibration Setup

  16. Analysis (1) • ψ1-ψ2 =2π(2L1 – 2L2)/λ=4π(L1 – L2) v / c. • △v = c / (2 (L1 – L2)) =15/39X10^9Hz ~ 0.385GHz. • Calibration setup with 20 Hz, 3 V scaning • 43 Oscillations in 3V of scanning. • △v  3/43 V=0.07V=70mV • So the calibration is 5.5 GHz/V

  17. Analysis (2) • Doppler Broadening full-width at half maximum (FWHM) • In the experiment, we can let T=300K. c/ v0=781.6nm, M=87u(in the second formula, M is in unit of u), △v is at the magnitude order of 0.51GHz

  18. 85Rb (72%) 87Rb (28%)

  19. Analysis (3) • Peak 1 to Peak 4 ~ 9.12ms Peak 2 to Peak 3 ~ 4.0ms • As20Hz->4V, So 25ms->4V, Calibration is 5.5 GHz/V • Peak 1 to Peak 4 ~ 1.46V ~ 8.02GHz (6.83GHz)* Peak 2 to Peak 3 ~ 0.64V ~ 3.52GHz (3.06GHz) * This is theoretical value, cited from “Saturation Spectroscopy of Rubidium” Je®reyBorowitz, 2006

  20. Analysis (4) • As 1.74ms  278 mV Calibration is 5.5 GHz/V • FWHM for fine structure in our experiment is 1.02ms ~ 1ms ~160mV ~ 0.88GHz • FWHM for Hyperfine structure in our experiment is ~ 150 us ~22mV ~ 0.12GHz

  21. Analysis (4) • 1st peak to 2nd peak ~ 144us~23mV ->126MHz • 2nd peak to 3rd peak ~ 224us~35.8mV ->197MHz

  22. Theory From Lab Manual, Brown University

  23. Thanks

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