Initial look at the TeachSpin hyperfine apparatus.

{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:pxl_20240521_192626460.jpg?400 |}}

{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:pxl_20240521_192644551.jpg?400 |}}

====== First Data ======

----


===== Peak 1 =====

{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:tek0002.jpg?400 |}}
{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:tek0003.jpg?400 |}}


^ Dip  ^ t1 (ms)  ^ t2 (ms)  ^
| 1    | -3.6     | -3.66    |
| 2    | -3.16    | -3.22    |
| 3    | -2.72    | -2.48    |
| 4    | -2.42    | -2.48    |
| 5    | -1.98    | -2.04    |
| 6    | -1.24    | -1.30    |

Measured $\Delta t$ between lines 1,2 and 2,3.

1,2 = 0.88ms

2,3 = 1.48ms

Calculated energy differences between lines 1,2 and 2,3.

1,2 = 147 MHz

2,3 = 247 MHz
===== Peak 2 =====

{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:tek0000.jpg?400 |}}
{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:tek0001.jpg?400 |}}

^ Dip  ^ t1 (ms)  ^ t2 (ms)  ^
| 1    | -1.59    | -1.77    |
| 2    | -1.42    | -1.6     |
| 3    | -1.25    | -1.43    |
| 4    | -1.095   | -1.275   |
| 5    | -0.930   | -1.11    |
| 6    | -0.61    | -0.78    |

Measured $\Delta t$ between lines 1,2 and 2,3.

1,2 = 0.34ms

2,3 = 0.64ms

Calculated energy differences between lines 1,2 and 2,3.

1,2 = 56.8 MHz

2,3 = 107 MHz
===== Interferometer =====

{{ :phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:tek0004.jpg?400 |}}

$\Delta \phi = \frac{4 \pi \Delta f}{c} (l_{1} - l_{2})$

Frequency sweep calculated from average of first 4 interference cycles as this is the portion of the sweep where most of the spectra were collected. 
$\frac{\Delta f}{\Delta t} = 1.67x10^{11} \frac{Hz}{s}$

l1 = 47mm

l2 = 421mm

^ tmax (ms)  ^ tmin (ms)  ^
| 0.0        | 1.2        |
| 2.4        | 3.6        |
| 4.8        | 6.0        |
| 7.0        | 8.2        |
| 9.4        | 10.4       |
| 11.6       | 12.6       |
| 13.6       | 14.8       |
| 15.8       | 16.8       |
| 18.0       | 19.0       |
| 20.0       | 21.0       |

====== Energy Level Diagram ======

{{phylabs:lab_courses:phys-211-wiki-home:hyperfine-spectroscopy-of-rubidium:start:energy_level_diagram.png}}