Rabi Oscillations:
Teachspin manual gives the period of rabi oscillations as $T = 1/\gamma B_{RF}$ where $\gamma = g_f \frac{\mu_0}{\hbar}$ is the gyromagnetic ratio and $B_{RF} = \dfrac{3 \mu_0 I_{RF} R^2}{(x^2+R^2)^{3/2}} $ is the magnetic field in the RF coil (Assuming field is from 6 coils total). For our apparatus, $R = D/2 = 6.45 cm/2 = .03225 m $. $x = .054 m$ if we're at the center of the coils. $I_{RF} = 50 \Omega / V$ for the sense resistor. This means we can roll a lot up into a constant term
$$B_{RF} = \dfrac{3 \mu_0 I_{RF} R^2}{.00025 m^3} = 12.54m^{-1} \times \mu_0 I_{RF} = 12.54m^{-1} \times 4\pi × 10^{−7} H m^{-1} I_{RF} = 1.576 × 10^{−5} m^{-2} H \times I_{RF} = \frac{7880× 10^{−7}}{V} T = \frac{7.880× 10^{−4}}{V} T$$
$$B_{RF} = \dfrac{3 \mu_0 I_{RF} R^2}{.00025 m^3} = 12.54m^{-1} \times \mu_0 I_{RF} = \frac{627}{V} \frac{\Omega}{m} \times \mu_0 = $$
$$f = \gamma B_{RF} = g_f \frac{\mu_0}{\hbar} \times \frac{627}{V} \frac{\Omega}{m} \times \mu_0 = \frac{g_f}{\hbar} \times \frac{627}{V} \frac{\Omega}{m} = \frac{g_f}{V} \times 6.6148*10^{-32} \frac{\Omega J s}{m} = $$???
$[H] = [T\cdot m^2 / A]$
$[\gamma] = [1/T\cdot s]$
or, $\gamma \approx 4.12577 MHz T^{-1}$
$$f = \gamma B_{RF} = 4.12577 \times 10^6 Hz * \frac{7.880× 10^{−4}}{V} = \frac{3250 Hz}{V} $$
