Theory of double resonance magnetometers based on atomic alignment

We present a theoretical study of the spectra produced by optical–radio-frequency double resonance devices, in which resonant linearly polarized light is used in the optical pumping and detection processes. We extend previous work by presenting algebraic results which are valid for atomic states with arbitrary angular momenta, arbitrary rf intensities, and arbitrary geometries. The only restriction made is the assumption of low light intensity. The results are discussed in view of their use in optical magnetometers.

Figure 1

Parametrization of the DRAM geometry, in which ${\mathit{B}}_1$ is perpendicular to ${\mathit{B}}_0$. The rotating wave (rw) frame and the rotating magnetic field ${\mathit{B}}_1$ are shown for one particular moment in time $(t=0)$.

Figure 2

Angular dependence of the first ($h_{\omega }$, left) and second($h_{2\omega }$, right) harmonic signals on the angle $\gamma$ between the light polarization $ϵ$ and the magnetic offset field ${\mathit{B}}_0$.

Figure 3

(Color online) Top line: Line shapes of the absorptive $\left(A_{\omega }\right)$ and dispersive $\left(D_{\omega }\right)$ components of the first harmonic signal for different values of the rf saturation parameter $S_{\mathrm{rf}}$. Bottom line: Shape of the phase signal ${\phi }_{\omega }$ for the same values of $S_{\mathrm{rf}}$. $x=(\omega -{\omega }_0)∕\Gamma$ is the normalized detuning of the rf frequency $\omega$ with respect to the Larmor frequency ${\omega }_0$.

Figure 4

(Color online) Top line: Line shapes of the absorptive $\left(A_{2\omega }\right)$ and dispersive $\left(D_{2\omega }\right)$ components of the second harmonic signal for different values of the rf saturation parameter $S_{\mathrm{rf}}$. Bottom line: Shape of the phase signal ${\phi }_{2\omega }$ for the same values of $S_{\mathrm{rf}}$.

Figure 5

(Color online) Slopes $s_{\omega ,2\omega }$ of the dispersive signals on resonance $(x=0)$ as a function of the rf saturation parameter for two different ranges of $S_{\mathrm{rf}}$.