Orientational effects on the amplitude and phase of polarimeter signals in double-resonance atomic magnetometry

Double-resonance optically pumped magnetometry can be used to measure static magnetic fields with high sensitivity by detecting a resonant atomic spin response to a small oscillating field perturbation. Determination of the resonant frequency yields a scalar measurement of static field $\left(B_0\right)$ magnitude. We present calculations and experimental data showing that the on-resonance polarimeter signal of light transmitted through an atomic vapor in arbitrarily oriented $B_0$ may be modeled by considering the evolution of alignment terms in atomic polarization. We observe that the amplitude and phase of the magnetometer signal are highly dependent upon $B_0$ orientation and present precise measurements of the distribution of these parameters over the full $4\pi$ solid angle.

Figure 1

Schematic of the apparatus used in this work, showing external cavity diode laser (ECDL), Glan-Thompson linear polarizer (GT), quarter-wave plate $\left(\lambda /4\right)$, magnetometer cell, five-layer mu-metal shield, three-axis Helmholtz coils, polarizing beam splitter (PBS), differential photodetector (DPD), low-noise coil driver (LNCD), and data acquisition system (DAC/ADC). The data acquisition system is controlled using a PC (not shown).

Figure 2

Schematic showing the geometry of the magnetometer system in the laboratory frame. The orientation of the static field $B_0$ is defined by the angles to the light propagation and vertical axes, ${\theta }_L$ and ${\theta }_V$, respectively. Inset, alternative polar basis angles $\alpha$ and $\beta$ are defined. The orientations of the oscillating fields $B_{RFZ}$ and $B_{RFY}$, and the polarization analyser (PBS), are also shown.

Figure 3

Calculated (top) and observed (bottom) distribution of on-resonance first-harmonic polarimeter signal amplitude over $4\pi$ solid angle in response to a field modulation $B_{RF}$ applied parallel to the light propagation $\left(y\right)$ axis.

Figure 4

Calculated (top) and observed (bottom) distribution of on-resonance first-harmonic polarimeter signal amplitude over $4\pi$ solid angle in response to a field modulation $B_{RF}$ applied parallel to the vertical $\left(z\right)$ axis.

Figure 5

Calculated (top) and observed (bottom) distribution of on-resonance first-harmonic polarimeter signal phase over $4\pi$ solid angle in response to a field modulation $B_{RF}$ applied parallel to the light propagation $\left(y\right)$ axis.

Figure 6

Calculated (top) and observed (bottom) distribution of on-resonance first-harmonic polarimeter signal phase over $4\pi$ solid angle in response to a field modulation $B_{RF}$ applied parallel to the vertical $\left(z\right)$ axis.