Atomic Compass: Detecting 3D Magnetic Field Alignment with Vector Vortex Light

We describe and demonstrate how 3D magnetic field alignment can be inferred from single absorption images of an atomic cloud. While optically pumped magnetometers conventionally rely on temporal measurement of the Larmor precession of atomic dipoles, here a cold atomic vapor provides a spatial interface between vector light and external magnetic fields. Using a vector vortex beam, we inscribe structured atomic spin polarization in a cloud of cold rubidium atoms and record images of the resulting absorption patterns. The polar angle of an external magnetic field can then be deduced with spatial Fourier analysis. This effect presents an alternative concept for detecting magnetic vector fields and demonstrates, more generally, how introducing spatial phases between atomic energy levels can translate transient effects to the spatial domain.

Figure 1

Schematic energy levels and laser transitions: ${\mathrm{Rb}}^{87}$ atoms are cooled and trapped in a standard MOT and then transferred into a SpOT, populating the $F=1$ ground state. A vector vortex beam drives a $\mathrm{\Lambda }$ transition, where the ${\sigma }_{\pm }$ transitions carry opposite phase profiles and an external magnetic field couples the ground states. The phase profiles of the probe light are shown for $\ell =\pm 2$, with hue representing values between 0 and $2\pi$. The top inset shows the corresponding intensity and polarization profile.

Figure 2

Illustration of the transition probability $T_{1\to e}$ based on Fermi’s golden rule. (a) Predicted absorption profiles for vector beams with $\ell =1$ and 2 for the indicated inclination angles. (b) $T_{1\to e}$ as a function of the magnetic field alignment.

Figure 3

Schematic diagram of the experimental geometry. The atoms are in the far field of the $q$ plate ($Q$) and are imaged to the camera plane. The optical pumping configuration for the SpOT is explained in [46]. The bottom left inset shows the defining coordinate system and the alignment of the magnetic field. HWP, half wave plate; L, lens; RP, repump.

Figure 4

Magnetic field alignment from Fourier analysis of the atomic absorption profiles. (a) Example images ($600\times 600\mu {\mathrm{m}}^2$) in gray scale of the probe intensity $I_{\text{probe}}$, transmitted light $I_{\text{trans}}$, and resulting transmission profile OD (where black corresponds to high OD), with the analysis region indicated in red. (b),(c) Dependence of the $2\ell$ and $4\ell$ Fourier components on ${\varphi }_B$ and ${\theta }_B$ of the $\mathbf{B}$ and comparison with FGR and optical Bloch model (OB). Error bars of the data points (blue) represent the standard deviation of 3 or 5 runs. (d),(e) Corresponding compilations of the unwrapped OD images for steps of 70 and 87 mrad, respectively, with the FGR prediction as insets.