Unambiguous Vector Magnetometry with Structured Light in Atomic Vapor

Abstract

Absorption profiles of vector light upon interaction with atomic vapor carries distinct signatures of external magnetic field vector. However, this signature becomes ambiguous for anti parallel magnetic field vectors of equal magnitude, which makes their absorption profiles visually indistinguishable. To resolve this ambiguity, we present theoretical analysis of the interaction of vector light with optically polarized atoms immersed in reference and test magnetic fields. Furthermore, we demonstrate the complete characterization of the arbitrarily oriented (transverse) test magnetic field via Fourier analysis of the absorption profile. This analysis reveals a one to one correspondence between the magnetic field properties and the profiles contrast and rotational angle. Our findings open an avenue to design an optical vector atomic magnetometer based on structured light fields.

Figures (3)

• Figure 1: Geometrical setup of the system. (a) The vector light field of frequency $\omega$ with its inhomogeneous intensity and polarization texture propagates along the $z$ axis, and interacts with optically polarized atoms in the vapor cell. Here, the vapor cell is approximated by thin layer of randomly distributed atoms in the $xy$ plane. The reference field $\bm{B}_{\mathrm{ref}}$ is applied along the $y-$ axis, while the test $\bm{B}_{\mathrm{test}}$ magnetic field is a three dimensional vector. For such a system, the total magnetic field $\bm{B}_{T}$ lies suspended in the space and serves as the quantization axis (not shown in the diagram). The absorption profile of the vector light and its corresponding polar plot for a fixed radius of $b= 2000\, \mu m$ are shown in the detection plane. (b) The coupling between vector light and atomic target. The figure illustrates the interaction between vector light and polarized atoms for a $50$ mG test field applied at $\phi_{B} = 30^\circ$, and $0.1$ G reference magnetic field. The central polar plot shows the (normalized) transition amplitude for atoms along the blue dotted circle ($b = 2000\, \mu\text{m}$). This azimuthally varying interaction forms the absorption profile shown adjacent to it. Atoms in the dark regions absorb maximum light, as they are strongly coupled by the $M_{g} = 0 \rightarrow M_{e} = 0$ transition. Conversely, atoms in the lighter regions absorb less light, as they are mainly coupled via the $M_{g} = \pm 1 \rightarrow M_{e} = 0$ transition. (c) The energy level diagram of the rubidium atoms. In our scenario, the pump, linearly polarized plane wave couples $M_{g} = 0$ to $M_{e} = 0$ (weakly) and $M_{g} = \pm 1$ to $M_{e} = 0$ (strongly), leading to relatively maximum population in magnetic sublevels $M_{g} = 0$.
• Figure 2: Absorption profiles of the vector beam. (a) The test magnetic field is shown at four different directions in a simplified geometry. (b) The corresponding four absorption profiles of the vector light (c) The corresponding population of excited state $\rho_{ee}$ for an atom at radial distance $b = 2000\, \mu m$ as a function of its azimuthal coordinate $\phi_{b}$. (d) The magnitude of $\bm{B}_{\mathrm{T}}$ as a function of test field's strength for $\phi_{B} = 120\degree$. (e) The angle between the local polarization vector and the quantization axis as a function of azimuthal coordinate of the atom. Left plot shows $\delta$ for two different azimuthal angle of test magnetic field of same strength, and right plot shows the variation for anti-parallel test magnetic field of same azimuthal angle $\phi_{B}$. For all these plots, the strength of reference $B_{\mathrm{ref}} = 0.1$ G
• Figure 3: Variation of absorption profile with increasing strength of arbitrarily directed test magnetic field. (a) Left: Absorption profile of the vector light for a test magnetic field of azimuthal angle $\phi_{B} = 120\degree$ and strength of $10$ mG. Right: The corresponding polar plots for various strengths of constant test $B_{\mathrm{test}} = 10, 75$, and 250 mG considering the atoms to be positioned along the white dashed circle of radius $b = 2000\, \mu m$. (b)Trajectory of the normalized fourth Fourier harmonic, $\mathcal{F}_{4}$, for various strengths of the constant test magnetic field. Here, the strength of $B_{\mathrm{ref}} = 0.1$ G.