Structured-Light Magnetometry in a Coherently Controlled Atomic Medium

Abstract

A structured-light-based approach for detecting magneto-optical rotation is presented, in which polarization rotation is mapped onto a directly observable spatial degree of freedom. A radially polarized Laguerre-Gaussian beam interacts with cold $^{87}\mathrm{Rb}$ atoms in the presence of a longitudinal magnetic field, where magnetically induced circular birefringence introduces a relative phase shift between the $σ_+$ and $σ_-$ components of the field, manifesting as a rotation of the interference pattern. The MOR angle is extracted directly from the angular displacement of the petal-shaped intensity distribution, eliminating the need for polarizers or Stokes-parameter analysis. This method converts conventional polarization-based magnetometry into a topology-based spatial readout, enabling spatially resolved magnetic-field sensing with potential applications in optical magnetometry and quantum sensing.

Figures (8)

• Figure 1: (a) Relevant energy-level configuration of the four-level atomic system interacting with the optical fields. (b) Schematic of the experimental setup for a structured-light-based magnetometer. $\mathrm{OVR}_1$ and $\mathrm{OVR}_2$ denote optical vortex retarders used to generate radially polarized LG beams. The beam emerging from $\mathrm{OVR}_1$ carries the OAM index $\ell_1$, while the beam from $\mathrm{OVR}_2$ serves as the reference beam with index $\ell_2$. Here, BS represents beam splitters, and $M_1$ and $M_2$ denote mirrors.
• Figure 2: Variation of the atomic coherences $\rho_{41}$ and $\rho_{43}$ as functions of the normalized magnetic field $B/\gamma$. The results correspond to a control field strength $\Omega_c = 3\gamma$, equal probe components $\Omega_{+}=\Omega_{-}=0.05\gamma$, and resonance conditions $\Delta_c=\Delta_p=0$.
• Figure 3: Contour plots of the probe coherence as functions of the normalized control field strength $\Omega_c/\gamma$ and magnetic field $B/\gamma$. The color bars show the real parts in panels (a)--(c) and the imaginary parts in panels (d)--(f) of $\rho_{41}$, $\rho_{43}$, and $\rho_{43}-\rho_{41}$, respectively. The calculations are performed for equal probe components $\Omega_{+}=\Omega_{-}=0.05\gamma$ under resonance conditions $\Delta_c=\Delta_p=0$.
• Figure 4: Interference pattern in the presence of a static magnetic field for different propagation lengths. Figures (a)–(d) correspond to $\ell_1 = 1$, $\ell_2 = -1$, while (e)–(h) correspond to $\ell_1 = 1$, $\ell_2 = -2$. The parameters used are: $\Omega_{0p} = \Omega_{0ref} = 0.05\gamma$, $\Omega_c = 2\gamma$, $B = 0.5\gamma$, $\Delta_p = \Delta_c = 0$, atomic number density $N = 2 \times 10^9 \,\text{cm}^{-3}$, wavelength $\lambda$ = 780 nm, radial index $m =0$, and beam waist $\omega_0 = 90\,\mu\text{m}$.
• Figure 5: Interference pattern in the presence of a static magnetic field for different propagation lengths with radial index $m =1$ and the other parameters are the same as in Fig. \ref{['3']}.