Intrinsic atomic calibration of oscillating magnetic fields in ULF and VLF bands

We present a method for absolute calibration of received radio-frequency in the ultra low frequency (ULF), and very low frequency (VLF) range. This is achieved with the use of a radio frequency optically pumped magnetometer (RF-OPM). We describe a method using an optically pumped sample where the RF broadening of the Cs magnetic resonance allows the magnitude of the received field to be calibrated against the ground-state gyromagnetic ratio of the Cs atoms. This frequency-based calibration avoids the geometric and electrostatic response functions that affect inductive sensors, such as fluxgates, search coils, and SQUID magnetometers. We demonstrate calibration of magnetic measurement using oscillating magnetic fields in the 300 Hz - 20 kHz range and a sensor noise floor of 15 fT.Hz-1/2. This radio-frequency sensor may be used as a widely tunable narrowband receiver for communication, ranging, or penetrative conductivity imaging.

💡 Research Summary

The authors present a method for absolute calibration of radio‑frequency magnetic fields in the ultra‑low‑frequency (ULF) and very‑low‑frequency (VLF) bands (300 Hz–20 kHz) using a radio‑frequency optically pumped magnetometer (RF‑OPM) based on a cesium vapor cell. The sensor operates on a double‑resonance principle: a circularly polarized pump laser on the D₂ line creates a spin‑polarized ensemble, while a linearly polarized probe on the D₁ line monitors the transverse spin component via Faraday rotation. A static magnetic field B₀ defines the Larmor frequency ω_L = γB₀, and an orthogonal RF coil supplies an oscillating field B_RF that drives magnetic‑dipole transitions with Rabi frequency Ω_RF = γB_RF.

The key insight is that the RF‑induced broadening and saturation of the magnetic resonance provide a direct, atom‑based reference for the field amplitude. By measuring the absorptive (M_y) and dispersive (M_x) components of the resonance and forming the quadrature sum R = √(M_x²+M_y²), the authors remove phase dependence and obtain a scalar response that depends only on Ω_RF, the detuning Δ = ω_L – ω_RF, and the relaxation rates Γ₁ (longitudinal) and Γ₂ (transverse). In the linear regime (Ω_RF ≪ Γ) the response is proportional to Ω_RF, but the covariance between the amplitude and Ω_RF prevents an independent determination of the field. In the saturated regime (Ω_RF Γ⁻¹ > 1) the resonance widens and the on‑resonance amplitude follows M_y(Δ=0)=M₀ Ω_RF/