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

TL;DR

This work introduces an intrinsic, atom-based calibration method for RF fields in the ULF and VLF bands using a Cs RF-OPM. By saturating the atomic response and fitting the resonance with a Bloch-equation–inspired model, the authors extract an RF coil calibration parameter $C_{RF}$ that matches geometric expectations, yielding a coil-geometry–independent standard. The method achieves a broadband sensor noise floor of about 15 fT/√Hz with a photon-shot-noise limit near 11 fT/√Hz at optimal probe power, and demonstrates applicability to communications, ranging, and magnetic induction tomography in attenuating media. This calibration framework provides a transferable, high-precision reference for magnetic metrology at low frequencies and can be extended to even lower bands with further noise suppression.

Abstract

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.

Figures (5)

• Figure 1: Schematic of apparatus used. Double resonance magnetometer comprised of a volume holographic grating (VHG) pump and distributed Bragg reflector (DBR) probe laser, 4 layer mu-metal magnetic shielding which houses a 28 mm diameter glass blown paraffin coated cell containing a thermal vapour of caesium, internal RF modulation coil and internal static field generation coil. Two reference cells with their respective photodiode (PD), and a balanced polarimeter comprised of a half-wave plate (HWP), polarising beam splitter (PBS) and balanced photodetector (BPD).
• Figure 2: Magnetic resonance generated from a frequency sweep of 100 samples over a detuning range of 80 Hz, for a total sampling time of 5 seconds. Both $M_{y}$ (red) and $M_{x}$ (blue) are fitted simultaneously with the best fit shown with solid lines, and the best fit parameters $M_{0}$ = 0.560 V, $\omega_{L}$ = 2.00 kHz, $\Gamma$ = 4.67 Hz, $\Omega_{RF}$ = 4.08 Hz.
• Figure 3: Multiple R, resonant response to a swept RF frequency data with a global fit at a single Larmor frequency. Each resonant response represents the same detuning range across a central Larmor frequency with increasing RF drive from 0.73 $nT$ (orange) up to 5.80 $nT$ (black).
• Figure 4: (A) - single resonance of width 180 Hz at a given Larmor frequency. (B) - Ten resonances for a single given Larmor frequency, varying in RF modulation driving depth. (C) - All resonances for varied Larmor frequency and varied RF modulation driving depths.
• Figure 5: Analysis of different sources of noise in the magnetometer system, each trace denotes a different source of noise and its relative contribution. Operational with test signal of 10 pT (blue), no test signal (orange), optical noise of probe (yellow), detector noise (purple), and electronic DAQ noise (green). The black dashed line represents the average broadband sensitivity in the system, measuring 15 fT/$\sqrt Hz$. The red dashed line is that of the calculated photon shot-noise of 11 fT/$\sqrt Hz$.