Magnetic field measurement technologies are widely required in aerospace, navigation, geophysical prospecting, and medical diagnostics, with each application imposing distinct demands on the stability, accuracy, and dynamic range of magnetic sensors. Conventional magnetometers such as fluxgate and superconducting quantum interference device (SQUID) magnetometers have achieved significant maturity, yet their inherent limitations including zero drift and environmental sensitivity restrict practical deployments in long-term, unmonitored environments. In contrast, the cold atom magnetometers, using laser-cooled atomic ensembles, with unique properties such as negligible interatomic interactions and ultra-long coherence time, have emerged as competitive candidates for next-generation precision magnetometry. This work proposes a novel magnetometry approach that integrates cold atoms within a diffuse light integral sphere and utilizes the nonlinear magneto-optical rotation (NMOR) effects for high-sensitivity magnetic field detection. Quantum sensors constructed using cold atoms exhibit advantages of minimal drift and long-term stability, which possess considerable application prospects in the domain of precision measurement.

The experiment employs a cold atom source in an integral sphere, eliminating the need for strict magneto-optical trap (MOT) generated magnetic fields, thereby avoiding remanent magnetic field interference. The integral sphere is covered within a three-layer permalloy magnetic shield to suppress geomagnetic fluctuations. Cold atoms are prepared by injecting frequency-detuned cooling laser beams into the integral sphere, producing a uniform diffuse light field via multiple internal reflections, effectively cooling cesium atoms. The NMOR measurement system utilizes three distributed Bragg reflector (DBR) lasers: one for generating the cooling and probe light at 852 nm, the second as the repump light at the same wavelength, and the third as the pump laser at 895 nm. The pump laser is intensity-modulated by an acousto-optic modulator (AOM). A balance detection scheme involving polarizing beam splitters and a lock-in amplifier is used to detect the minute changes in the probe light polarization state which are induced by the cold atom ensemble spin precession under an external magnetic field. During the experimental operations, the periodic pump pulses synchronize the atomic spin polarization. When the modulation frequency of the pump light matches the Larmor precession frequency of atomic spins, the system achieves the maximum polarization, and the NMOR signal amplitude reaches the peak value. The resonance condition is exploited to determine the external magnetic induction intensity (B) through the relationship B=ω/γ, where ω is the measured Larmor frequency and γ is the gyromagnetic ratio.

The experimental setup realizes a cold atom magnetometry based on NMOR in a diffuse light field. The time sequence includes a 47.5 ms cooling stage followed by a 5 ms probing stage per cycle. The periodic modulation of the pump light mitigates spin depolarization and decoherence effects (Fig. 5 and Fig. 6), significantly improving the atomic polarization stability and the signal strength over multiple pumping cycles. A linear correlation between the applied magnetic induction intensity and the experimental result is obtained across a magnetic induction intensity range of up to 5 μT, with a linear fit coefficient R² exceeding 0.999 (Fig. 7). The residual magnetic induction intensity inside the magnetic shield is determined to be approximately less than 0.07 μT. Noise analysis identifies the primary limitations arising from the residual field gradient (approximately 0.2 μT) within the shield, the magnetic noise from the external field source, and the laser frequency/power noise affecting the probe signal stability. The time-domain and frequency-domain noise characteristics of the magnetometer are evaluated along both x and y axes under an applied static magnetic induction intensity of 1.86 μT (Fig. 8 and Fig. 9). The system achieves a sensitivity of 30 pT/Hz^1/2 at 1 Hz and a long-term Allan deviation of 20 pT over 1000 s (Fig. 10). Optimization strategies including increasing cold atom density, improving magnetic shielding, enhancing current source stability, and reducing laser noise are identified for future refinement.

This study presents the experimental implementation of NMOR magnetometry using cold atoms within a diffuse light integral sphere. The system achieves a magnetic induction intensity sensitivity of 30 pT/Hz^1/2 and a 1000 s stability of 20 pT. The integration of the NMOR technique with a diffuse cold atom source paves the way for developing high-precision, low-drift, and long-term stable quantum magnetometers. Future work will focus on enhancing cold atom density, magnetic shielding effectiveness, and detector sensitivity, as well as minimizing laser noise to further elevate measurement sensitivity and dynamic range, ultimately enabling field-ready portable quantum magnetometers.