Fig. 1. Schematic diagram of the system. VCO, voltage-controlled oscillator; DDS, direct digital synthesizer; AOM, acousto-optic modulator; PBS, polarization beam splitter; HWP, half-wave plate; BPD, balanced photodetector.

Fig. 2. (a) Typical in-phase (X) and quadrature (Y) output signals versus the modulation frequency ω_m when B_set = 500 nT. (b) The resonant in-phase value X₀ and inverse of the linear slope k_slop for different B_set. (c) Time variation of the BPD output S_out for each cyclic light pulse when B_set = {100, 1000, 4000, 7000} nT. (d) The maximum and minimum values of the BPD output S_max and S_min for different B_set.

Fig. 3. Flowchart of magnetic field measurement, consisting of the search (blue), lock (yellow), and output (pink) parts. The right-top inset is the large-scale scanning curves of the detected in-phase values X(ω_m) when setting B = 500 and 4000 nT.

Fig. 4. (a) Examples of the magnetic field search where B_set =500 and 5000 nT. (b) Comparison of the set and measured values B_set and B_out, where δB = B_out − B_set is the deviation.

Fig. 5. (a) Comparison between B_set (black) and B_out (red) when linearly pulling up the magnetic field on a scale of 500 to 1500 nT within 10 s. (b) Response time of the atomic polarization when abruptly switching the magnetic field from 500 to 1000 nT. (c) Measurement response of the magnetometer when setting the sinusoidal amplitude oscillation f =60 Hz of the field within a small scale of 497 to 503 nT. (d) Amplitude ratio between B_out and B_set versus the frequency f.

Fig. 6. Sensitivity of our single-beam magnetometer. The black line is related to the power spectral density of the in-phase signal without light. The red line is measured when the light power is 40 µW without modulation, and the yellow line is measured when the magnetometer is feedback-locked (B_set = 500 nT).