| Summary: | The low-frequency fluctuations of the atomic density within the cell can induce the longterm drift of the K-Rb-<sup>21</sup>Ne spin-exchange relaxation-free (SERF) co-magnetometer output, such that the accurate measurement of in situ atomic density is of great significance for improving the performance of co-magnetometer. In this paper, the complex refractive index model of the spin ensembles under the hybrid optical pumping condition is established first, according to which the relation between atomic density and its complex refractive index is revealed and an optical heterodyne-based scheme for atomic density detection is proposed. The dependence of the atomic density on the demodulated phase signal from the optical heterodyne-based scheme is provided by numerical simulations. After that, a dual acousto-optics frequency shifter (AOFS)-based optical heterodyne interferometry is constructed with a noise level below 1 mrad/<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>Hz</mi></msqrt></mrow></semantics></math></inline-formula> for frequencies > 1 Hz, and a compact SERF co-magnetometer is implemented as the testing medium, by which the atomic density detection with resolution of 0.40 K @ 473 K is reached and the experimental results agree well with theoretical simulations. Moreover, the detection scheme proposed in this paper has the properties of high detection sensitivity and immunity to laser power fluctuation, which are also proved experimentally.
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