Spin correlations in recirculating multipass alkali cells for advancing quantum magnetometry

• Recirculating multipass cell enables improved beam coverage and active volume. • Analytical model predicts beam distribution and astigmatism effects. • General framework developed for spin noise in multipass alkali cells. • Beam geometry shown to influence spin diffusion noise. • Recirculating design demonstrates reduced spin noise under optimized conditions. Multipass cells enable long optical path lengths in compact volumes and are central to quantum technologies such as atomic magnetometers and optical quantum memories. In optical magnetometry, multipass geometries enhance sensitivity by increasing optical depth, reducing photon shot noise, and enabling quantum non-demolition detection. However, in conventional cylindrical multipass cells, Lissajous beam trajectories lead to repeated revisiting and incomplete mirror coverage, limiting effective volume utilization. Here we present a recirculating multipass alkali cell that overcomes these limitations by increasing the active-to-cell volume ratio and minimizing beam spot overlap. We develop an analytical ABCD-matrix model to predict beam trajectories, spot sizes, and astigmatism, validated by Zemax simulations. We further introduce a general analytical framework for spin correlation noise that incorporates astigmatism and spatial intensity distributions. By deriving the spin-noise time-correlation function and spectrum, we show how beam intensity profiles influence spin diffusion noise. Our results demonstrate improved beam coverage, reduced spot overlap, and enhanced spin correlation, particularly for concave mirrors with long focal lengths, while showing that avoiding tightly-focused regions significantly suppresses spin diffusion noise. These findings establish recirculating multipass cells as a practical, high-performance platform for precision atomic sensing and other multipass-cavity-based quantum devices.