Spin-Dependent Phase Shifts in Atom Interferometry and Limits on Torsion Gradients

This paper examines what differential phase sensitivity in a caesium atom interferometer implies for a spatial gradient of axial torsion across the two arms. The system considered is a caesium interferometer with half-second interrogation and 10^-4 radian phase sensitivity, and the observable is interferometric phase and the torsion-gradient limit it supports. Evaluating the ordinary behaviour of the system and the spin-torsion contribution under explicit assumptions about polarisation and uniformity, and inverting the comparison at the stated laboratory precision, gives a quantitative bound rather than a qualitative assertion of smallness. The computed record is: phase_sensitivity_rad = 1.000e-04; interrogation_s = 0.5; torsion_gradient_bound_per_m2 = 6.671e-13; differential_acceleration_m_s2 = 9.810e-12; k_per_m = 7.375e+06. The torsion-related contribution is far below the level that would alter the ordinary behaviour of the system at current precision, and the value that would have produced a visible residual is stated so that future improvements can be assessed against it directly. No new measurement is reported. This study is simulated and computed from stated assumptions, not measured.