= Cyclic phase of a spin in a rotating field
{title2=$e^{i\Phi_\mu}=(-1)^{2s}e^{-i\mu\Omega T}$}
An <eigenstate> of the <rotating-frame Rabi Hamiltonian> returns to the same laboratory ray after a full drive period. Its <quantum phase> includes both the rotating-frame <energy> and the sign of a full <spin> rotation. For <spin> $s$ and magnetic label $\mu$, the factor is $(-1)^{2s}e^{-i\mu\Omega T}$. Expanding the rotating-frame splitting to first order in the drive <frequency> and subtracting the adiabatic <dynamical phase> leaves $-\mu$ times the oriented <solid angle> of the field loop. Dropping the full-rotation sign gives a spurious half-integer-spin offset.
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