Net electron spin rotation in a plane-wave pulse: Holonomy set by the anomalous magnetic moment

Abstract

We compute the spin rotation that survives after a relativistic electron has crossed a plane-wave laser pulse of finite duration. In the interaction picture built on the exact $g=2$ evolution, the Thomas-Bargmann-Michel-Telegdi equation becomes parallel transport by a connection with constant coefficients on the polarization plane, and the pulse enters only through the closed curve that the transverse vector potential traces there. The net rotation is the holonomy of that connection: an angle $-\frac{1}{2}a_e^2\mathcal{A}$ about the propagation direction, with $a_e=(g-2)/2$ the anomaly and $\mathcal{A}$ twice the signed area enclosed by the curve. That area is the spin angular momentum the pulse carries per unit area, so the rotation measures the helicity of the light. Reduction of the residual dynamics to a rotation coupled through the anomaly alone is an exact result of the 1960s [Ternov, Bagrov, and Klimenko, Sov. Phys. J. 11, 29 (1968); Bagrov and Gitman, The Dirac Equation and its Solutions (De Gruyter, Berlin, 2014), Sec. 5.3], which yields two closed-form cases; the area law is the general second order that those two cases bound. The same area governs the orientation memory of a neutral magnetic dipole [Oblak and Seraj, Phys. Rev. D 109, 044037 (2024)] with a coupling of order unity. For a charged electron on a Volkov orbit the coupling $g/2$ cancels identically, which suppresses the rotation by $1.3\times10^{-6}$ and leaves a channel with no $g$-independent part. We verify the cancellation at $g=2$ over 180 pulse configurations and the area law over 89 more. Finite focusing restores that part at second order in $1/kw_0$, and it exceeds the anomalous signal unless $w_0\gtrsim16\lambda$ at $\gamma=10$, or $270\lambda$ at $\gamma=1$.