Anomalous radiation reaction in a circularly polarized field

Quantum corrections to electron dynamics in a circularly polarized electromagnetic field are found within the Floquet theory of periodically driven quantum systems. It is demonstrated that emission of photons by an electron rotating under the field leads to the quantum recoil force acting on the electron perpendicularly to the velocity of its forward movement, which differs crucially from the known classical recoil force directed oppositely to the velocity. Physically, such an anomalous radiation reaction arises from the one-loop QED correction to the photon emission and has no analog within the classical electrodynamics. Possible manifestations of this phenomenon are discussed for electrons in strong laser fields.

💡 Research Summary

In this paper the author investigates the quantum corrections to the dynamics of an electron immersed in a circularly polarized electromagnetic field, using Floquet theory to treat the strong, periodic driving non‑perturbatively while handling the electron‑photon interaction perturbatively. The classical picture predicts that a radiating electron experiences a radiation‑reaction (LAD) force opposite to its instantaneous velocity. By constructing the exact Floquet eigenstates of the non‑relativistic Hamiltonian ˆH₀ = (ˆp − eA/c)²/2mₑ with the vector potential A = (cE₀/ω)(cos ωt, sin ωt, 0), the author first recovers the familiar electron motion: a forward drift velocity vₖ plus a circular “quiver” velocity v₀ induced by the rotating electric field.

The one‑vertex (tree‑level) photon‑emission diagram is then evaluated. The resulting emission probability W^{(a)}ₖ(q) yields the standard Larmor power P₀ = (2e²/3c³)·\dot{v}² and a recoil force Fₖ = −(2e⁴E₀²/3mₑ²c⁵) vₖ, which is precisely the classical Lorentz‑Abraham‑Dirac (LAD) force when averaged over a field period. Thus, at tree level the quantum calculation reproduces the classical radiation reaction, and the Planck constant ħ cancels out.

The novel result emerges from the one‑loop diagram in which the emitted photon is preceded by a virtual photon exchange (Fig. 1b). By performing a third‑order time‑dependent perturbation expansion, the author derives an additional amplitude T^{(b)}ₖ(q) containing denominators that become singular when the intermediate virtual photon goes on‑shell. Integrating over the photon phase space yields an extra contribution wₖ(q) to the emission probability and, crucially, a new force term

F⊥ = ( e⁴E₀² / 3mₑ²c⁵ )(v₀/c)²