Scattering of intense laser radiation by a single-electron wave packet

A quantum theoretical description of photoemission by a single laser-driven electron wave packet is presented. Energy-momentum conservation ensures that the partial emissions from individual momentum components of the electron wave packet do not interfere when the driving field is unidirectional. In other words, light scattering by an electron packet is independent of the phases of the pure momentum states comprising the packet; the size of the electron wave packet does not matter. This result holds also in the case of high-intensity multiphoton scattering. Our analysis is first presented in the QED framework. Since QED permits the second-quantized entangled electron-photon final state to be projected onto pure plane-wave states, the Born probability interpretation requires these projections to be first squared and then summed to find an overall probability of a scattering event. The QED treatment indicates how a semiclassical framework can be developed to recover the key features of the correct result.

Figure 1

Light pulse (comprised of a range of $k_z$) incident on an electron wave packet (comprised of a range of $\mathbf{p}$). We consider scattering into a state $|{\mathbf{p}}^{\prime };{\mathbf{k}}^{\prime }{\lambda }^{\prime };\left\{n_{k_z{\lambda }_z}\right\}\rangle$.

Figure 2

Electron may be inside or outside of a laser focus depending on the phases of ${\beta }_{\mathbf{p}}$.