Fig. 2. Enhanced directionality in atomic bremsstrahlung through shaped electron wavepackets.

In the typical atomic bremsstrahlung scenario a, a single momentum state electron scatters off a carbon atom and emits radiation. Shaping the input electron wavepacket through the use of multiple states as in b, where the input is a superposition of states $∣1⟩$ and $∣2⟩$, can enhance the output photon properties through coherent interference between the processes associated with each individual electron state. To illustrate this, c–e show the differential cross section $\mathrm{d}\sigma /\mathrm{d}\mathrm{\Omega }\mathrm{d}\omega$ of the emission process for 20 keV electrons, with a single z-directed input electron state in c, and two input electron states of opposite phase and oriented at ${\theta }_{1,2}=\pm 15^{\mathrm{o}}$ with respect to the z-axis in d and e. A donut-shaped emission pattern, as indicated by the off-axis peaks, is expected for the single-state c and incoherent double-state d cases. In contrast, quantum interference between the constituent processes in e strongly suppresses off-axis emission, resulting in an emission pattern that is more directional and peaked on-axis. Cross-section emission patterns at θ = 0 are compared in (f). The enhanced directionality also holds at other choices of electron energies and angles, as shown in g–j, which presents the emission spectra corresponding to the scenarios in c–f, respectively, but for 200 keV electrons, at ${\theta }_{1,2}=\pm 15^{\mathrm{o}}$.