Fig. 3. Enhanced monochromaticity of magnetic bremsstrahlung (undulator radiation) through shaped electron wavepackets.

We consider the scattering of an input electron off the magnetic field of a nano-undulator, for the case of a single momentum state input electron (a) and that of an input electron made up of two states $∣1⟩$ and $∣2⟩$ (b). c shows the differential cross section $\mathrm{d}\sigma /\mathrm{d}\mathrm{\Omega }\mathrm{d}\omega$ of the emission process for the single-state input electron scenario in (a). In addition to a relatively monochromatic peak, there is a strong synchrotron-radiation-like signature leading to relatively broadband radiation, with significant radiation components at lower photon energies. d and e show the emission patterns for the double-state input electron scenario in (b), with incoherent and coherent processes considered in (d) and (e), respectively. As e shows, the quantum coherence leads to destructive interference that strongly suppresses the broad synchrotron peak at low photon energies, leading to a more monochromatic output in a given direction. Cross sections of the emission patterns at θ = 0 are compared in (f). The suppression of low photon energies continues to hold at other choices of electron energies, as shown in g–j, which presents the emission spectra for electrons of 200 keV, corresponding to the scenarios in c–f. The undulator considered is of period 1 μm and has an effective length of 5.3 μm. The two input electron states are of opposite phase and oriented at ${\theta }_{1,2}=\pm 0.5^{\mathrm{o}}$ with respect to the z-axis in d and e, and at ${\theta }_{1,2}=\pm 0.025^{\mathrm{o}}$ in h and i.