BEAMS
In the literature: open
Free-electron beams with quantum degeneracy approaching one
In plain words
Even in the best beams, far fewer than one electron occupies each smallest quantum cell of position and momentum; reaching about one per cell would allow quantum-optics experiments with free electrons.
Precise statement
The degeneracy $\delta$ is the mean number of electrons per phase-space cell of volume $h^{3}$ (per spin state), proportional to the 6D normalized brightness. Determine whether any free-electron source (cold field emitter, laser-triggered nanotip, cryogenic photocathode) can reach $\delta \ge 0.1$ over a pulse, and identify what limits it (Coulomb heating, Boersch energy broadening, emitter temperature).
What would settle it
A measured 6D phase-space density of a pulsed source giving $\delta \ge 0.1$, or a bound from Coulomb heating that excludes it.