Direct Observation of Sub-Poissonian Temporal Statistics in a Continuous Free-Electron Beam with Subpicosecond Resolution

We present a novel method to measure the arrival time statistics of continuous electron beams with subpicosecond resolution, based on the combination of an rf deflection cavity and fast single electron imaging. We observe Poissonian statistics within time bins from 100 to 2 ns and increasingly pronounced sub-Poissonian statistics as the time bin decreases from 2 ps to 340 fs. This 2D streak camera, in principle, enables femtosecond-level arrival time measurements, paving the way to observing Pauli blocking effects in electron beams and thus serving as an essential diagnostic tool toward degenerate electron beam sources for free-electron quantum optics.

Figure 1

Distribution of the simultaneous electron occurrences measured in $\mathrm{\Delta }t=100$, 10, 2 ns using the Timepix3 camera and the corresponding expected Poisson distribution. Total number of analyzed electron events is $\simeq 26\times {10}^6$ for $\mathrm{\Delta }t=100$, 10, 2 ns.

Figure 2

(a) Illustration of the rf-cavity-based UTEM at TU/e. Inset: schematic representations include a (a.1) cut-through view and (a.2) top view of the rf cavity. (b) Lissajous pattern at $I=0.1\mathrm{nA}$, imaged on the Timepix3 with $5\mathrm{\mu }\mathrm{s}$ exposure. (c) Sum of 200 images.

Figure 3

(a) Composite image showing the sum of 1000 Lissajous patterns at $I=0.1$ nA. (b) Lissajous function $L(t)$ fitted to the measured pattern [24]. (c) Composite image of six overlapped enlarged Lissajous patterns at $I=46.2\mathrm{nA}$, each magnified 1850 times and captured using the Timepix3 detector with a $50\mathrm{\mu }\mathrm{s}$ exposure.

Figure 4

(a)–(d) The distributions of the measured number of 0–5 simultaneous electron events, alongside the corresponding expected Poisson distributions with $⟨n⟩=(\mathrm{a})0.52$, (b) 0.26, (c) 0.13, (d) 0.09 for different time windows $\mathrm{\Delta }t$. The corresponding deviations from the expected Poisson distribution are shown in (e)–(h). The dotted orange line represents the expectation for randomly distributed data according to a Poisson distribution.