Figure 1

Sketch of the decoherence experiment. Electron waves emerging from the source are split by the negatively charged biprism filament, placed between earthed plates, and deflected apart from each other. The electrostatic quadrupole directs them toward each other again. Before they meet, they travel over a resistive plate at the same, small height $z$, but with a lateral separation $\Delta x$. The induced charges moving with the beam electron lead to a disturbance in the electron (and phonon) gas inside the plate. For the two electron trajectories, the corresponding disturbance (shaded areas) is located in different regions. Therefore entanglement between beam electron and plate is formed. The available which-path information increases with decreasing height over the plate, leading to decreasing fringe contrast in the interferogram (right-hand side). On the bottom of the fringe pattern the shadow of the plate is visible in black.Reuse & Permissions

Figure 2

Electron interferograms showing continuously increasing decoherence with decreasing height $z$ above the plate. The lateral separation $\Delta x$ between the interfering beams increases from (a) to (h), causing both increasing decoherence and decreasing angular coherence. The bending of the area of overlap between the two parts of the beam and also of the interference fringes in the vicinity of the plate is due to the charging of dust particles on the surface of the plate. As this effect occurs only for very small heights in which fringe visibility is already nearly zero, it does not deteriorate the results. The shown CCD images are flat and dark corrected.Reuse & Permissions

Figure 3

Quantitative results of the decoherence experiment. (a)–(g) ”Normalized” visibility ${\mathcal{V}}_{\mathrm{rel}}$ (corrected for the influence of angular coherence, etc.; see text) as a function of height $z$, for different lateral separations $\Delta x$ between the interfering beams. Dots: visibility determined from experimental data; dashed line: fit with $\exp [-b/(z/\mu \mathrm{m}{)}^3]$ according to Anglin and Zurek’s calculation [12, 13]; full line: $\exp [-f\gamma (\Delta x/z)]$ with $\gamma (\Delta x/z)\approx (\pi /16)(\Delta x/z{)}^2$ and $f=4.13$ resulting from the fits corresponding to Machnikowski’s calculation [16]. The fluctuations of visibility are mainly due to shot noise [especially in (a)], and for (g) due to the fact that fringe spacing is not much larger than the pixel size. The magnitude of the visibility fluctuations for (a)–(g) is 0.101, 0.054, 0.028, 0.039, 0.040, 0.057, and 0.067, respectively. The interferogram in Fig. 2h was not used for evaluation because of its low signal-to-noise ratio, caused by lack of angular coherence at large lateral separation of the interfering beams. (h) $\Delta x$ dependence of the parameter $b$ in the fits (a)–(g) according to Anglin and Zurek’s calculation: data points and fit with $b=a(\Delta x/\mu \mathrm{m}{)}^2$.Reuse & Permissions