Figure 1

(Color online) (a) Coupled electron ring guides. The wave packet illustrates the amplitude of the circulating electron. The guide potential $U_{\mathrm{eff}}\left(r,z\right)$ couples the localized electron states $|T⟩$ and $|B⟩$ in a double-well potential. (b) Interaction-free imaging with electrons. The grid in the lower ring is the object being imaged, which is composed of opaque and transparent regions (i.e., black and white pixels). (c) Example of high-contrast TEM imaging at 100 KeV. Gold nanoparticles labeled with antibody against vesicular monoamine transporter appear as black dots while the rest of the tissue in the background is significantly transparent to the incident electrons. The image contrast is reduced to make the background visible. Image courtesy of Kathryn Commons.Reuse & Permissions

Figure 2

(Color online) Accuracy of interaction-free imaging and probability of electron scattering from the imaged object in the presence of decoherence. (a) The solid (blue) and dash-dot (red) curves are plots of the imaging accuracy $\eta$ and the probability of scattering $P\left(\mathrm{scat}\right)$ versus $N$, respectively. The squares show points of maximum accuracy and corresponding values of scattering probability. The ${\alpha }^{-1}$ values $4.4\times {10}^3$ and $4.4\times {10}^4$ correspond to 100 KeV electrons circulating a ring of radius $R=1\text{cm}$ and 1 mm, respectively, with a decoherence time of ${\tau }_D=1.7\mu \text{s}$. (b) The solid (blue) and dash-dot (red) curves are, respectively, the maximum values of $\eta$ and the minimum values of $P\left(\mathrm{scat}\right)$ as functions of ${\alpha }^{-1}$.Reuse & Permissions

Figure 3

(Color online) Multilayered structure equivalent to the v-shaped trap arrangement but more suitable for microfabrication. Black and dark gray (red) rectangles are grounded and RF electrodes (Au), respectively, and light gray (green) is insulating ${\text{SiO}}_2$. The effective potential $U_{\mathrm{eff}}\left(r,z\right)$ is superimposed on the structure; dark (blue) and light (red) shades are low and high potentials, respectively, and white regions have potentials $>20\text{meV}$. RF voltage in this example is driven at 10 GHz with a magnitude of 2 V. The dimensions are $b=48.5\mu \text{m}$, $a=24\mu \text{m}$, and $d=50\mu \text{m}$. The electrode width and spacing are $4\mu \text{m}$. The inset shows an expanded view of the double well. Near the trap minima the potential is harmonic with characteristic frequencies of $f_r,f_z=33\text{MHz}$, yielding a tunneling rate of ${\Delta }^{\prime }=2\pi \times 14\text{MHz}$ and an electron spot size (i.e., resolution) of 19 nm and $1.4\mu \text{m}$ in the $\vec{r}$ and $\vec{z}$ directions, respectively (accounting for $B_0=1\text{T}$ for $R=1\text{mm}$).Reuse & Permissions