Electron imaging theory for a quantum resonator

Reducing radiation damage is becoming a crucial factor in the development of future electron microscopes. The concept of interaction-free imaging utilizing a Mach–Zehnder interferometer has been proposed originally in. 1993 by Elitzur and Vaidman. Using the quantum Zeno effect the quantum efficiency for interaction-free measurements can be increased to near 100 % with increasing number of interrogations provided the sample is a perfect (thick) absorber. However, for an electron beam the sample is in general semi-transparent depending on the thickness. In electron microscopy the interaction-free experiment is complicated by the presence of elastic and inelastic scattering processes in the electron-sample interaction. The ratio of inelastically versus elastically scattered electrons is determined by the nature of the sample and the thickness and cannot be reduced arbitrarily. Because inelastically scattered electrons transfer energy to the sample and cause radiation damage this puts a limit to the elastically scattered electrons and consequently to the resolution of electron imaging. In this paper, the inelastic scattering is modeled as an “absorption” function on the modulus of the electron wave. Image simulations and Argand plots are used to investigate the convergence rate of the Zeno iterations versus different type of samples, in particular a double strained DNA helical sample. It is found that the stronger objects reach maximum quantum efficiency faster than weaker objects for which more interrogations are needed to reach the maximum quantum efficiency. For a general hybrid amplitude/phase object the “phase” information tends to converge to zero as the number of interrogation increases.