Abstract text (incl. figure legends and references)

Quantum Electron Microscopy technique (QEM) is aimed for improvement of electron dose limited resolution by implementing interaction free measurements [1]. One of the QEM approaches is to build a Mach-Zehnder interferometer for electrons using grated mirrors as electron beam-splitters [2]. Earlier, it was shown that a sample with different transparency levels can be imaged by QEM in interaction free manner [3]. Now we consider the case of phase-only sample which represents a typical cryo-EM situation. We conduct theoretical analysis on the dose limited phase resolution of QEM in order to prove it is worthwhile to build.

Cryo-Electron Microscopy suffers from sensitivity of biological samples to electron damage. Large proteins and protein complexes can be studied in cryo-EM, while for smaller proteins the X-ray diffraction is still the technique of choice. Modern aberration corrected TEMs and STEMs provide atomic resolution in crystalline samples with illumination doses higher than ~10⁴ e-/A². Protein structure degrades severely already at doses of two orders of magnitude lower. Novel EM techniques aim for higher dose efficiency that will allow new areas for the cryo-EM investigation. One of such techniques is QEM.

In QEM an electron is split into two states, a sample state |S> and reference state |R>, so that initially <S|S> << <R|R>. The sample state is used as a STEM focused probe while the reference state passes through the empty space. The |S>-state experiences phase shift passing through the sample . After the sample plane, the two states are directed back to the beam-splitter where they exchange some of their amplitudes. This cycle is repeated N times and the electron is taken out to the detector plane to collapse in either the |S>-state or in the |R>-state, with probablity depending on the pahse shift in the sample (see Fig. 1)

Phase shift can be tuned such that for a blank sample electrons always arrive in the |S>-state. Then for large the interference on the beam-splitter is inconsistent and probability to find the electron in the |R>-state is overwhelming. The maximal dose is reached at zero phase shift with a value of ≈N/2 representing the fact that electron spends half of the time in the sample arm on average. At large pahse shifts the dose is lower since the |S>-state

Figure 1 Phase dependent behavior of a QEM with N=24 cycles. Phase shift in the sample controls collapse probabilities of electrons. For large phase shifts electrons are mostly locked in the initial reference state (blue). For large phase shifts more electrons are detected in the sample sate (red). Electron dose also depends on the phase (black, right axis), with the receiving maximum dose of ≈N/2 (per electron).

Using a dose-limited phase resolution as a metric we show that the QEM achieves at least twice as good phase contrast as a TEM for a typical cry-EM protein imaging setup (see Fig. 2).

Figure 2 Simulated images (10x10nm²) of a viral protein (PDB DOI: 10.2210/pdb5I4T/pdb) at 200kV tension for aTEM (left panel) and QEM (right panel).The exaggerted doses applied for image clarity.