We propose the use of interaction-free quantum measurements with electrons to eliminate sample damage in electron microscopy. This might allow noninvasive molecular-resolution imaging. We show the possibility of such measurements in the presence of experimentally measured quantum decoherence rates and using a scheme based on existing charged particle trapping techniques.
We propose the use of interaction-free quantum measurements with electrons to eliminate sample damage in electron microscopy. This might allow noninvasive molecular-resolution imaging. We show the possibility of such measurements in the presence of experimentally measured quantum decoherence rates and using a scheme based on existing charged particle trapping techniques.
Feynman once asked physicists to build better electron microscopes to be able to watch biology at work. While electron microscopes can now provide atomic resolution, electron beam induced specimen damage precludes high resolution imaging of sensitive materials, such as single proteins or polymers. Here, we use simulations to show that an electron microscope based on a multi-pass measurement protocol enables imaging of single proteins, without averaging structures over multiple images. While we demonstrate the method for particular imaging targets, the approach is broadly applicable and is expected to improve resolution and sensitivity for a range of electron microscopy imaging modalities, including, for example, scanning and spectroscopic techniques. The approach implements a quantum mechanically optimal strategy which under idealized conditions can be considered interaction-free.
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
We discuss the effect of semitransparency in a quantum-Zeno-like interaction-free measurement setup, a quantum-physics based approach that might significantly reduce sample damage in imaging and microscopy. With an emphasis on applications in electron microscopy, we simulate the behavior of probe particles in an interaction-free measurement setup with semitransparent samples, and we show that the transparency of a sample can be measured in such a setup. However, such a measurement is not possible without losing (i.e., absorbing or scattering) probe particles in general, which causes sample damage. We show how the amount of lost particles can be minimized by adjusting the number of round trips through the setup, and we explicitly calculate the amount of lost particles in measurements which either aim at distinguishing two transparencies or at measuring an unknown transparency precisely. We also discuss the effect of the sample causing phase shifts in interaction-free measurements. Comparing the resulting loss of probe particles with a classical measurement of transparency, we find that interaction-free measurements only provide a benefit in two cases: first, if two semitransparent samples with a high contrast are to be distinguished, interaction-free measurements lose less particles than classical measurements by a factor that increases with the contrast. This implies that interaction-free measurements with zero loss are possible if one of the samples is perfectly transparent. A second case where interaction-free measurements outperform classical measurements is if three conditions are met: the particle source exhibits Poissonian number statistics, the number of lost particles cannot be measured, and the transparency is larger than approximately 21. In all other cases, interaction-free measurements lose as many probe particles as classical measurements or more. Aside from imaging of gray levels, another possible application for interaction-free measurements is the detection of arbitrarily small phase shifts in transparent samples.
Interaction-free measurement (IFM) has been proposed as a means of high-resolution, low-damage imaging of radiation-sensitive samples, such as biomolecules and proteins. The basic setup for IFM is a Mach-Zehnder interferometer, and recent progress in nanofabricated electron-diffraction gratings has made it possible to incorporate a Mach-Zehnder interferometer in a transmission electron microscope (TEM). Therefore, the limits of performance of IFM with such an interferometer and a shot-noise limited electron source (such as that in a TEM) are of interest. In this paper, we compare the error probability and sample damage for ideal IFM and classical imaging schemes, through theoretical analysis and numerical simulation. We consider a sample that is either completely transparent or completely opaque at each pixel. In our analysis, we also evaluate the impact of an additional detector for scattered electrons. Inclusion of the scattering detector results in reduction of error by up to an order of magnitude, for both IFM and classical schemes. We also investigate a sample reillumination scheme based on updating priors after each round of illumination and find that this scheme further reduces error. Implementation of these methods is likely achievable with existing instrumentation and would result in improved resolution in low-dose electron microscopy.
Electron microscopes provide a powerful platform for exploring physical phenomena with nanoscale resolution, based on the interaction of free electrons with the excitations of a sample such as phonons, excitons, bulk plasmons, and surface plasmons. The interaction usually results in the absorption or emission of such excitations, which can be detected directly through cathodoluminescence or indirectly through electron energy loss spectroscopy (EELS). However, as we show here, the underlying interaction of a free electron and an arbitrary optical excitation goes beyond what was predicted or measured so far, due to the interplay of entanglement and decoherence of the electron-excitation system. The entanglement of electrons and optical excitations can provide new analytical tools in electron microscopy. For example, it can enable measurements of optical coherence, plasmonic lifetimes, and electronic length scales in matter (such as the Bohr radius of an exciton). We show how these can be achieved using common configurations in electron diffraction and EELS, revealing significant changes in the electron’s coherence, as well as in other quantum information theoretic measures such as purity. Specifically, we find that the purity after interaction with nanoparticles can only take discrete values, versus a continuum of values for interactions with surface plasmons. We quantify the post-interaction density matrix of the combined electron-excitation system by developing a framework based on macroscopic quantum electrodynamics. The framework enables a quantitative account of decoherence due to excitations in any general polarizable material (optical environment). This framework is thus applicable beyond electron microscopy. Particularly in electron microscopy, our work enriches analytical capabilities and informs the design of quantum information experiments with free electrons, allowing control over their quantum states and their decoherence by the optical environment.
Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.