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.
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 present progress towards demonstrating multi-passed stimulated Raman scattering microscopy and multi-passed transmission electron microscopy. A multi-pass microscope interrogates a sample multiple times in a cyclical and deterministic fashion. This can lead to a metrological advantage for imaging weak scatterers. The enhanced sensitivity can yield a significant reduction in damage imparted to biological samples or can reduce image acquisition time. The approach compares favorably with imaging techniques using squeezed or entangled probe states, but avoids the technical complexity associated with the production of such states.
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.
Microscopy of biological specimens often requires low light levels to avoid damage. This yields images impaired by shot noise. An improved measurement accuracy at the Heisenberg limit can be achieved exploiting quantum correlations. If sample damage is the limiting resource, an equivalent limit can be reached by passing photons through a specimen multiple times sequentially. Here we use self-imaging cavities and employ a temporal post-selection scheme to present full-field multi-pass polarization and transmission micrographs with variance reductions of 4.4±0.8 dB (11.6±0.8 dB in a lossless setup) and 4.8±0.8 dB, respectively, compared with the single-pass shot-noise limit. If the accuracy is limited by the number of detected probe particles, our measurements show a variance reduction of 25.9±0.9 dB. The contrast enhancement capabilities in imaging and in diffraction studies are demonstrated with nanostructured samples and with embryonic kidney 293T cells. This approach to Heisenberg-limited microscopy does not rely on quantum state engineering.
What are the ultimate limits of accuracy for techniques in transmission electron microscopy (TEM)? For example, for a given electron dose, what is the ultimate accuracy that can be achieved for the atomic structure of a material? And what determines this accuracy? In this work, we show how quantum estimation theory can be used to provide some quantitative answers to such “big” questions. Quantum estimation theory (also known as quantum metrology theory) is concerned with measurements made at the quantum level. In recent years, the theory has been applied to an increasingly broad range of scientific techniques [1,2]. Here, we apply it to the problem of multiple electron scattering from an atomic structure in a TEM [3]. We focus on cases where the parameters of interest are those which characterize the sample, an extremely relevant and very general scenario. We report the following: We have obtained a quantitative prediction of the ultimate accuracy allowed by quantum mechanics for the precision of atom coordinates within a sample. As expected, this ultimate precision is a function of the electron dose (among other factors), and so this result has important consequences for the precision achievable for the atomic structure of radiation-sensitive materials. We demonstrate that the ultimate (quantum) limit for a simultaneous estimation of multiple sample parameters can be achieved under the condition of weak electron scattering, such as when the phase-object or weak-phase-object approximation is applicable. We demonstrate that this same quantum limit cannot be achieved under the condition of strong multiple scattering, due to the incompatibility of the projection measurements required. Hence strong multiple scattering precludes the quantum limit (with few exceptions) - a fascinating result. In the theory, a TEM experiment (which could be imaging, diffraction, holography, etc.) is divided into three stages: the incident electron beam |ψ0⟩, the beam scattered by the sample S|ψ0⟩, and the beam incident on the electron detector AS|ψ0⟩. Here, S and A are mathematical operators that account, respectively, for the scattering by the sample and the post-sample electron optics (e.g., lens aberrations). This description applies to many TEM modalities, which allows the theory to make general predictions. Fig. 1 shows the specific case of TEM imaging. As will be shown, the quantum limit for an arbitrary set of sample parameters can be achieved by phase-contrast imaging under the Zernike phase condition. Fig. 2 shows a quantitative prediction of the ultimate precision achievable for the lateral coordinate of an atom in a material, as measured in the TEM. Higher doses allow better precision, as expected. For a given dose, better precision is possible for heavier atoms, and for lower beam energies. The results show a strong and unexpected "threshold" effect which occurs at the onset of the asymptotic regime (where the dose is high enough for the statistics to become Gaussian). Finally, while our main focus here is TEM, the generality of the theory means that several of our important conclusions extend to other techniques which utilize the scattering of coherent radiation, such as coherent x-ray scattering in a synchrotron and neutron scattering. Optics for TEM imaging, showing the mathematical notation relevant to this work. Ultimate limits for the precision of a (lateral) atom position measured using TEM. Results are shown for two representative atomic species and beam energies 30-300 keV. Squares and diamonds show results from maximum likelihood estimation (MLE) applied to Monte Carlo image simulations.
A notorious problem in high-resolution biological electron microscopy is radiation damage caused by probe electrons. Hence, acquisition of data with minimal number of electrons is of critical importance. Quantum approaches may represent the only way to improve the resolution in this context, but all proposed schemes to date demand delicate control of the electron beam in highly unconventional electron optics. Here we propose a scheme that involves a flux qubit based on a radio-frequency superconducting quantum interference device, inserted in a transmission electron microscope. The scheme significantly improves the prospect of realizing a quantum-enhanced electron microscope for radiation-sensitive specimens.